Metrics for Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample752.0ms (17.6%)

Memory

13.6MiB live, 521.7MiB allocated

Samples

521.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 264.0ms

ival-mult: 139.0ms (52.6% of total)

ival-sub: 109.0ms (41.3% of total)

exact: 7.0ms (2.6% of total)

ival-true: 6.0ms (2.3% of total)

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

Bogosity

explain99.0ms (2.3%)

Memory

-21.2MiB live, 99.7MiB allocated

FPErrors

Click to see full error table

Overpredictions	Example	Example	Subexpression
0	-	-	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`#s(literal 1 binary64)`
1	(1.5111408903645234e-162)	-	`(.f64 (.f64 x x) #s(literal 2 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

48.0ms

512×

valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 21.0ms (86.6% of total)

ival-sub: 2.0ms (8.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess282.0ms (6.6%)

Memory

23.0MiB live, 179.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	31	15
2	100	14
3	345	14
4	896	14
5	1235	14
6	1655	14
7	3283	14
8	5074	14
9	6926	14
0	6	7
0	9	7
1	23	7
2	52	7
3	205	7
4	668	7
5	1074	7
6	1691	7
7	3592	7
8	5349	7
9	6778	7
0	8207	6

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Outputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))

Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify353.0ms (8.3%)

Memory

7.5MiB live, 82.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) #s(literal 2 binary64))
cost-diff	128	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	23	18
2	52	18
3	205	18
4	668	18
5	1074	18
6	1691	18
7	3592	18
8	5349	18
9	6778	18
0	8207	17

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal 1 binary64)

Outputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal 1 binary64)

localize103.0ms (2.4%)

Memory

-30.6MiB live, 25.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))

Samples

98.0ms

256×

valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-mult: 50.0ms (53.8% of total)

ival-sub: 42.0ms (45.2% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated

Counts

3 → 5

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)

Outputs
-1
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(pow x 2)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))
1.0ms	x	@	-inf	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))
1.0ms	x	@	0	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))

simplify119.0ms (2.8%)

Memory

-18.8MiB live, 138.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	21	23
2	55	23
3	217	23
4	980	23
5	3390	23
6	5308	23
0	8049	21

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 5

Calls

Call 1

Inputs
-1
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(pow x 2)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))

Outputs
-1
#s(literal -1 binary64)
(- (* 2 (pow x 2)) 1)
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))

rewrite180.0ms (4.2%)

Memory

30.6MiB live, 256.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	38	15
2	215	15
3	2231	15
0	9536	14

Stop Event

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

Counts

3 → 375

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)

Outputs
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) (fma.f64 #s(literal 512 binary64) (pow.f64 x #s(literal 18 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (-.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))))
(.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))))
(.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))))) (neg.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 512 binary64) (pow.f64 x #s(literal 18 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))))) (neg.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -4 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal -8 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -2 binary64)))) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (/.f64 #s(literal -4 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))) #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -4 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -4 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))) (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))))))
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(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -2 binary64) (.f64 x x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(neg.f64 (.f64 #s(literal -2 binary64) (.f64 x x)))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x) (*.f64 x x))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x) (*.f64 x x))
(fma.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 x x))
(fma.f64 (sqrt.f64 x) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (*.f64 x x))
(fma.f64 (-.f64 x #s(literal 0 binary64)) (-.f64 x #s(literal 0 binary64)) (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x x))
(fma.f64 x x (*.f64 x x))
(sqrt.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -2 binary64) (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -2 binary64) (.f64 x x))))
(-.f64 #s(literal 0 binary64) (.f64 #s(literal -2 binary64) (.f64 x x)))
(-.f64 (.f64 x x) (.f64 x x))
(fabs.f64 (-.f64 (.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 0 binary64)))
(fabs.f64 (.f64 (.f64 #s(literal -2 binary64) x) (-.f64 x #s(literal 0 binary64))))
(fabs.f64 (.f64 (-.f64 x #s(literal 0 binary64)) (.f64 #s(literal -2 binary64) x)))
(fabs.f64 (.f64 #s(literal -2 binary64) (.f64 x x)))
(exp.f64 (/.f64 (log.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 2 binary64))))
(+.f64 (cosh.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 (sqrt.f64 x) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (-.f64 x #s(literal 0 binary64)) (-.f64 x #s(literal 0 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(fabs.f64 (-.f64 (*.f64 x x) #s(literal 0 binary64)))
(fabs.f64 (*.f64 (-.f64 x #s(literal 0 binary64)) x))
(fabs.f64 (*.f64 x (-.f64 x #s(literal 0 binary64))))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (/.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval102.0ms (2.4%)

Memory: -14.5MiB live, 106.3MiB allocated
Compiler: Compiled 8 678 to 902 computations (89.6% saved)

prune6.0ms (0.1%)

Memory

25.6MiB live, 25.6MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	377	2	379
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	378	2	380

Accuracy

100.0%

Counts

380 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
▶	48.9%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify173.0ms (4%)

Memory

-22.9MiB live, 172.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
cost-diff	0	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
0	13	21
1	26	21
2	63	21
3	219	21
4	678	21
5	1073	21
6	1719	21
7	3625	21
8	5382	21
9	6807	21
0	8237	21

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal -1 binary64)

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal -1 binary64)

localize20.0ms (0.5%)

Memory

15.3MiB live, 53.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
accuracy	0	(*.f64 x x)
accuracy	32.733186076310055	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Samples

14.0ms

256×

valid

Compiler

Compiled 45 to 21 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sub: 4.0ms (47.5% of total)

ival-mult: 3.0ms (35.6% of total)

ival-add: 1.0ms (11.9% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

3 → 5

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(*.f64 x x)

Outputs
-1
(- (* 2 (pow x 2)) 1)
(pow x 2)
(* 2 (pow x 2))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((- (* (* x x) 2) 1) (+ (* (* x x) 2) -1) (* x x))
0.0ms	x	@	-inf	((- (* (* x x) 2) 1) (+ (* (* x x) 2) -1) (* x x))
0.0ms	x	@	0	((- (* (* x x) 2) 1) (+ (* (* x x) 2) -1) (* x x))

simplify114.0ms (2.7%)

Memory

12.4MiB live, 176.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	21	23
2	55	23
3	217	23
4	980	23
5	3384	23
6	5308	23
0	8052	21

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 5

Calls

Call 1

Inputs
-1
(- (* 2 (pow x 2)) 1)
(pow x 2)
(* 2 (pow x 2))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))

Outputs
-1
#s(literal -1 binary64)
(- (* 2 (pow x 2)) 1)
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))

rewrite409.0ms (9.6%)

Memory

-0.2MiB live, 237.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
0	13	17
1	50	17
2	298	17
3	3184	17
0	9624	17

Stop Event

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

Counts

3 → 290

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(*.f64 x x)

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) (fma.f64 #s(literal -512 binary64) (pow.f64 x #s(literal 18 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (-.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))))
(.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))
(/.f64 (-.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64))) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))))
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(fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(fma.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal -1 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x x) (-.f64 (.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (-.f64 (.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 #s(literal 2 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(literal 2 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 x (sqrt.f64 (.f64 #s(literal -2 binary64) (.f64 #s(literal -2 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(fma.f64 x (exp.f64 (log.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal -1 binary64))
(fma.f64 x (pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 x (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))))
(fma.f64 x (*.f64 #s(literal -2 binary64) x) #s(literal -1 binary64))
(fma.f64 x x (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 x x (fma.f64 x x #s(literal -1 binary64)))
(expm1.f64 (/.f64 (log.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)))
(expm1.f64 (*.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal -2 binary64))) #s(literal 1 binary64)))
(expm1.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal -2 binary64))))
(-.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (.f64 x x))
(-.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))))) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(-.f64 (.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) (.f64 x x)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (.f64 x x))
(+.f64 (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(+.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))))) (neg.f64 (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64))))
(+.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64))))) (pow.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal -2 binary64) (.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(+.f64 (.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal -1 binary64))
(+.f64 (.f64 x x) (-.f64 (.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))
(+.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) (.f64 x x)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 (sqrt.f64 x) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (-.f64 x #s(literal 0 binary64)) (-.f64 x #s(literal 0 binary64)))
(.f64 (.f64 x x) #s(literal -1 binary64))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(fabs.f64 (-.f64 (*.f64 x x) #s(literal 0 binary64)))
(fabs.f64 (*.f64 (-.f64 x #s(literal 0 binary64)) x))
(fabs.f64 (*.f64 x (-.f64 x #s(literal 0 binary64))))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (/.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval74.0ms (1.7%)

Memory: 7.4MiB live, 82.9MiB allocated
Compiler: Compiled 7 437 to 691 computations (90.7% saved)

prune128.0ms (3%)

Memory

-37.5MiB live, 53.9MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	292	3	295

Accuracy

100.0%

Counts

295 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
▶	52.0%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	48.9%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify193.0ms (4.5%)

Memory

32.8MiB live, 189.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) #s(literal 2 binary64))
cost-diff	0	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
0	11	23
1	25	23
2	54	23
3	206	23
4	675	23
5	1082	23
6	1728	23
7	3649	23
8	5411	23
9	6838	23
0	8261	22

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)

Outputs
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)

localize17.0ms (0.4%)

Memory

1.2MiB live, 40.0MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	30.727397380781557	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))

Samples

10.0ms

256×

valid

Compiler

Compiled 42 to 18 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 3.0ms (62.1% of total)

ival-sub: 1.0ms (20.7% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

-33.9MiB live, 4.2MiB allocated

Counts

3 → 5

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)

Outputs
-1
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(pow x 2)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))
1.0ms	x	@	inf	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))
1.0ms	x	@	-inf	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))

simplify167.0ms (3.9%)

Memory

16.2MiB live, 173.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	21	23
2	55	23
3	217	23
4	980	23
5	3384	23
6	5308	23
0	8052	21

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 5

Calls

Call 1

Inputs
-1
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(pow x 2)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))

Outputs
-1
#s(literal -1 binary64)
(- (* 2 (pow x 2)) 1)
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))

rewrite242.0ms (5.7%)

Memory

-15.5MiB live, 245.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
0	11	21
1	40	21
2	217	21
3	2241	21
0	9527	20

Stop Event

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

Counts

3 → 91

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)

Outputs
#s(approx (- (* (* x x) 2) 1) (.f64 #s(literal -2 binary64) (.f64 x x)))
(.f64 (fabs.f64 (.f64 (*.f64 #s(literal -2 binary64) x) #s(literal -1 binary64))) x)
(.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) x)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (*.f64 #s(literal -2 binary64) x)))
(*.f64 (hypot.f64 x x) (hypot.f64 x x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))))
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (.f64 x x))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal -2 binary64) x))) x)
(.f64 (pow.f64 (.f64 (*.f64 #s(literal -2 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) x)
(.f64 (.f64 (*.f64 #s(literal -2 binary64) x) #s(literal -1 binary64)) x)
(.f64 #s(literal -2 binary64) (.f64 x x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) x) x)
(.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) (*.f64 x x)))
(.f64 (.f64 #s(literal -2 binary64) (*.f64 x x)) #s(literal -1 binary64))
(.f64 (.f64 #s(literal -2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 (.f64 x x) #s(literal -2 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) (*.f64 x x)))
(.f64 #s(literal 2 binary64) (fabs.f64 (.f64 (*.f64 x x) #s(literal -1 binary64))))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal -1 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 x (fabs.f64 (.f64 (*.f64 #s(literal -2 binary64) x) #s(literal -1 binary64))))
(.f64 x (exp.f64 (log.f64 (.f64 #s(literal -2 binary64) x))))
(.f64 x (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)))
(.f64 x (.f64 (*.f64 #s(literal -2 binary64) x) #s(literal -1 binary64)))
(.f64 x (.f64 #s(literal -2 binary64) x))
(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal -2 binary64) (.f64 x x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal -2 binary64) (.f64 x x)))
(/.f64 (fabs.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fabs.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -2 binary64) (.f64 x x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(neg.f64 (.f64 #s(literal -2 binary64) (.f64 x x)))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x) (*.f64 x x))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x) (*.f64 x x))
(fma.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 x x))
(fma.f64 (sqrt.f64 x) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (*.f64 x x))
(fma.f64 (-.f64 x #s(literal 0 binary64)) (-.f64 x #s(literal 0 binary64)) (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x x))
(fma.f64 x x (*.f64 x x))
(sqrt.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -2 binary64) (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -2 binary64) (.f64 x x))))
(-.f64 #s(literal 0 binary64) (.f64 #s(literal -2 binary64) (.f64 x x)))
(-.f64 (.f64 x x) (.f64 x x))
(fabs.f64 (-.f64 (.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 0 binary64)))
(fabs.f64 (.f64 (.f64 #s(literal -2 binary64) x) (-.f64 x #s(literal 0 binary64))))
(fabs.f64 (.f64 (-.f64 x #s(literal 0 binary64)) (.f64 #s(literal -2 binary64) x)))
(fabs.f64 (.f64 #s(literal -2 binary64) (.f64 x x)))
(exp.f64 (/.f64 (log.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 2 binary64))))
(+.f64 (cosh.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 (sqrt.f64 x) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (-.f64 x #s(literal 0 binary64)) (-.f64 x #s(literal 0 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(fabs.f64 (-.f64 (*.f64 x x) #s(literal 0 binary64)))
(fabs.f64 (*.f64 (-.f64 x #s(literal 0 binary64)) x))
(fabs.f64 (*.f64 x (-.f64 x #s(literal 0 binary64))))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (/.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval41.0ms (1%)

Memory: -8.7MiB live, 29.3MiB allocated
Compiler: Compiled 1 576 to 298 computations (81.1% saved)

prune4.0ms (0.1%)

Memory

13.6MiB live, 13.6MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	95	3	98

Accuracy

100.0%

Counts

98 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
✓	52.0%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	48.9%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 63 to 38 computations (39.7% saved)

regimes10.0ms (0.2%)

Memory

-12.0MiB live, 25.2MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Outputs
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))

Calls

4 calls:

4.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
2.0ms	x
2.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
100.0%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes6.0ms (0.1%)

Memory

17.5MiB live, 17.5MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))

Calls

4 calls:

2.0ms	x
1.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	(*.f64 x x)
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
99.1%	2	`x`
99.1%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
99.1%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
99.1%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes9.0ms (0.2%)

Memory

-26.1MiB live, 17.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Calls

4 calls:

5.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
1.0ms	x
1.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
48.9%	1	`x`
48.9%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
48.9%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
48.9%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch13.0ms (0.3%)

Memory

34.6MiB live, 34.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	4.0427914411380476e-17	3426.8599224686473

Samples

5.0ms

176×

valid

Compiler

Compiled 230 to 219 computations (4.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-sub: 1.0ms (43.9% of total)

ival-mult: 1.0ms (43.9% of total)

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

exact: 0.0ms (0% of total)

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

simplify31.0ms (0.7%)

Memory

-31.9MiB live, 82.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	19	43

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))

(if (<=.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64)) #s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64))))

#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Outputs
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(approx (- ( (* x x) 2) 1) #s(literal -1 binary64)) #s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64))))
(if (<=.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(approx (- ( (* x x) 2) 1) #s(literal -1 binary64)) #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

soundness540.0ms (12.7%)

Memory

11.6MiB live, 325.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	21	23
2	55	23
3	217	23
4	980	23
5	3384	23
6	5308	23
0	8052	21
0	10	23
1	21	23
2	55	23
3	217	23
4	980	23
5	3390	23
6	5308	23
0	8049	21
0	6	15
0	9	15
1	38	15
2	215	15
3	2231	15
0	9536	14

Stop Event

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

Compiler

Compiled 64 to 34 computations (46.9% saved)

preprocess75.0ms (1.8%)

Memory: 12.5MiB live, 95.6MiB allocated
Remove: (abs x)
Compiler: Compiled 112 to 54 computations (51.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample752.0ms (17.6%)

explain99.0ms (2.3%)

preprocess282.0ms (6.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify353.0ms (8.3%)

localize103.0ms (2.4%)

series2.0ms (0.1%)

simplify119.0ms (2.8%)

rewrite180.0ms (4.2%)

eval102.0ms (2.4%)

prune6.0ms (0.1%)

simplify173.0ms (4%)

localize20.0ms (0.5%)

series1.0ms (0%)

simplify114.0ms (2.7%)

rewrite409.0ms (9.6%)

eval74.0ms (1.7%)

prune128.0ms (3%)

simplify193.0ms (4.5%)

localize17.0ms (0.4%)

series5.0ms (0.1%)

simplify167.0ms (3.9%)

rewrite242.0ms (5.7%)

eval41.0ms (1%)

prune4.0ms (0.1%)

regimes10.0ms (0.2%)

regimes6.0ms (0.1%)

regimes9.0ms (0.2%)

bsearch13.0ms (0.3%)

simplify31.0ms (0.7%)

soundness540.0ms (12.7%)

preprocess75.0ms (1.8%)

end0.0ms (0%)

Profiling