Metrics for Herbie run

Date:	Wednesday, November 27th, 2024
Commit:	a25f782f on bhargav-double-double
Hostname:	nightly with Racket 8.10
Seed:	2024332
Parameters:	256 points for 4 iterations
Flags:	`localize:costslocalize:errorsreduce:regimesreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs` default

sample1.3min (28.6%)

Memory

433.8MiB live, 95 105.2MiB allocated

Samples

53.2s	262 406×	0	valid
2.5s	7 878×	1	valid
2.0s	11 141×	0	invalid
609.0ms	2 163×	2	valid
308.0ms	1 580×	1	exit
235.0ms	667×	1	invalid
0.0ms	1×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 47.5s

ival-mult: 9.8s (20.5% of total)

const: 7.0s (14.6% of total)

ival-<=: 5.2s (11.1% of total)

ival-div: 4.3s (9.1% of total)

ival-add: 2.2s (4.7% of total)

ival-log: 1.9s (3.9% of total)

ival-sub: 1.8s (3.8% of total)

ival-sqrt: 1.6s (3.3% of total)

ival-fabs: 1.5s (3.3% of total)

ival-sin: 1.2s (2.6% of total)

ival-and: 1.2s (2.6% of total)

ival-pow: 999.0ms (2.1% of total)

ival-floor: 921.0ms (1.9% of total)

ival-exp: 845.0ms (1.8% of total)

ival-sinu: 728.0ms (1.5% of total)

ival-e: 536.0ms (1.1% of total)

ival-cosu: 525.0ms (1.1% of total)

ival-cos: 487.0ms (1% of total)

ival-neg: 481.0ms (1% of total)

exact: 464.0ms (1% of total)

ival->: 446.0ms (0.9% of total)

adjust: 434.0ms (0.9% of total)

ival-pow2: 426.0ms (0.9% of total)

ival-tan: 380.0ms (0.8% of total)

ival-fmax: 308.0ms (0.6% of total)

ival-pi: 268.0ms (0.6% of total)

ival-log1p: 259.0ms (0.5% of total)

ival-if: 212.0ms (0.4% of total)

ival-<: 202.0ms (0.4% of total)

ival-log2: 185.0ms (0.4% of total)

ival-asin: 148.0ms (0.3% of total)

ival-==: 135.0ms (0.3% of total)

ival-assert: 113.0ms (0.2% of total)

ival-atan: 89.0ms (0.2% of total)

ival-sinh: 76.0ms (0.2% of total)

ival->=: 47.0ms (0.1% of total)

ival-true: 23.0ms (0% of total)

Bogosity

simplify34.3s (12.2%)

Memory

119.2MiB live, 33 897.2MiB allocated

Algorithm

207×	egg-herbie

Stop Event

279×	iter limit
153×	node limit
51×	saturated
3×	unsound

Counts

10 856 → 10 778

regimes27.5s (9.8%)

Memory

-168.0MiB live, 37 730.4MiB allocated

Counts

13 011 → 240

Calls

122 calls:

1.4s	s
754.0ms	cosTheta_i
753.0ms	maxCos
750.0ms	u
724.0ms	r

Compiler

Compiled 12 680 to 10 137 computations (20.1% saved)

soundness26.1s (9.3%)

Memory

173.2MiB live, 16 664.3MiB allocated

Stop Event

209×	iter limit
131×	node limit
22×	fuel
4×	unsound
1×	done

Compiler

Compiled 24 597 to 10 299 computations (58.1% saved)

analyze20.5s (7.3%)

Memory

17.7MiB live, 27 187.1MiB allocated

Algorithm

33×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	11.5%	88.5%	0%	0%	0%	0
52.8%	6.1%	5.4%	88.5%	0%	0%	0%	1
54.4%	6.2%	5.2%	88.5%	0%	0%	0%	2
54.5%	6.3%	5.2%	88.5%	0%	0%	0%	3
55.4%	6.4%	5.1%	88.5%	0%	0%	0%	4
62.6%	7.2%	4.3%	88.5%	0%	0%	0%	5
66.9%	7.6%	3.8%	88.5%	0%	0.1%	0%	6
76.4%	8.4%	2.6%	88.5%	0%	0.4%	0%	7
76.8%	8.5%	2.6%	88.5%	0%	0.4%	0%	8
81.4%	9%	2%	88.5%	0%	0.4%	0%	9
85.1%	9.3%	1.6%	88.5%	0%	0.5%	0%	10
86.3%	9.4%	1.5%	88.5%	0%	0.5%	0%	11
87.3%	9.5%	1.4%	88.5%	0%	0.6%	0%	12

Compiler

Compiled 2 648 to 1 114 computations (57.9% saved)

rewrite18.6s (6.6%)

Memory

-40.8MiB live, 20 720.0MiB allocated

Stop Event

205×	iter limit
83×	node limit
9×	unsound

Counts

1 763 → 56 915

localize18.3s (6.5%)

Memory

107.4MiB live, 20 991.5MiB allocated

Samples

9.6s	20 035×	0	valid
1.5s	1 292×	1	valid
1.3s	1 792×	0	invalid
430.0ms	355×	2	valid
197.0ms	59×	5	exit
35.0ms	18×	3	valid
1.0ms	1×	4	valid

Compiler

Compiled 102 914 to 9 256 computations (91% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.9s

ival-mult: 2.9s (29% of total)

ival-div: 1.4s (13.9% of total)

ival-add: 974.0ms (9.8% of total)

ival-sub: 647.0ms (6.5% of total)

ival-sin: 544.0ms (5.5% of total)

ival-pow: 435.0ms (4.4% of total)

ival-sqrt: 374.0ms (3.8% of total)

ival-log: 345.0ms (3.5% of total)

ival-pow2: 338.0ms (3.4% of total)

adjust: 262.0ms (2.6% of total)

ival-cos: 211.0ms (2.1% of total)

ival-neg: 208.0ms (2.1% of total)

ival-exp: 164.0ms (1.7% of total)

ival-sinu: 151.0ms (1.5% of total)

ival-cosu: 148.0ms (1.5% of total)

const: 137.0ms (1.4% of total)

ival-log1p: 94.0ms (1% of total)

ival-pi: 85.0ms (0.9% of total)

ival-atan: 83.0ms (0.8% of total)

ival-tan: 81.0ms (0.8% of total)

exact: 73.0ms (0.7% of total)

ival-e: 58.0ms (0.6% of total)

ival-log2: 53.0ms (0.5% of total)

ival-expm1: 47.0ms (0.5% of total)

ival-fmax: 27.0ms (0.3% of total)

ival-floor: 22.0ms (0.2% of total)

ival-true: 21.0ms (0.2% of total)

ival-fabs: 20.0ms (0.2% of total)

ival-sinh: 14.0ms (0.1% of total)

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

ival-tanu: 11.0ms (0.1% of total)

ival-assert: 11.0ms (0.1% of total)

explain13.5s (4.8%)

Memory

-96.8MiB live, 19 417.0MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`#f`	sensitivity	805	78
`-.f32`	`#f`	cancellation	393	30
`sqrt.f64`	`#f`	oflow-rescue	284	0
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancelation	202	0
`-.f64`	`#f`	cancellation	201	0
`cos.f32`	`#f`	cancelation	195	0
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (pow.f64 (E.f64) x) #s(literal 1 binary64)) y)))`	sensitivity	177	1
`/.f32`	`#f`	u/n	101	0
`sqrt.f32`	`(sqrt.f32 (fmax.f32 (+.f32 (+.f32 (.f32 (.f32 (floor.f32 w) dX.u) (.f32 (floor.f32 w) dX.u)) (.f32 (.f32 (floor.f32 h) dX.v) (.f32 (floor.f32 h) dX.v))) (.f32 (.f32 (floor.f32 d) dX.w) (.f32 (floor.f32 d) dX.w))) (+.f32 (+.f32 (.f32 (.f32 (floor.f32 w) dY.u) (.f32 (floor.f32 w) dY.u)) (.f32 (.f32 (floor.f32 h) dY.v) (.f32 (floor.f32 h) dY.v))) (.f32 (.f32 (floor.f32 d) dY.w) (.f32 (floor.f32 d) dY.w)))))`	oflow-rescue	93	0
↳	`(.f32 (.f32 (floor.f32 h) dY.v) (*.f32 (floor.f32 h) dY.v))`	overflow	18
↳	`(fmax.f32 (+.f32 (+.f32 (.f32 (.f32 (floor.f32 w) dX.u) (.f32 (floor.f32 w) dX.u)) (.f32 (.f32 (floor.f32 h) dX.v) (.f32 (floor.f32 h) dX.v))) (.f32 (.f32 (floor.f32 d) dX.w) (.f32 (floor.f32 d) dX.w))) (+.f32 (+.f32 (.f32 (.f32 (floor.f32 w) dY.u) (.f32 (floor.f32 w) dY.u)) (.f32 (.f32 (floor.f32 h) dY.v) (.f32 (floor.f32 h) dY.v))) (.f32 (.f32 (floor.f32 d) dY.w) (.f32 (floor.f32 d) dY.w))))`	overflow	93
↳	`(+.f32 (.f32 (.f32 (floor.f32 w) dY.u) (.f32 (floor.f32 w) dY.u)) (.f32 (.f32 (floor.f32 h) dY.v) (.f32 (floor.f32 h) dY.v)))`	overflow	29
↳	`(.f32 (.f32 (floor.f32 h) dX.v) (*.f32 (floor.f32 h) dX.v))`	overflow	20
↳	`(.f32 (.f32 (floor.f32 w) dX.u) (*.f32 (floor.f32 w) dX.u))`	overflow	26
↳	`(+.f32 (.f32 (.f32 (floor.f32 w) dX.u) (.f32 (floor.f32 w) dX.u)) (.f32 (.f32 (floor.f32 h) dX.v) (.f32 (floor.f32 h) dX.v)))`	overflow	43
↳	`(.f32 (.f32 (floor.f32 w) dY.u) (*.f32 (floor.f32 w) dY.u))`	overflow	12
↳	`(+.f32 (+.f32 (.f32 (.f32 (floor.f32 w) dX.u) (.f32 (floor.f32 w) dX.u)) (.f32 (.f32 (floor.f32 h) dX.v) (.f32 (floor.f32 h) dX.v))) (.f32 (.f32 (floor.f32 d) dX.w) (*.f32 (floor.f32 d) dX.w)))`	overflow	58
↳	`(.f32 (.f32 (floor.f32 d) dY.w) (*.f32 (floor.f32 d) dY.w))`	overflow	16
↳	`(+.f32 (+.f32 (.f32 (.f32 (floor.f32 w) dY.u) (.f32 (floor.f32 w) dY.u)) (.f32 (.f32 (floor.f32 h) dY.v) (.f32 (floor.f32 h) dY.v))) (.f32 (.f32 (floor.f32 d) dY.w) (*.f32 (floor.f32 d) dY.w)))`	overflow	44
↳	`(.f32 (.f32 (floor.f32 d) dX.w) (*.f32 (floor.f32 d) dX.w))`	overflow	18
`+.f64`	`(+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (pow.f64 (E.f64) x) #s(literal 1 binary64)) y))`	cancellation	31	0
`*.f32`	`#f`	*nu**	29	0
`/.f32`	`#f`	u/u	11	0
`sqrt.f64`	`#f`	uflow-rescue	6	0
`*.f64`	`#f`	*no**	3	0
`*.f32`	`#f`	*uo**	2	0
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (pow.f64 (E.f64) x) #s(literal 1 binary64)) y)))`	oflow-rescue	1	0
↳	`(*.f64 (-.f64 (pow.f64 (E.f64) x) #s(literal 1 binary64)) y)`	overflow	1
↳	`(+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (pow.f64 (E.f64) x) #s(literal 1 binary64)) y))`	overflow	1
↳	`(pow.f64 (E.f64) x)`	overflow	1
↳	`(-.f64 (pow.f64 (E.f64) x) #s(literal 1 binary64))`	overflow	1

Confusion

	Predicted +	Predicted -
+	1748	42
-	490	3608

Precision

0.7810545129579982

Recall

0.976536312849162

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1748	32	10
-	490	109	3499

Precision?

0.748213535098781

Recall?

0.994413407821229

Freqs

test

number	freq
0	3650
1	1942
2	296

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	13	2	1
-	4	1	2

Precision?

0.75

Recall?

0.9375

Samples

1.9s	14 130×	0	valid
180.0ms	582×	1	valid
43.0ms	136×	2	valid
1.0ms	2×	4	valid
1.0ms	2×	3	valid

Compiler

Compiled 23 165 to 4 401 computations (81% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-mult: 417.0ms (28.7% of total)

ival-div: 178.0ms (12.3% of total)

ival-sub: 112.0ms (7.7% of total)

ival-add: 84.0ms (5.8% of total)

ival-sqrt: 71.0ms (4.9% of total)

ival-log: 68.0ms (4.7% of total)

ival-sinu: 58.0ms (4% of total)

ival-sin: 51.0ms (3.5% of total)

ival-exp: 41.0ms (2.8% of total)

ival-pow: 37.0ms (2.5% of total)

ival-floor: 29.0ms (2% of total)

const: 28.0ms (1.9% of total)

adjust: 27.0ms (1.9% of total)

ival-pow2: 27.0ms (1.9% of total)

ival-cos: 27.0ms (1.9% of total)

ival-neg: 27.0ms (1.9% of total)

ival-cosu: 24.0ms (1.7% of total)

ival-pi: 23.0ms (1.6% of total)

ival-e: 22.0ms (1.5% of total)

ival-tan: 21.0ms (1.4% of total)

ival-true: 15.0ms (1% of total)

exact: 15.0ms (1% of total)

ival-fabs: 12.0ms (0.8% of total)

ival-assert: 7.0ms (0.5% of total)

ival-log1p: 7.0ms (0.5% of total)

ival-log2: 6.0ms (0.4% of total)

ival-atan: 6.0ms (0.4% of total)

ival-sinh: 5.0ms (0.3% of total)

ival-asin: 4.0ms (0.3% of total)

ival-fmax: 3.0ms (0.2% of total)

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

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

ival->=: 0.0ms (0% of total)

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

eval12.6s (4.5%)

Memory: 28.4MiB live, 18 341.9MiB allocated
Compiler: Compiled 3 550 886 to 322 655 computations (90.9% saved)

prune11.4s (4.1%)

Memory: -151.2MiB live, 17 848.8MiB allocated
Counts: 72 147 → 5 412
Compiler: Compiled 542 906 to 263 411 computations (51.5% saved)

series11.3s (4%)

Memory

-46.4MiB live, 13 855.4MiB allocated

Counts

1 763 → 10 856

Calls

888 calls:

Time	Variable		Point	Expression
221.0ms	u1	@	inf	((+ (* u1 2) 1/2) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (sqrt (/ 1 (+ (/ (/ u0 (- 1 u0)) (+ (/ (pow (sin (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2) (* alphay alphay)) (/ (pow (cos (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* u1 2) 1/2)))))) 2) (* alphax alphax)))) 1))) (/ 1 (+ (/ (/ u0 (- 1 u0)) (+ (/ (pow (sin (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2) (* alphay alphay)) (/ (pow (cos (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* u1 2) 1/2)))))) 2) (* alphax alphax)))) 1)) (- 1 (/ (* u0 (* alphay alphay)) (* (- 1 (cos (* (atan (* (tan (* (+ (* u1 2) 1/2) (PI))) (/ alphay alphax))) 2))) (- 1 u0)))) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (* (/ (- 1 (cos (* (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))) 2))) alphay) (/ 1/2 alphay)) (pow (/ (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphax) 2))) u0) (- 1 u0))))) (* u0 (* alphay alphay)) (* alphay alphay) (* (- (/ 1 (* alphay alphay)) (/ (/ u0 (- 1 u0)) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (* (+ (* 2 u1) 1/2) (PI))) (cos (* (+ (* 2 u1) 1/2) (PI)))))) 2))))) (* alphay alphay)) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (* (/ (- 1 (cos (* (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))) 2))) alphay) (/ 1/2 alphay)) (pow (/ (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphax) 2))) u0) (- 1 u0))))) (- 1 (/ (/ (* (* alphay alphay) u0) (- 1 u0)) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (+ (* (* (PI) u1) 2) (* 1/2 (PI)))) (cos (+ (* (* (PI) u1) 2) (* 1/2 (PI))))))) 2))))) (- (/ 1 (* alphay alphay)) (/ (/ u0 (- 1 u0)) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (* (+ (* 2 u1) 1/2) (PI))) (cos (* (+ (* 2 u1) 1/2) (PI)))))) 2))))) (+ (* (* (PI) u1) 2) (* 1/2 (PI))) (- 1 (/ (/ (* (* alphay alphay) u0) (- 1 u0)) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (+ (* (* (PI) u1) 2) (* 1/2 (PI)))) (+ (* (cos (* u1 (* (PI) 2))) (cos (* 1/2 (PI)))) (* (neg (sin (* u1 (* (PI) 2)))) (sin (* 1/2 (PI)))))))) 2))))) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (* (/ (- 1 (cos (* (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))) 2))) alphay) (/ 1/2 alphay)) (pow (/ (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphax) 2))) u0) (- 1 u0))))) (/ (/ (* (* alphay alphay) u0) (- 1 u0)) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (+ (* (* (PI) u1) 2) (* 1/2 (PI)))) (+ (* (cos (* u1 (* (PI) 2))) (cos (* 1/2 (PI)))) (* (neg (sin (* u1 (* (PI) 2)))) (sin (* 1/2 (PI)))))))) 2)))) (pow (pow (+ (/ (/ u0 (- 1 u0)) (+ (pow (/ (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphay) 2) (pow (/ alphax (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))))) -2))) 1) 1/4) 2) (+ (* 1/2 (PI)) (* u1 (* (PI) 2))) (/ 1 (pow (pow (+ (/ (/ u0 (- 1 u0)) (+ (pow (/ (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphay) 2) (pow (/ alphax (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))))) -2))) 1) 1/4) 2)) (pow (+ (/ (/ u0 (- 1 u0)) (+ (pow (/ (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphay) 2) (pow (/ alphax (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))))) -2))) 1) 1/4) (+ (* 2 u1) 1/2) (cos (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* u1 2) 1/2)))))) (cos (* (PI) (+ (* u1 2) 1/2))) (cos (* (PI) (+ (* 2 u1) 1/2))) (tan (* (+ (* u1 2) 1/2) (PI))) (+ (* u1 2) 1/2) (- 1 (cos (* (atan (* (tan (* (+ (* u1 2) 1/2) (PI))) (/ alphay alphax))) 2))) (cos (* (+ (* 2 u1) 1/2) (PI))) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (* (+ (* 2 u1) 1/2) (PI))) (cos (* (+ (* 2 u1) 1/2) (PI)))))) 2))) (cos (* 1/2 (PI))) (+ (* (cos (* u1 (* (PI) 2))) (cos (* 1/2 (PI)))) (* (neg (sin (* u1 (* (PI) 2)))) (sin (* 1/2 (PI))))) (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (pow (/ alphax (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))))) -2))
162.0ms	c	@	0	((* (log (+ 1 (* y (- (exp x) 1)))) c) (log (+ 1 (* y (- (exp x) 1)))) (* y (- (exp x) 1)) (- (exp x) 1) (* c (log (+ 1 (* (- (pow (E) x) 1) y)))) (* (* c y) x) (* c y) (+ (* (* c (+ (* (* 1/6 x) (+ (* (* y y) (+ (* 2 y) -3)) y)) (* (- y (* y y)) 1/2))) x) (* c y)) (+ (* (* 1/6 x) (+ (* (* y y) (+ (* 2 y) -3)) y)) (* (- y (* y y)) 1/2)) (* (- y (* y y)) 1/2) (* c (log (+ 1 (* (- (pow (E) x) 1) y)))) (+ 1 (* (- (pow (E) x) 1) y)) (log (+ 1 (* (- (pow (E) x) 1) y))) (* c (log (+ 1 (* (- (pow (E) x) 1) y)))) (* (- (pow (E) x) 1) y) (* c (- (log (+ 1 (pow (* y (- (exp x) 1)) 3))) (log (+ 1 (* (+ (* y (- (exp x) 1)) -1) (* y (- (exp x) 1))))))) (- (log (+ 1 (pow (* y (- (exp x) 1)) 3))) (log (+ 1 (* (+ (* y (- (exp x) 1)) -1) (* y (- (exp x) 1)))))) (log (+ 1 (pow (* y (- (exp x) 1)) 3))) (pow (* y (- (exp x) 1)) 3) (* (+ (* (* c (+ (* (* 1/6 x) (+ (* (* y y) (+ (* 2 y) -3)) y)) (* (- y (* y y)) 1/2))) x) (* c y)) x) (- (pow (E) x) 1) (pow (E) x) (log (+ 1 (* (+ (* y (- (exp x) 1)) -1) (* y (- (exp x) 1))))))
161.0ms	u1	@	-inf	((* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (+ (* (* 2 (PI)) u1) (* 1/2 (PI))) (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (+ (* (* (PI) u1) 2) (* 1/2 (PI))) (- 1 (/ (/ (* (* alphay alphay) u0) (- 1 u0)) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (+ (* (* (PI) u1) 2) (* 1/2 (PI)))) (cos (+ (* (* (PI) u1) 2) (* 1/2 (PI))))))) 2))))) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (* (/ (- 1 (cos (* (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))) 2))) alphay) (/ 1/2 alphay)) (pow (/ (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphax) 2))) u0) (- 1 u0))))) (/ (/ (* (* alphay alphay) u0) (- 1 u0)) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (+ (* (* (PI) u1) 2) (* 1/2 (PI)))) (cos (+ (* (* (PI) u1) 2) (* 1/2 (PI))))))) 2)))) (+ (* (- 1 (cos (* (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))) 2))) (/ 1/2 (* alphay alphay))) (pow (/ alphax (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))))) -2)) (* (/ 1 (+ (* (- 1 (cos (* (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))) 2))) (/ 1/2 (* alphay alphay))) (pow (/ alphax (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))))) -2))) u0) (+ (* 1/2 (PI)) (* u1 (* (PI) 2))) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (* (- 1 (cos (* (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))) 2))) (/ 1/2 (* alphay alphay))) (pow (/ alphax (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))))) -2))) u0) (- 1 u0))))) (+ 1 (/ (* (/ 1 (/ (+ (* (/ (pow (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) 2) alphay) alphax) (* alphay (/ (pow (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) 2) alphax))) (* alphay alphax))) u0) (- 1 u0))) (/ 1 (/ (+ (* (/ (pow (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) 2) alphay) alphax) (* alphay (/ (pow (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) 2) alphax))) (* alphay alphax))) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (/ (+ (* (/ (pow (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) 2) alphay) alphax) (* alphay (/ (pow (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) 2) alphax))) (* alphay alphax))) u0) (- 1 u0))))) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (sqrt (/ 1 (+ (/ (/ u0 (- 1 u0)) (+ (/ (pow (sin (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2) (* alphay alphay)) (/ (pow (cos (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2) (* alphax alphax)))) 1))) (/ 1 (+ (/ (/ u0 (- 1 u0)) (+ (/ (pow (sin (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2) (* alphay alphay)) (/ (pow (cos (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2) (* alphax alphax)))) 1)) (+ (/ (/ u0 (- 1 u0)) (+ (/ (pow (sin (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2) (* alphay alphay)) (/ (pow (cos (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2) (* alphax alphax)))) 1) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))) (cos (+ (* (* (PI) u1) 2) (* 1/2 (PI)))) (- 1 (cos (* (atan (* (/ alphay alphax) (/ (sin (+ (* (* (PI) u1) 2) (* 1/2 (PI)))) (cos (+ (* (* (PI) u1) 2) (* 1/2 (PI))))))) 2))) (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (+ (* (/ (pow (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) 2) alphay) alphax) (* alphay (/ (pow (cos (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) 2) alphax))) (+ (* 2 u1) 1/2) (cos (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) (cos (* (PI) (+ (* 2 u1) 1/2))) (pow (cos (atan (/ (* (/ alphay alphax) (sin (* (PI) (+ (* 2 u1) 1/2)))) (cos (* (PI) (+ (* 2 u1) 1/2)))))) 2))
158.0ms	s	@	0	((/ -1 (/ 3/4 (- u 1/4))) (* (* 3 s) (log (/ 1 (+ (/ -1 (/ 3/4 (- u 1/4))) 1)))) (/ 1 (+ (/ -1 (/ 3/4 (- u 1/4))) 1)) (+ (/ -1 (/ 3/4 (- u 1/4))) 1) (* (* 3 s) (log (/ 1 (- 1 (/ (- u 1/4) 3/4))))) (* s (+ (* (+ (log 3/4) u) 3) (* (* 3/2 u) u))) (* (* (* u s) u) 3/2) (* (* u s) u) (+ (* (* (log (+ 1 (+ (* u 4/3) -1/3))) s) -3) 0) (* (log (+ 1 (+ (* u 4/3) -1/3))) s) (log (+ 1 (+ (* u 4/3) -1/3))) (+ (* u 4/3) -1/3) (+ (* (* s 3) 0) (* (* -3 (log (+ 1 (* -4/3 (- u 1/4))))) s)) (* s 3) (* (* -3 (log (+ 1 (* -4/3 (- u 1/4))))) s) (* -3 (log (+ 1 (* -4/3 (- u 1/4))))) (+ (* (* s 3) 0) (* (* -3 (log (+ 1 (+ (* u -4/3) 1/3)))) s)) (+ (* u -4/3) 1/3) (* (* -3 (log (+ 1 (+ (* u -4/3) 1/3)))) s) (log (/ 1 (+ (/ -1 (/ 3/4 (- u 1/4))) 1))) (log (+ 1 (* -4/3 (- u 1/4)))) (- (log 4/3) u) (log 4/3) (log (+ 1 (+ (* u -4/3) 1/3))) (* u -4/3))
134.0ms	dX.u	@	inf	((* (* (floor d) dY.w) (* (floor d) dY.w)) (* (* (pow (floor w) 2) dX.u) dX.u) (log2 (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (pow (* dY.u (floor w)) 2) (pow (* dY.v (floor h)) 2)) (* (* (floor d) dY.w) (* (floor d) dY.w)))))) (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (pow (* dY.u (floor w)) 2) (pow (* dY.v (floor h)) 2)) (* (* (floor d) dY.w) (* (floor d) dY.w))))) (pow (pow (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (pow (* dY.w (floor d)) 2) (+ (pow (* dY.u (floor w)) 2) (pow (* dY.v (floor h)) 2)))) 1/4) 2) (log2 (pow (pow (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (pow (* dY.w (floor d)) 2) (+ (pow (* dY.u (floor w)) 2) (pow (* dY.v (floor h)) 2)))) 1/4) 2)) (pow (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (pow (* dY.w (floor d)) 2) (+ (pow (* dY.u (floor w)) 2) (pow (* dY.v (floor h)) 2)))) 1/4) (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (pow (* dY.w (floor d)) 2) (+ (pow (* dY.u (floor w)) 2) (pow (* dY.v (floor h)) 2)))) (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (* (floor d) dX.w) (* (floor d) dX.w)) (* (* (pow (floor w) 2) dY.u) dY.u) (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)) (+ (* (* (pow (floor h) 2) dX.v) dX.v) (+ (pow (* dX.u (floor w)) 2) (pow (* dX.w (floor d)) 2))) (pow (* dX.w (floor d)) 1) (pow (* (floor d) (* dX.w dX.w)) 1/2) (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (pow (* dY.u (floor w)) 2) (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (* (* (pow (floor d) 2) dY.w) dY.w) (* (* (pow (floor w) 2) dY.u) dY.u)) (+ (* (* (pow (floor w) 2) dY.u) dY.u) (+ (pow (* dY.w (floor d)) 2) (pow (* dY.v (floor h)) 2))) (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (* (* (pow (floor w) 2) dY.u) dY.u) (+ (pow (* dY.w (floor d)) 2) (pow (* dY.v (floor h)) 2))))) (sqrt (fmax (+ (* (* (pow (floor h) 2) dX.v) dX.v) (+ (pow (* dX.u (floor w)) 2) (pow (* dX.w (floor d)) 2))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))))) (sqrt (fmax (+ (* (pow (* dX.w (floor d)) 1) (* (sqrt (floor d)) (pow (* (floor d) (* dX.w dX.w)) 1/2))) (+ (pow (* dX.v (floor h)) 2) (pow (* dX.u (floor w)) 2))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))))) (+ (* (pow (* dX.w (floor d)) 1) (* (sqrt (floor d)) (pow (* (floor d) (* dX.w dX.w)) 1/2))) (+ (pow (* dX.v (floor h)) 2) (pow (* dX.u (floor w)) 2))))

preprocess6.4s (2.3%)

Memory

97.0MiB live, 6 231.9MiB allocated

Algorithm

23×	egg-herbie

Stop Event

46×	iter limit
27×	saturated
19×	node limit

Compiler

Compiled 40 137 to 15 274 computations (61.9% saved)

bsearch253.0ms (0.1%)

Memory

58.5MiB live, 308.4MiB allocated

Algorithm

32×	left-value
26×	binary-search

Stop Event

25×	narrow-enough
1×	predicate-same

Samples

92.0ms	921×	0	valid
6.0ms	74×	0	invalid
2.0ms	7×	1	valid

Compiler

Compiled 5 787 to 4 508 computations (22.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-pow2: 14.0ms (18.9% of total)

ival-mult: 12.0ms (16.2% of total)

ival-pow: 11.0ms (14.8% of total)

ival-e: 9.0ms (12.1% of total)

ival-add: 6.0ms (8.1% of total)

ival-sub: 5.0ms (6.7% of total)

ival-fabs: 4.0ms (5.4% of total)

ival-log1p: 4.0ms (5.4% of total)

ival-div: 3.0ms (4% of total)

ival-sqrt: 3.0ms (4% of total)

ival-true: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

adjust: 0.0ms (0% of total)

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

start3.0ms (0%)

Memory: 6.4MiB live, 6.3MiB allocated

end0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated

sample1.3min (28.6%)

simplify34.3s (12.2%)

regimes27.5s (9.8%)

soundness26.1s (9.3%)

analyze20.5s (7.3%)

rewrite18.6s (6.6%)

localize18.3s (6.5%)

explain13.5s (4.8%)

eval12.6s (4.5%)

prune11.4s (4.1%)

series11.3s (4%)

preprocess6.4s (2.3%)

bsearch253.0ms (0.1%)

start3.0ms (0%)

end0.0ms (0%)

Profiling