Metrics for sintan (problem 3.4.5)

analyze363.0ms (2.8%)

Memory

10.3MiB live, 436.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.9%	50.1%	0%	0%	0%	0
0%	0%	49.9%	50.1%	0%	0%	0%	1
0%	0%	49.9%	50.1%	0%	0%	0%	2
0%	0%	49.9%	50.1%	0%	0%	0%	3
0%	0%	49.9%	50.1%	0%	0%	0%	4
0%	0%	49.9%	50.1%	0%	0%	0%	5
0%	0%	49.9%	50.1%	0%	0%	0%	6
0%	0%	49.9%	50.1%	0%	0%	0%	7
0%	0%	49.9%	50.1%	0%	0%	0%	8
0%	0%	49.9%	50.1%	0%	0%	0%	9
0%	0%	49.9%	50.1%	0%	0%	0%	10
0%	0%	49.9%	50.1%	0%	0%	0%	11
0%	0%	49.9%	50.1%	0%	0%	0%	12

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample9.5s (72.9%)

Memory

112.1MiB live, 10 904.5MiB allocated

Samples

6.3s	4 536×	2	valid
2.1s	1 258×	3	valid
604.0ms	2 377×	1	valid
8.0ms	85×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.6s

ival-tan: 4.6s (53.5% of total)

ival-sin: 2.9s (34.2% of total)

const: 288.0ms (3.3% of total)

adjust: 284.0ms (3.3% of total)

ival-sub: 249.0ms (2.9% of total)

ival-div: 117.0ms (1.4% of total)

ival-<=: 107.0ms (1.2% of total)

ival-and: 12.0ms (0.1% of total)

ival-assert: 3.0ms (0% of total)

Bogosity

preprocess93.0ms (0.7%)

Memory

-28.8MiB live, 54.4MiB allocated

Algorithm

2×	egg-herbie

Rules

320×	`accelerator-lowering-fma.f32`
320×	`accelerator-lowering-fma.f64`
192×	`-lowering-.f32`
192×	`-lowering-.f64`
142×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	37	30
2	84	27
3	247	27
4	508	27
5	690	27
6	714	27
7	752	27
8	781	27
0	6	9
1	13	9
2	23	9
3	40	9
4	74	9
5	146	9
6	322	9
7	622	9
8	936	9
9	951	9
10	952	9
0	952	9

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Call 2

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(/ (- eps (sin eps)) (- eps (tan eps)))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))
(/ (- eps (sin eps)) (- (tan eps) eps))

Symmetry

(abs eps)

explain545.0ms (4.2%)

Memory

6.1MiB live, 625.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
183	-	4	(5.5744143547919696e-104)	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`
77	-	0	-	`(-.f64 eps (tan.f64 eps))`
77	-	0	-	`(-.f64 eps (sin.f64 eps))`
0	-	0	-	`(tan.f64 eps)`
0	-	0	-	`eps`
0	-	0	-	`(sin.f64 eps)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`	u/u	179	0
↳	`(-.f64 eps (sin.f64 eps))`	underflow	179
↳	`(-.f64 eps (tan.f64 eps))`	underflow	179
`-.f64`	`(-.f64 eps (sin.f64 eps))`	cancellation	77	0
`-.f64`	`(-.f64 eps (tan.f64 eps))`	cancellation	77	0

Confusion

	Predicted +	Predicted -
+	255	0
-	1	0

Precision

0.99609375

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	255	0	0
-	1	0	0

Precision?

0.99609375

Recall?

1.0

Freqs

test

number	freq
1	179
2	77

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

342.0ms	284×	2	valid
93.0ms	100×	3	valid
35.0ms	128×	1	valid

Compiler

Compiled 68 to 28 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 442.0ms

ival-tan: 274.0ms (62% of total)

ival-sin: 131.0ms (29.6% of total)

ival-sub: 18.0ms (4.1% of total)

adjust: 12.0ms (2.7% of total)

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

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	0.8%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify27.0ms (0.2%)

Memory

-6.3MiB live, 34.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(-.f64 eps (tan.f64 eps))
✓	cost-diff	(sin.f64 eps)
✓	cost-diff	(-.f64 eps (sin.f64 eps))
✓	cost-diff	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Rules

320×	`accelerator-lowering-fma.f32`
320×	`accelerator-lowering-fma.f64`
192×	`-lowering-.f32`
192×	`-lowering-.f64`
142×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
1	13	22
2	23	22
3	40	22
4	74	22
5	146	22
6	322	22
7	622	22
8	936	22
9	951	22
10	952	22
0	952	22

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(- eps (sin eps))
eps
(sin eps)
(- eps (tan eps))
(tan eps)

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(- eps (sin eps))
(-.f64 eps (sin.f64 eps))
eps
(sin eps)
(sin.f64 eps)
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
(tan eps)
(tan.f64 eps)

localize256.0ms (2%)

Memory

-20.2MiB live, 414.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	73.2%	(-.f64 eps (tan.f64 eps))
✓	accuracy	73.2%	(-.f64 eps (sin.f64 eps))
✓	accuracy	30.1%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Samples

174.0ms	142×	2	valid
55.0ms	50×	3	valid
10.0ms	64×	1	valid

Compiler

Compiled 24 to 8 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 226.0ms

ival-tan: 141.0ms (62.4% of total)

ival-sin: 65.0ms (28.8% of total)

adjust: 9.0ms (4% of total)

ival-sub: 8.0ms (3.5% of total)

ival-div: 3.0ms (1.3% of total)

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

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

series4.0ms (0%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/ (- eps (sin eps)) (- eps (tan eps)))>
#<alt (- eps (sin eps))>
#<alt (sin eps)>
#<alt (- eps (tan eps))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	-inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	0	(/ (- eps (sin eps)) (- eps (tan eps)))
0.0ms	eps	@	-inf	(- eps (tan eps))
0.0ms	eps	@	inf	(- eps (tan eps))

rewrite351.0ms (2.7%)

Memory

22.1MiB live, 617.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 318×	`-lowering-.f32`
4 318×	`-lowering-.f64`
3 264×	`/-lowering-/.f32`
3 264×	`/-lowering-/.f64`
2 758×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	46	19
2	403	19
3	5950	19
0	8261	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 419

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(- eps (sin eps))
(sin eps)
(- eps (tan eps))

Outputs
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps))
(+.f64 (.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(+.f64 (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 eps (tan.f64 eps)) (-.f64 eps (sin.f64 eps)))) #s(literal -1 binary64)))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)) (.f64 eps eps))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)) (.f64 eps eps))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 (/.f64 (.f64 eps eps) (+.f64 eps (sin.f64 eps))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)) (.f64 eps eps)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)) (.f64 eps eps)))))
(-.f64 (/.f64 (.f64 eps eps) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 eps eps)))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))))
(-.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
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(/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps eps)) (-.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) eps))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps))) #s(literal 2 binary64))) (fma.f64 eps (/.f64 (.f64 eps eps) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 eps eps) (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64))) (fma.f64 eps (/.f64 eps (+.f64 eps (tan.f64 eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps)))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 9 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))) (+.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (pow.f64 (.f64 eps (tan.f64 eps)) #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (+.f64 (fma.f64 eps (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 4 binary64))) (pow.f64 (.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))) #s(literal 1 binary64)))
(.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))))
(*.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) #s(literal 1 binary64)))
(*.f64 (+.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (tan.f64 eps))))
(.f64 (+.f64 eps (tan.f64 eps)) (.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))))
(*.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps)))))
(.f64 (+.f64 (neg.f64 (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 eps (tan.f64 eps)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps))) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 eps eps (.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) eps))))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 eps (tan.f64 eps)))
(.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (fma.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (*.f64 eps eps))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))

simplify724.0ms (5.5%)

Memory

-4.6MiB live, 671.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 288×	`accelerator-lowering-fma.f32`
12 288×	`accelerator-lowering-fma.f64`
6 122×	`-lowering-.f32`
6 122×	`-lowering-.f64`
1 424×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	561
1	422	524
2	1321	499
3	5650	444
0	8479	418

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(fma.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(fma.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 (.f64 eps eps) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) eps)) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(fma.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 1 binary64))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps) #s(literal -1 binary64)) (sin.f64 eps)) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) eps) (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps))
(* 1/6 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/6 binary64))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* -1/3 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/3 binary64))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -2/15 binary64)) #s(literal -1/3 binary64))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -17/315 binary64)) #s(literal -2/15 binary64)) #s(literal -1/3 binary64)))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -62/2835 binary64) #s(literal -17/315 binary64)) #s(literal -2/15 binary64))) #s(literal -1/3 binary64))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))

eval56.0ms (0.4%)

Memory: -1.4MiB live, 72.4MiB allocated
Compiler: Compiled 12 601 to 1 231 computations (90.2% saved)

prune78.0ms (0.6%)

Memory

1.7MiB live, 122.3MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	465	2	467
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	466	2	468

Accuracy

100.0%

Counts

468 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
▶	99.7%	#s(literal -1/2 binary64)

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify4.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
8×	`accelerator-lowering-fma.f32`
8×	`accelerator-lowering-fma.f64`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	10	14
2	13	14
0	13	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
-1/2
(+ (* 9/40 (* eps eps)) -1/2)
9/40
(* eps eps)
eps
-1/2

Outputs
-1/2
#s(literal -1/2 binary64)
(+ (* 9/40 (* eps eps)) -1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
9/40
#s(literal 9/40 binary64)
(* eps eps)
(*.f64 eps eps)
eps
-1/2
#s(literal -1/2 binary64)

localize23.0ms (0.2%)

Memory

8.0MiB live, 47.1MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)

Samples

15.0ms

256×

valid

Compiler

Compiled 15 to 8 computations (46.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (41.9% of total)

const: 4.0ms (41.9% of total)

ival-add: 1.0ms (10.5% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (+ (* 9/40 (* eps eps)) -1/2)>
#<alt (* eps eps)>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(+ (* 9/40 (* eps eps)) -1/2)
0.0ms	eps	@	inf	(+ (* 9/40 (* eps eps)) -1/2)
0.0ms	eps	@	0	(* eps eps)
0.0ms	eps	@	inf	(* eps eps)
0.0ms	eps	@	-inf	(+ (* 9/40 (* eps eps)) -1/2)

rewrite481.0ms (3.7%)

Memory

-38.2MiB live, 740.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 744×	`accelerator-lowering-fma.f32`
7 744×	`accelerator-lowering-fma.f64`
4 816×	`/-lowering-/.f32`
4 816×	`/-lowering-/.f64`
4 494×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	27	10
2	171	10
3	1413	10
0	8174	9

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 257

Calls

Call 1

Inputs
(+ (* 9/40 (* eps eps)) -1/2)
(* eps eps)

Outputs
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(+.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal -9/40 binary64)))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal -9/40 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal -9/40 binary64)))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal -9/40 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 531441/4096000000 binary64))) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 1/8 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 1/8 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 531441/4096000000 binary64))) (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 81/6400 binary64) #s(literal 1/16 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 81/6400 binary64) #s(literal 1/16 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps))))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 531441/4096000000 binary64))) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1/64 binary64) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 1/8 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 531441/4096000000 binary64))) (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 81/6400 binary64) #s(literal 1/16 binary64))))) (/.f64 #s(literal 1/64 binary64) (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 81/6400 binary64) #s(literal 1/16 binary64))))))
(-.f64 (/.f64 (.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (/.f64 (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))) (fma.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (fma.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))))) (/.f64 (.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))) (fma.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (fma.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (fma.f64 (.f64 eps eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))) (/.f64 (.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64)))) (fma.f64 (.f64 eps eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 #s(literal 9/40 binary64) (/.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (.f64 eps eps)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64)))))
(fma.f64 eps (*.f64 #s(literal 9/40 binary64) eps) #s(literal -1/2 binary64))
(fma.f64 eps (pow.f64 (*.f64 #s(literal 9/40 binary64) eps) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (exp.f64 (log.f64 (*.f64 #s(literal 9/40 binary64) eps))) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/4 binary64) (fma.f64 (*.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 eps eps) (exp.f64 (log.f64 #s(literal 9/40 binary64))) #s(literal -1/2 binary64))
(fma.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) (/.f64 (.f64 (.f64 eps eps) #s(literal -9/40 binary64)) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64)))))
(fma.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64)))))
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(.f64 (/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 531441/4096000000 binary64)) #s(literal -1/64 binary64)) (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 81/6400 binary64) #s(literal 1/16 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -9/40 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -1/16 binary64)) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal 1/8 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (fma.f64 (.f64 eps eps) #s(literal -9/80 binary64) #s(literal 1/4 binary64))))))
(.f64 (/.f64 (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -1/16 binary64)) (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -1/16 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64))) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -1/16 binary64)) (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -1/16 binary64)) (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal -9/40 binary64)))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64))) (fma.f64 #s(literal 729/64000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 81/1600 binary64) #s(literal 9/80 binary64)) #s(literal 1/4 binary64))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -9/40 binary64)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 eps)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 eps)) #s(literal 1 binary64)))
(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 eps))
(*.f64 eps eps)

simplify178.0ms (1.4%)

Memory

6.7MiB live, 277.0MiB allocated

Algorithm

1×	egg-herbie

Rules

3 324×	`-lowering-.f32`
3 324×	`-lowering-.f64`
3 000×	`accelerator-lowering-fma.f32`
3 000×	`accelerator-lowering-fma.f64`
1 530×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	110
1	27	110
2	58	110
3	135	110
4	371	110
5	706	110
6	1162	110
7	2173	110
8	3640	110
9	4730	110
10	5703	110
11	6850	110
0	8022	101

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))
(pow eps 2)
(fma.f64 eps eps #s(literal 0 binary64))

eval40.0ms (0.3%)

Memory: 6.2MiB live, 85.7MiB allocated
Compiler: Compiled 13 182 to 750 computations (94.3% saved)

prune30.0ms (0.2%)

Memory

-8.1MiB live, 69.4MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	281	2	283

Accuracy

100.0%

Counts

283 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
✓	99.7%	#s(literal -1/2 binary64)

Compiler

Compiled 26 to 17 computations (34.6% saved)

regimes3.0ms (0%)

Memory

7.4MiB live, 7.4MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Outputs
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Calls

2 calls:

2.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
100.0%	1	`eps`
100.0%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes2.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)

Outputs
#s(literal -1/2 binary64)

Calls

2 calls:

1.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.7%	1	`eps`
99.7%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify7.0ms (0%)

Memory

12.7MiB live, 12.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

Outputs
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

soundness208.0ms (1.6%)

Memory

-25.6MiB live, 130.3MiB allocated

Rules

12 288×	`accelerator-lowering-fma.f32`
12 288×	`accelerator-lowering-fma.f64`
6 122×	`-lowering-.f32`
6 122×	`-lowering-.f64`
1 424×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	561
1	422	524
2	1321	499
3	5650	444
0	8479	418

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 17 to 12 computations (29.4% saved)

preprocess67.0ms (0.5%)

Memory: 14.7MiB live, 133.5MiB allocated
Remove: (abs eps)
Compiler: Compiled 142 to 88 computations (38% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	32
1	37	30
2	84	27
3	247	27
4	508	27
5	690	27
6	714	27
7	752	27
8	781	27
0	6	9
1	13	9
2	23	9
3	40	9
4	74	9
5	146	9
6	322	9
7	622	9
8	936	9
9	951	9
10	952	9
0	952	9

Iter	Nodes	Cost
0	6	22
1	13	22
2	23	22
3	40	22
4	74	22
5	146	22
6	322	22
7	622	22
8	936	22
9	951	22
10	952	22
0	952	22

Iter	Nodes	Cost
0	13	32
1	37	30
2	84	27
3	247	27
4	508	27
5	690	27
6	714	27
7	752	27
8	781	27
0	6	9
1	13	9
2	23	9
3	40	9
4	74	9
5	146	9
6	322	9
7	622	9
8	936	9
9	951	9
10	952	9
0	952	9

Iter	Nodes	Cost
0	6	22
1	13	22
2	23	22
3	40	22
4	74	22
5	146	22
6	322	22
7	622	22
8	936	22
9	951	22
10	952	22
0	952	22

analyze363.0ms (2.8%)

sample9.5s (72.9%)

preprocess93.0ms (0.7%)

explain545.0ms (4.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify27.0ms (0.2%)

localize256.0ms (2%)

series4.0ms (0%)

rewrite351.0ms (2.7%)

simplify724.0ms (5.5%)

eval56.0ms (0.4%)

prune78.0ms (0.6%)

simplify4.0ms (0%)

localize23.0ms (0.2%)

series2.0ms (0%)

rewrite481.0ms (3.7%)

simplify178.0ms (1.4%)

eval40.0ms (0.3%)

prune30.0ms (0.2%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify7.0ms (0%)

soundness208.0ms (1.6%)

preprocess67.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	32
1	37	30
2	84	27
3	247	27
4	508	27
5	690	27
6	714	27
7	752	27
8	781	27
0	6	9
1	13	9
2	23	9
3	40	9
4	74	9
5	146	9
6	322	9
7	622	9
8	936	9
9	951	9
10	952	9
0	952	9

Iter	Nodes	Cost
0	6	22
1	13	22
2	23	22
3	40	22
4	74	22
5	146	22
6	322	22
7	622	22
8	936	22
9	951	22
10	952	22
0	952	22