Herbie run

Date:Sunday, January 19th, 2025
Commit:455c599f on main
Seed:2025019
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
Memory:452 578.8 MB

Time bar (total: 6.0min)

sample1.8min (29.5%)

Memory
1 737.4MiB live, 130 854.0MiB allocated; 37.8s collecting garbage
Samples
57.9s262 171×0valid
19.4s1 558×5exit
3.7s8 060×1valid
2.0s10 982×0invalid
690.0ms2 216×2valid
359.0ms695×1invalid
0.0ms1×3valid
Precisions
Click to see histograms. Total time spent on operations: 1.2min
ival-pow: 17.9s (25.1% of total)
ival-mult: 9.8s (13.8% of total)
const: 7.2s (10.1% of total)
ival-<=: 5.9s (8.2% of total)
ival-div: 4.6s (6.5% of total)
ival-e: 2.9s (4% of total)
ival-add: 2.6s (3.6% of total)
ival-fabs: 2.3s (3.2% of total)
ival-sub: 2.3s (3.2% of total)
ival-log: 2.1s (2.9% of total)
ival-sqrt: 1.5s (2.1% of total)
ival-exp: 1.3s (1.9% of total)
ival-sin: 1.3s (1.8% of total)
ival-and: 1.2s (1.6% of total)
adjust: 1.1s (1.5% of total)
ival-pi: 798.0ms (1.1% of total)
ival-floor: 710.0ms (1% of total)
ival-neg: 671.0ms (0.9% of total)
ival-cosu: 595.0ms (0.8% of total)
ival-sinu: 572.0ms (0.8% of total)
ival-if: 480.0ms (0.7% of total)
ival-log1p: 470.0ms (0.7% of total)
ival-pow2: 456.0ms (0.6% of total)
ival-cos: 451.0ms (0.6% of total)
exact: 432.0ms (0.6% of total)
ival-fmax: 373.0ms (0.5% of total)
ival-tan: 371.0ms (0.5% of total)
ival-<: 207.0ms (0.3% of total)
ival-log2: 204.0ms (0.3% of total)
ival-==: 184.0ms (0.3% of total)
ival->: 159.0ms (0.2% of total)
ival-asin: 117.0ms (0.2% of total)
ival-assert: 103.0ms (0.1% of total)
ival-atan: 83.0ms (0.1% of total)
ival-sinh: 79.0ms (0.1% of total)
ival->=: 49.0ms (0.1% of total)
ival-true: 25.0ms (0% of total)
Bogosity

simplify52.6s (14.7%)

Memory
751.2MiB live, 58 738.6MiB allocated; 13.1s collecting garbage
Stop Event
396×iter limit
296×node limit
1×saturated
Counts
18 489 → 18 489

regimes32.7s (9.1%)

Memory
586.0MiB live, 47 023.0MiB allocated; 7.0s collecting garbage
Counts
12 519 → 515
Calls

160 calls:

1.3s
uy
1.1s
(*.f32 (*.f32 uy #s(literal 2 binary32)) (PI.f32))
854.0ms
(*.f32 uy #s(literal 2 binary32))
803.0ms
ux
745.0ms
s
Compiler

Compiled 26 236 to 21 002 computations (19.9% saved)

eval32.6s (9.1%)

Memory
-205.6MiB live, 46 238.7MiB allocated; 11.8s collecting garbage
Compiler

Compiled 34 049 357 to 424 493 computations (98.8% saved)

localize28.0s (7.8%)

Memory
-238.8MiB live, 35 859.1MiB allocated; 6.1s collecting garbage
Samples
13.3s29 402×0valid
3.2s698×5exit
1.8s1 652×1valid
836.0ms955×0invalid
368.0ms813×0exit
231.0ms255×2valid
16.0ms16×3valid
1.0ms1×4valid
Compiler

Compiled 135 020 to 6 465 computations (95.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.7s
ival-mult: 4.7s (30.2% of total)
ival-div: 1.7s (11% of total)
adjust: 1.3s (8.5% of total)
ival-add: 1.3s (8% of total)
ival-sub: 863.0ms (5.5% of total)
ival-pow: 667.0ms (4.2% of total)
ival-log: 496.0ms (3.2% of total)
ival-exp: 471.0ms (3% of total)
ival-pow2: 457.0ms (2.9% of total)
const: 438.0ms (2.8% of total)
ival-sqrt: 409.0ms (2.6% of total)
ival-log1p: 378.0ms (2.4% of total)
ival-neg: 344.0ms (2.2% of total)
ival-sin: 323.0ms (2.1% of total)
ival-sinu: 270.0ms (1.7% of total)
ival-cosu: 194.0ms (1.2% of total)
ival-cos: 194.0ms (1.2% of total)
ival-atan: 139.0ms (0.9% of total)
ival-floor: 128.0ms (0.8% of total)
ival-e: 121.0ms (0.8% of total)
ival-fabs: 119.0ms (0.8% of total)
ival-fmax: 114.0ms (0.7% of total)
ival-if: 79.0ms (0.5% of total)
ival-pi: 71.0ms (0.5% of total)
ival-tan: 64.0ms (0.4% of total)
exact: 62.0ms (0.4% of total)
ival-log2: 54.0ms (0.3% of total)
ival-tanu: 40.0ms (0.3% of total)
ival-expm1: 34.0ms (0.2% of total)
ival-true: 27.0ms (0.2% of total)
ival-cbrt: 20.0ms (0.1% of total)
ival->: 15.0ms (0.1% of total)
ival-assert: 13.0ms (0.1% of total)
ival-asin: 10.0ms (0.1% of total)
ival-sinh: 10.0ms (0.1% of total)
ival->=: 10.0ms (0.1% of total)
ival-<: 8.0ms (0.1% of total)
ival-acos: 6.0ms (0% of total)
ival-then: 0.0ms (0% of total)

analyze22.0s (6.2%)

Memory
224.1MiB live, 30 380.1MiB allocated; 7.1s collecting garbage
Algorithm
33×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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)

rewrite18.1s (5.1%)

Memory
-45.3MiB live, 20 255.8MiB allocated; 4.5s collecting garbage
Stop Event
389×iter limit
118×node limit
14×unsound
Counts
2 504 → 42 077

series17.8s (5%)

Memory
140.3MiB live, 23 186.0MiB allocated; 5.5s collecting garbage
Counts
2 504 → 18 489
Calls

1452 calls:

TimeVariablePointExpression
460.0ms
s
@inf
((/ 1 (+ (exp (/ (neg (PI)) s)) 1)) (/ 1 (+ (exp (/ (PI) s)) 1)) (* (neg s) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1))) (neg s) (* (neg s) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1))) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1)) (/ (PI) s) (* (* (PI) (PI)) 0) (+ (* (/ (- (/ (+ (* (pow (+ (* (* -1/2 (PI)) u) (* 1/4 (PI))) 2) -8) (* (* (* (PI) (PI)) 0) -4)) s) (* (+ (* (* -1/2 (PI)) u) (* 1/4 (PI))) 4)) s) -1) 1) (+ (* (* -1/2 (PI)) u) (* 1/4 (PI))) (* (* (* (PI) (PI)) 0) -4) (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s))))) (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))) (* (neg s) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1))) (* (neg s) (- (log (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -3) 1)) (log (+ (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -2) -1) (/ 1 (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s)))))))))))) (- (log (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -3) 1)) (log (+ (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -2) -1) (/ 1 (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))))))) (log (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -3) 1)) (PI) (exp (/ (PI) s)) (exp (/ (neg (PI)) s)) (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1) (* (PI) (PI)) (* (neg s) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1))) (exp (/ (PI) s)) (log (+ 1 (exp (/ (PI) s)))))
435.0ms
alphay
@-inf
((+ (* 1/2 (PI)) (* u1 (* (PI) 2))) (pow (- (/ (/ u0 (+ (pow (/ (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphay) 2) (pow (/ (/ 1 (sqrt (+ (pow (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI)))) 2) 1))) alphax) 2))) (- 1 u0)) -1) -1/2) (- (/ (/ u0 (+ (pow (/ (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphay) 2) (pow (/ (/ 1 (sqrt (+ (pow (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI)))) 2) 1))) alphax) 2))) (- 1 u0)) -1) (/ (/ u0 (+ (pow (/ (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) alphay) 2) (pow (/ (/ 1 (sqrt (+ (pow (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI)))) 2) 1))) alphax) 2))) (- 1 u0)) (- 1/2 (* (cos (* (atan (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI))))) 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))))) (+ (* (/ -1/2 (- 1/2 (* (cos (* (atan (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI))))) 2)) 1/2))) (/ (* (* alphay alphay) u0) (- 1 u0))) 1) (/ -1/2 (- 1/2 (* (cos (* (atan (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI))))) 2)) 1/2))) (/ 1 (sqrt (- (/ (* (/ 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)) -1))) (sqrt (- (/ (* (/ 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)) -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)) -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)) (/ 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))))) (+ (* (/ -1/2 (pow (sin (atan (* (/ (sin (* (PI) (+ (* 2 u1) 1/2))) alphax) (/ alphay (cos (* (PI) (+ (* 2 u1) 1/2))))))) 2)) (/ (* (* alphay alphay) u0) (- 1 u0))) 1) (/ -1/2 (pow (sin (atan (* (/ (sin (* (PI) (+ (* 2 u1) 1/2))) alphax) (/ alphay (cos (* (PI) (+ (* 2 u1) 1/2))))))) 2)) (pow (sin (atan (* (/ (sin (* (PI) (+ (* 2 u1) 1/2))) alphax) (/ alphay (cos (* (PI) (+ (* 2 u1) 1/2))))))) 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 (/ (* (/ 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)))) (+ 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))) (/ (* (/ 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)) (PI) (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax))) (sin (atan (* (tan (+ (* 1/2 (PI)) (* u1 (* (PI) 2)))) (/ alphay alphax)))) (sqrt (+ (pow (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI)))) 2) 1)) (atan (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI))))) (cos (* (atan (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI))))) 2)) (* (/ 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) (sin (atan (* (/ alphay alphax) (tan (* (+ (* 2 u1) 1/2) (PI)))))) (* (/ (sin (* (PI) (+ (* 2 u1) 1/2))) alphax) (/ alphay (cos (* (PI) (+ (* 2 u1) 1/2))))) (atan (* (/ (sin (* (PI) (+ (* 2 u1) 1/2))) alphax) (/ alphay (cos (* (PI) (+ (* 2 u1) 1/2)))))) (* (/ 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))
374.0ms
u1
@-inf
((+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* 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))) (+ (* (* 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) (/ 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))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))) (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)))
242.0ms
s
@0
((* (+ (* -64 (pow u 3)) -1) (* -4 u)) (+ (* (* u u) 16) (+ (* -4 u) 1)) (* (neg (- (log (+ 1 (pow (* u -4) 3))) (log (+ 1 (/ (* (+ (* -64 (pow u 3)) -1) (* -4 u)) (+ (* (* u u) 16) (+ (* -4 u) 1))))))) s) (neg (- (log (+ 1 (pow (* u -4) 3))) (log (+ 1 (/ (* (+ (* -64 (pow u 3)) -1) (* -4 u)) (+ (* (* u u) 16) (+ (* -4 u) 1))))))) (* s (log (/ 1 (- 1 (* 4 u))))) (* (* s (+ (* 8 u) 4)) u) (* s (+ (* 8 u) 4)) (+ (* 8 u) 4) (+ (* (* (* s (+ (* (+ (* 64 u) 64/3) u) 8)) u) u) (* (* 4 s) u)) (* s (log (/ 1 (- 1 (* 4 u))))) (* (* s (+ (* (+ (* 64 u) 64/3) u) 8)) u) (* s (+ (* (+ (* 64 u) 64/3) u) 8)) (* (neg (log (+ 1 (* -4 u)))) s) (neg (log (+ 1 (* -4 u)))) (log (+ 1 (* -4 u))) (* (+ (* (- (* (+ (* -64 u) -64/3) u) 8) u) -4) u) (log (/ 1 (+ (* u -4) 1))) (* (log (/ 1 (+ (* u -4) 1))) s) (/ 1 (+ (* u -4) 1)) (+ (* u -4) 1) (log (+ 1 (/ (* (+ (* -64 (pow u 3)) -1) (* -4 u)) (+ (* (* u u) 16) (+ (* -4 u) 1))))) (/ (* (+ (* -64 (pow u 3)) -1) (* -4 u)) (+ (* (* u u) 16) (+ (* -4 u) 1))) (* (+ (* -64 u) -64/3) u) (+ (* -64 u) -64/3))
240.0ms
s
@0
((/ 1 (+ (exp (/ (neg (PI)) s)) 1)) (/ 1 (+ (exp (/ (PI) s)) 1)) (* (neg s) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1))) (neg s) (* (neg s) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1))) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1)) (/ (PI) s) (* (* (PI) (PI)) 0) (+ (* (/ (- (/ (+ (* (pow (+ (* (* -1/2 (PI)) u) (* 1/4 (PI))) 2) -8) (* (* (* (PI) (PI)) 0) -4)) s) (* (+ (* (* -1/2 (PI)) u) (* 1/4 (PI))) 4)) s) -1) 1) (+ (* (* -1/2 (PI)) u) (* 1/4 (PI))) (* (* (* (PI) (PI)) 0) -4) (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s))))) (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))) (* (neg s) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1))) (* (neg s) (- (log (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -3) 1)) (log (+ (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -2) -1) (/ 1 (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s)))))))))))) (- (log (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -3) 1)) (log (+ (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -2) -1) (/ 1 (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))))))) (log (- (pow (+ (* (- (exp (neg (log (+ 1 (exp (/ (neg (PI)) s)))))) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) u) (exp (neg (log (+ 1 (exp (/ (PI) s))))))) -3) 1)) (PI) (exp (/ (PI) s)) (exp (/ (neg (PI)) s)) (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1) (* (PI) (PI)) (* (neg s) (log (- (/ 1 (+ (* u (- (/ 1 (+ 1 (exp (/ (neg (PI)) s)))) (/ 1 (+ 1 (exp (/ (PI) s)))))) (/ 1 (+ 1 (exp (/ (PI) s)))))) 1))) (exp (/ (PI) s)) (log (+ 1 (exp (/ (PI) s)))))

derivations17.3s (4.8%)

Memory
-475.9MiB live, 14 036.3MiB allocated; 5.3s collecting garbage
Stop Event
33×fuel
Compiler

Compiled 28 912 to 4 085 computations (85.9% saved)

prune11.6s (3.3%)

Memory
191.6MiB live, 19 737.6MiB allocated; 3.2s collecting garbage
Counts
104 495 → 4 057
Compiler

Compiled 562 504 to 213 636 computations (62% saved)

explain9.3s (2.6%)

Memory
-257.9MiB live, 14 226.2MiB allocated; 2.1s collecting garbage
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
log.f32#fsensitivity103355
-.f32#fcancellation38231
sqrt.f32#foflow-rescue3390
sqrt.f64#foflow-rescue2820
log.f64(log.f64 (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (pow.f64 (E.f64) x) #s(literal 1 binary64)) y)))sensitivity2000
cos.f32(cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32)))))))sensitivity1908
tan.f32(tan.f32 (+.f32 (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))cancellation18614
-.f64#fcancellation1580
/.f32#fo/n1120
exp.f32#fsensitivity3632
/.f32#fu/n230
sqrt.f32(sqrt.f32 (-.f32 (*.f32 eta eta) (/.f32 (*.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O))))))uflow-rescue190
↳(*.f32 sinTheta_O sinTheta_O)underflow314
↳(-.f32 (*.f32 eta eta) (/.f32 (*.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))underflow19
↳(/.f32 (*.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O))))underflow157
↳(*.f32 eta eta)underflow19
*.f64(*.f64 c (log.f64 (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (pow.f64 (E.f64) x) #s(literal 1 binary64)) y))))n*u110
/.f32#fo/o80
sqrt.f64#fuflow-rescue60
/.f32(/.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))n/o40
↳(/.f32 sin2phi (*.f32 alphay alphay))overflow10
↳(+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))overflow10
*.f32(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))n*u20
log.f32(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))oflow-rescue10
↳(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))overflow1
sin.f32(sin.f32 (*.f32 x (PI.f32)))cancellation10
Confusion
Predicted +Predicted -
+215754
-4345803
Precision
0.8324971053647241
Recall
0.9755766621438263
Confusion?
Predicted +Predicted MaybePredicted -
+21572529
-4341115692
Precision?
0.8001466813348002
Recall?
0.9868837630031659
Freqs
test
numberfreq
05857
12197
2386
38
Total Confusion?
Predicted +Predicted MaybePredicted -
+2111
-613
Precision?
0.7586206896551724
Recall?
0.9565217391304348
Samples
2.7s16 136×0valid
298.0ms614×1valid
56.0ms144×2valid
1.0ms2×3valid
Compiler

Compiled 16 934 to 1 875 computations (88.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.2s
ival-mult: 597.0ms (27.4% of total)
ival-div: 281.0ms (12.9% of total)
ival-sub: 158.0ms (7.3% of total)
ival-log: 142.0ms (6.5% of total)
ival-add: 106.0ms (4.9% of total)
ival-pow: 101.0ms (4.6% of total)
ival-pow2: 94.0ms (4.3% of total)
ival-neg: 80.0ms (3.7% of total)
ival-sqrt: 77.0ms (3.5% of total)
adjust: 53.0ms (2.4% of total)
ival-exp: 51.0ms (2.3% of total)
ival-floor: 50.0ms (2.3% of total)
ival-fabs: 45.0ms (2.1% of total)
ival-sin: 41.0ms (1.9% of total)
ival-cos: 39.0ms (1.8% of total)
ival-sinu: 38.0ms (1.7% of total)
ival-cosu: 31.0ms (1.4% of total)
ival-e: 27.0ms (1.2% of total)
ival-pi: 22.0ms (1% of total)
const: 21.0ms (1% of total)
ival-tan: 17.0ms (0.8% of total)
ival-fmax: 16.0ms (0.7% of total)
ival-if: 15.0ms (0.7% of total)
exact: 15.0ms (0.7% of total)
ival-true: 14.0ms (0.6% of total)
ival-log2: 12.0ms (0.6% of total)
ival-sinh: 8.0ms (0.4% of total)
ival-assert: 7.0ms (0.3% of total)
ival-log1p: 7.0ms (0.3% of total)
ival-atan: 5.0ms (0.2% of total)
ival-asin: 4.0ms (0.2% of total)
ival->: 3.0ms (0.1% of total)
ival->=: 3.0ms (0.1% of total)
ival-<: 1.0ms (0% of total)

preprocess9.2s (2.6%)

Memory
544.7MiB live, 11 042.6MiB allocated; 1.7s collecting garbage
Stop Event
66×iter limit
65×node limit
1×saturated
Compiler

Compiled 73 530 to 15 039 computations (79.5% saved)

bsearch736.0ms (0.2%)

Memory
25.1MiB live, 984.9MiB allocated; 193ms collecting garbage
Algorithm
82×binary-search
59×left-value
Stop Event
79×narrow-enough
3×predicate-same
Samples
260.0ms662×1valid
164.0ms1 022×0valid
77.0ms204×2valid
0.0ms1×0invalid
Compiler

Compiled 14 620 to 11 140 computations (23.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 438.0ms
ival-pow: 137.0ms (31.3% of total)
ival-e: 55.0ms (12.6% of total)
ival-sqrt: 49.0ms (11.2% of total)
adjust: 45.0ms (10.3% of total)
ival-mult: 39.0ms (8.9% of total)
ival-pow2: 33.0ms (7.5% of total)
ival-sub: 19.0ms (4.3% of total)
ival-add: 18.0ms (4.1% of total)
ival-div: 16.0ms (3.7% of total)
ival-fabs: 14.0ms (3.2% of total)
ival-log1p: 8.0ms (1.8% of total)
exact: 2.0ms (0.5% of total)
ival-assert: 1.0ms (0.2% of total)
ival-true: 1.0ms (0.2% of total)

start5.0ms (0%)

Memory
15.1MiB live, 15.0MiB allocated; 0ms collecting garbage

end0.0ms (0%)

Memory
0.6MiB live, 0.5MiB allocated; 0ms collecting garbage

Profiling

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