Metrics for invcot (example 3.9)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze6.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.7%	50.3%	0%	0%	0%	0
0%	0%	49.7%	50.3%	0%	0%	0%	1
0%	0%	49.7%	50.3%	0%	0%	0%	2
25%	12.4%	37.3%	50.3%	0%	0%	0%	3
62.5%	31.1%	18.6%	50.3%	0%	0%	0%	4
81.3%	40.4%	9.3%	50.3%	0%	0%	0%	5
90.6%	45%	4.7%	50.3%	0%	0%	0%	6
95.3%	47.4%	2.3%	50.3%	0%	0%	0%	7
97.7%	48.5%	1.2%	50.3%	0%	0%	0%	8
98.8%	49.1%	0.6%	50.3%	0%	0%	0%	9
99.4%	49.4%	0.3%	50.3%	0%	0%	0%	10
99.7%	49.5%	0.1%	50.3%	0%	0%	0%	11
99.9%	49.6%	0.1%	50.3%	0%	0%	0%	12

Compiler

Compiled 16 to 12 computations (25% saved)

sample9.8s (69.9%)

Memory

11.0MiB live, 7 910.3MiB allocated

Samples

7.8s	3 831×	2	valid
1.6s	4 346×	1	valid
7.0ms	79×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.9s

ival-tan: 7.3s (81.8% of total)

adjust: 638.0ms (7.1% of total)

ival-div: 454.0ms (5.1% of total)

const: 289.0ms (3.2% of total)

ival-sub: 162.0ms (1.8% of total)

ival-<: 59.0ms (0.7% of total)

ival-and: 14.0ms (0.2% of total)

exact: 6.0ms (0.1% of total)

ival-assert: 4.0ms (0% of total)

Bogosity

explain618.0ms (4.4%)

Memory

16.5MiB live, 686.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`
0	-	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(tan.f64 x)`
0	-	-	`(/.f64 #s(literal 1 binary64) (tan.f64 x))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`	cancellation	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

385.0ms	228×	2	valid
66.0ms	284×	1	valid

Compiler

Compiled 88 to 40 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 427.0ms

ival-tan: 381.0ms (89.2% of total)

ival-div: 27.0ms (6.3% of total)

adjust: 12.0ms (2.8% of total)

ival-sub: 6.0ms (1.4% of total)

ival-true: 1.0ms (0.2% of total)

ival-assert: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess22.0ms (0.2%)

Memory

-8.4MiB live, 33.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Outputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))

Symmetry

(negabs x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.5%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(tan.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (tan.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

Outputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

localize223.0ms (1.6%)

Memory

-1.6MiB live, 265.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	(tan.f64 x)
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy	60.46368170095316	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Samples

180.0ms	114×	2	valid
30.0ms	142×	1	valid

Compiler

Compiled 40 to 14 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 198.0ms

ival-tan: 178.0ms (89.7% of total)

ival-div: 10.0ms (5% of total)

adjust: 7.0ms (3.5% of total)

ival-sub: 3.0ms (1.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

4 → 16

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

Outputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ (cos x) (sin x))
(/ (sin x) (cos x))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))
1.0ms	x	@	inf	((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))
1.0ms	x	@	0	((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))

simplify172.0ms (1.2%)

Memory

15.3MiB live, 172.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	167
1	179	167
2	458	161
3	1332	161
4	2094	161
5	3093	161
6	3681	161
7	3948	161
8	5088	161
9	7270	161
0	8431	143

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 15

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ (cos x) (sin x))
(/ (sin x) (cos x))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -2/945 binary64) (.f64 x x) #s(literal -1/45 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite119.0ms (0.9%)

Memory

-6.6MiB live, 112.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	17
1	49	17
2	454	17
3	5706	17
0	9203	17

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 277

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

Outputs
(.f64 (/.f64 (-.f64 (tan.f64 x) x) (.f64 x (sin.f64 x))) (cos.f64 x))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (/.f64 (-.f64 (tan.f64 x) x) x)) (tan.f64 x))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (-.f64 (pow.f64 x #s(literal -4 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -4 binary64)) (pow.f64 (.f64 x (tan.f64 x)) #s(literal -2 binary64))))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal -6 binary64)))) (fma.f64 (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)) (-.f64 (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 x #s(literal -4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (tan.f64 x) x)) (.f64 x (tan.f64 x)))
(*.f64 (/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (sin.f64 x)) (neg.f64 (cos.f64 x)))
(*.f64 (/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (sin.f64 x)) (cos.f64 x))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) #s(literal 1 binary64)) (.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))))
(.f64 (.f64 (-.f64 (tan.f64 x) x) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (-.f64 (tan.f64 x) x)) (-.f64 (tan.f64 x) x))
(.f64 (.f64 (-.f64 (tan.f64 x) x) #s(literal 1 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x))
(*.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(*.f64 (-.f64 (tan.f64 x) x) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))))
(.f64 (.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))))
(.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))))
(.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) (.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x) (-.f64 (tan.f64 x) x))
(.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(pow.f64 (/.f64 (tan.f64 x) (/.f64 (-.f64 (tan.f64 x) x) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))) #s(literal -1 binary64))
(/.f64 (/.f64 (-.f64 (tan.f64 x) x) (tan.f64 x)) x)
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(*.f64 (sin.f64 x) (neg.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64))))
(*.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(*.f64 (tan.f64 x) #s(literal -1 binary64))
(*.f64 (tan.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (tan.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
(/.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (sin.f64 x) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (tan.f64 x) #s(literal -1 binary64))
(/.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(neg.f64 (tan.f64 x))
(tan.f64 x)
(-.f64 #s(literal 0 binary64) (tan.f64 x))
(+.f64 #s(literal 0 binary64) (tan.f64 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (tan.f64 x)))

eval31.0ms (0.2%)

Memory: 11.0MiB live, 48.0MiB allocated
Compiler: Compiled 5 199 to 765 computations (85.3% saved)

prune5.0ms (0%)

Memory

18.3MiB live, 18.3MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	291	2	293

Accuracy

99.5%

Counts

293 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
▶	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify30.0ms (0.2%)

Memory

-25.3MiB live, 17.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
0	19	54
1	29	54
2	46	54
3	61	54
4	77	54
5	97	54
6	136	54
7	167	54
8	296	54
9	673	54
10	893	54
11	906	54
0	906	54

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

localize396.0ms (2.8%)

Memory

16.8MiB live, 248.5MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
accuracy	0	(*.f64 x x)
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
accuracy	0.3359375	(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
accuracy	0.012382519536884034	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
accuracy	0.3359375	(*.f64 #s(literal 1/3 binary64) x)

Samples

338.0ms	114×	2	valid
47.0ms	142×	1	valid

Compiler

Compiled 99 to 29 computations (70.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 369.0ms

ival-tan: 322.0ms (87.3% of total)

ival-div: 12.0ms (3.3% of total)

const: 10.0ms (2.7% of total)

adjust: 9.0ms (2.4% of total)

ival-mult: 9.0ms (2.4% of total)

ival-sub: 3.0ms (0.8% of total)

ival-add: 2.0ms (0.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

6 → 13

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)

Outputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(pow x 2)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x))
1.0ms	x	@	-inf	((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x))
1.0ms	x	@	inf	((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x))

Time

Variable

Point

Expression

2.0ms

((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x))

1.0ms

-inf

((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x))

1.0ms

inf

((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x))

simplify142.0ms (1%)

Memory

-23.0MiB live, 104.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	100
1	112	100
2	283	100
3	657	100
4	1224	100
5	2800	100
6	3285	100
7	4026	100
8	7319	100
0	8872	91

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 13

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(pow x 2)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))

rewrite148.0ms (1.1%)

Memory

-11.6MiB live, 108.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
0	19	49
1	80	49
2	619	49
3	7475	49
0	8390	49

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

6 → 181

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(.f64 (.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) x))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1/3 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1/3 binary64) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal -1 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/135 binary64) (*.f64 x x) #s(literal 1/9 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64))) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/27 binary64)) x) (-.f64 (pow.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) (.f64 (*.f64 x x) #s(literal -1/135 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/27 binary64)) x) (fma.f64 #s(literal 1/8303765625 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal 4 binary64))))
(.f64 (.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #s(literal 1 binary64)) x)
(.f64 (.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 1/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/27 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) (/.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
(.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #s(literal -1 binary64)) x))
(.f64 (fma.f64 #s(literal 1/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/27 binary64)) (/.f64 x (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)))))
(.f64 (fma.f64 #s(literal 1/91125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/27 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64))) #s(literal -1 binary64)) x))
(.f64 (.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x) #s(literal 1 binary64))
(.f64 (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x))
(/.f64 (.f64 (neg.f64 x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) #s(literal -1 binary64))
(/.f64 (.f64 (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (.f64 (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))) (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (.f64 #s(literal 1/3 binary64) x)))
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eval43.0ms (0.3%)

Memory: 26.2MiB live, 61.7MiB allocated
Compiler: Compiled 5 294 to 743 computations (86% saved)

prune3.0ms (0%)

Memory

11.0MiB live, 11.0MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	191	3	194

Accuracy

100.0%

Counts

194 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

100.0%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))

✓

99.5%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))

✓

99.5%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 48 to 35 computations (27.1% saved)

simplify36.0ms (0.3%)

Memory

-22.2MiB live, 15.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	50
0	18	50
1	28	46
2	51	46
3	82	46
4	104	46
5	129	46
6	164	46
7	188	46
8	338	46
9	826	46
10	1093	46
11	1132	46
12	1134	46
13	1137	46
14	1138	46
0	1138	46

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)

localize463.0ms (3.3%)

Memory

-15.1MiB live, 259.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
accuracy	0	(*.f64 x x)
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))

Samples

405.0ms	114×	2	valid
46.0ms	142×	1	valid

Compiler

Compiled 94 to 29 computations (69.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 435.0ms

ival-tan: 387.0ms (89% of total)

ival-div: 17.0ms (3.9% of total)

adjust: 12.0ms (2.8% of total)

const: 10.0ms (2.3% of total)

ival-sub: 3.0ms (0.7% of total)

ival-mult: 3.0ms (0.7% of total)

ival-add: 2.0ms (0.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

5 → 21

Calls

Call 1

Inputs
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(*.f64 x x)

Outputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(pow x 2)
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (* x x))

1.0ms

-inf

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (* x x))

1.0ms

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (* x x))

simplify118.0ms (0.8%)

Memory

-11.1MiB live, 106.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	196
1	196	196
2	494	196
3	1178	196
4	2428	196
5	5331	196
0	8399	181

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 21

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(pow x 2)
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (.f64 x x) #s(literal 1/75 binary64)) (.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (.f64 x x)) #s(literal 45 binary64))) (.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (.f64 x x)) #s(literal 45 binary64))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))

rewrite120.0ms (0.9%)

Memory

-2.8MiB live, 115.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	46
0	18	46
1	90	42
2	706	42
0	8157	42

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

5 → 316

Calls

Call 1

Inputs
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(*.f64 x x)

Outputs
(.f64 (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal -1/27 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (fma.f64 #s(literal 1/135 binary64) (*.f64 x x) #s(literal 1/9 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) x) (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (.f64 (*.f64 x x) #s(literal -1/135 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) x) (fma.f64 (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal 1/8303765625 binary64) (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64))) (pow.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 4 binary64))))
(.f64 (pow.f64 (pow.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #s(literal -1 binary64))) (/.f64 x (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal -1/3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) #s(literal -1 binary64))) (/.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)))))
(.f64 (/.f64 x (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 x (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 x (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(.f64 (/.f64 x (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) x) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal -1/3 binary64)) #s(literal -1 binary64)) x))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) (.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64))) #s(literal -1 binary64)) x))
(.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (neg.f64 x))
(.f64 (neg.f64 x) (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)))
(pow.f64 (pow.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))) (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (.f64 #s(literal 1/3 binary64) x)))
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eval74.0ms (0.5%)

Memory: 24.0MiB live, 61.7MiB allocated
Compiler: Compiled 9 893 to 1 403 computations (85.8% saved)

prune19.0ms (0.1%)

Memory

-17.4MiB live, 26.4MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	334	1	335
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	335	3	338

Accuracy

100.0%

Counts

338 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

100.0%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

✓

99.5%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))

✓

99.5%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 51 to 37 computations (27.5% saved)

simplify31.0ms (0.2%)

Memory

-9.3MiB live, 27.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

cost-diff

#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))

cost-diff

(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))

cost-diff

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	48
0	17	48
1	25	48
2	36	48
3	45	48
4	58	48
5	78	48
6	117	48
7	149	48
8	241	48
9	426	48
10	555	48
11	656	48
12	773	48
13	810	48
14	841	48
15	859	48
16	864	48
17	865	48
0	865	45

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)

localize287.0ms (2.1%)

Memory

-3.5MiB live, 273.5MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

accuracy

(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))

accuracy

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

accuracy

0.012382519536884034

#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))

Samples

227.0ms	114×	2	valid
46.0ms	142×	1	valid

Compiler

Compiled 80 to 32 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 261.0ms

ival-tan: 204.0ms (78.2% of total)

ival-div: 26.0ms (10% of total)

const: 11.0ms (4.2% of total)

adjust: 10.0ms (3.8% of total)

ival-sub: 3.0ms (1.1% of total)

ival-add: 3.0ms (1.1% of total)

ival-mult: 3.0ms (1.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

3.4MiB live, 3.4MiB allocated

Counts

3 → 16

Calls

Call 1

Inputs

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))

#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))

Outputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)))

1.0ms

inf

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)))

1.0ms

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)))

simplify149.0ms (1.1%)

Memory

31.8MiB live, 106.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	173
1	189	173
2	475	173
3	1131	173
4	2204	173
5	3758	173
6	6189	173
0	8428	160

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 16

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (.f64 x x) #s(literal 1/75 binary64)) (.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 x x))

rewrite173.0ms (1.2%)

Memory

-1.3MiB live, 116.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
0	17	46
1	87	46
2	674	46
3	7664	46
0	8291	43

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

3 → 36

Calls

Call 1

Inputs

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))

#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(.f64 (pow.f64 (/.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (neg.f64 x))
(.f64 (pow.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)) x)
(.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(.f64 (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64))
(.f64 x (pow.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1 binary64))
(/.f64 (.f64 (pow.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64))
(/.f64 (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (.f64 (neg.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64)))
(/.f64 (neg.f64 x) (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))
(/.f64 (neg.f64 x) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) x))
(/.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64))
(/.f64 x (.f64 (neg.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x)))
(neg.f64 (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x)) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(.f64 #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
(/.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64))
(/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

eval5.0ms (0%)

Memory: 7.2MiB live, 7.2MiB allocated
Compiler: Compiled 1 317 to 197 computations (85% saved)

prune15.0ms (0.1%)

Memory

-33.3MiB live, 5.0MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	51	3	54

Accuracy

100.0%

Counts

54 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

✓

99.5%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))

✓

99.5%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 129 to 70 computations (45.7% saved)

regimes4.0ms (0%)

Memory

8.1MiB live, 8.1MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes2.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Calls

2 calls:

1.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify24.0ms (0.2%)

Memory

3.7MiB live, 40.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	27	53

Stop Event

1×

saturated

Calls

Call 1

Inputs

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Outputs

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

soundness678.0ms (4.8%)

Memory

-15.8MiB live, 300.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	196
1	196	196
2	494	196
3	1178	196
4	2428	196
5	5331	196
0	8399	181
0	14	49
0	19	49
1	80	49
2	619	49
3	7475	49
0	8390	49
0	67	167
1	179	167
2	458	161
3	1332	161
4	2094	161
5	3093	161
6	3681	161
7	3948	161
8	5088	161
9	7270	161
0	8431	143

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 118 to 74 computations (37.3% saved)

preprocess32.0ms (0.2%)

Memory: 36.1MiB live, 36.1MiB allocated
Remove: (negabs x)
Compiler: Compiled 208 to 126 computations (39.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Iter	Nodes	Cost
0	14	54
0	19	54
1	29	54
2	46	54
3	61	54
4	77	54
5	97	54
6	136	54
7	167	54
8	296	54
9	673	54
10	893	54
11	906	54
0	906	54

Iter	Nodes	Cost
0	16	48
0	17	48
1	25	48
2	36	48
3	45	48
4	58	48
5	78	48
6	117	48
7	149	48
8	241	48
9	426	48
10	555	48
11	656	48
12	773	48
13	810	48
14	841	48
15	859	48
16	864	48
17	865	48
0	865	45

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Iter	Nodes	Cost
0	14	54
0	19	54
1	29	54
2	46	54
3	61	54
4	77	54
5	97	54
6	136	54
7	167	54
8	296	54
9	673	54
10	893	54
11	906	54
0	906	54

Iter	Nodes	Cost
0	16	48
0	17	48
1	25	48
2	36	48
3	45	48
4	58	48
5	78	48
6	117	48
7	149	48
8	241	48
9	426	48
10	555	48
11	656	48
12	773	48
13	810	48
14	841	48
15	859	48
16	864	48
17	865	48
0	865	45

start0.0ms (0%)

analyze6.0ms (0%)

sample9.8s (69.9%)

explain618.0ms (4.4%)

preprocess22.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize223.0ms (1.6%)

series4.0ms (0%)

simplify172.0ms (1.2%)

rewrite119.0ms (0.9%)

eval31.0ms (0.2%)

prune5.0ms (0%)

simplify30.0ms (0.2%)

localize396.0ms (2.8%)

series4.0ms (0%)

simplify142.0ms (1%)

rewrite148.0ms (1.1%)

eval43.0ms (0.3%)

prune3.0ms (0%)

simplify36.0ms (0.3%)

localize463.0ms (3.3%)

series3.0ms (0%)

simplify118.0ms (0.8%)

rewrite120.0ms (0.9%)

eval74.0ms (0.5%)

prune19.0ms (0.1%)

simplify31.0ms (0.2%)

localize287.0ms (2.1%)

series2.0ms (0%)

simplify149.0ms (1.1%)

rewrite173.0ms (1.2%)

eval5.0ms (0%)

prune15.0ms (0.1%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify24.0ms (0.2%)

soundness678.0ms (4.8%)

preprocess32.0ms (0.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Iter	Nodes	Cost
0	14	54
0	19	54
1	29	54
2	46	54
3	61	54
4	77	54
5	97	54
6	136	54
7	167	54
8	296	54
9	673	54
10	893	54
11	906	54
0	906	54

Iter	Nodes	Cost
0	16	48
0	17	48
1	25	48
2	36	48
3	45	48
4	58	48
5	78	48
6	117	48
7	149	48
8	241	48
9	426	48
10	555	48
11	656	48
12	773	48
13	810	48
14	841	48
15	859	48
16	864	48
17	865	48
0	865	45