Herbie run

Date:Wednesday, October 30th, 2024
Commit:aeaf0403 on bhargav-double-double
Hostname:nightly with Racket 8.10
Seed:2024304
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

Time bar (total: 24.8min)

sample13.8min (55.8%)

Memory
27 156.1MiB live, 258 716.2MiB allocated
Samples
3.7min285 052×0valid
1.8min6 221×1invalid
1.5min1 801×3valid
1.2min106 721×1valid
1.1min22 458×2valid
27.9s2 495×1exit
26.1s14 456×5exit
5.1s35 401×0exit
4.7s20 186×0invalid
250.0ms754×2invalid
165.0ms24×4valid
3.0ms4exit
1.0ms3exit
Precisions
Click to see histograms. Total time spent on operations: 8.6min
ival-div: 1.2min (13.9% of total)
ival-mult: 1.1min (13.3% of total)
ival-log1p: 59.5s (11.6% of total)
ival-sqrt: 54.0s (10.5% of total)
ival-sub: 46.1s (9% of total)
ival-add: 43.0s (8.4% of total)
ival-cosu: 33.9s (6.6% of total)
adjust: 32.0s (6.2% of total)
ival-<: 27.6s (5.4% of total)
ival-pow: 21.2s (4.1% of total)
ival-pow2: 17.9s (3.5% of total)
ival-log: 11.0s (2.1% of total)
ival-cos: 7.6s (1.5% of total)
ival-sin: 5.7s (1.1% of total)
ival-exp: 4.3s (0.8% of total)
ival-sinu: 4.1s (0.8% of total)
ival-neg: 1.4s (0.3% of total)
const: 1.3s (0.3% of total)
ival-atan2: 608.0ms (0.1% of total)
ival-tan: 455.0ms (0.1% of total)
ival-hypot: 451.0ms (0.1% of total)
exact: 391.0ms (0.1% of total)
ival-acos: 349.0ms (0.1% of total)
ival-and: 343.0ms (0.1% of total)
ival-true: 303.0ms (0.1% of total)
ival-atan: 247.0ms (0% of total)
ival-assert: 223.0ms (0% of total)
ival-cbrt: 203.0ms (0% of total)
ival-asin: 134.0ms (0% of total)
ival-pi: 114.0ms (0% of total)
ival-fabs: 108.0ms (0% of total)
ival-<=: 100.0ms (0% of total)
ival-==: 1.0ms (0% of total)
ival-or: 0.0ms (0% of total)
Bogosity

soundness3.6min (14.7%)

Memory
441.7MiB live, 63 387.4MiB allocated
Stop Event
330×iter limit
220×node limit
35×fuel
done
saturated
Compiler

Compiled 64 959 to 23 927 computations (63.2% saved)

analyze1.7min (7%)

Memory
3 441.5MiB live, 36 154.1MiB allocated
Algorithm
53×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%79.4%20.6%0%0%0%0
17.2%13.7%65.7%20.6%0%0%0%1
25%19.6%58.5%20.6%0%1.3%0%2
35.2%26.6%48.9%20.6%0%3.8%0%3
42.3%31.7%43.1%20.6%0%4.5%0%4
47.9%35.6%38.7%20.6%0%5.1%0%5
51%37.6%36.1%20.6%0%5.7%0%6
54.4%39.7%33.2%20.6%0%6.5%0%7
56.2%40.7%31.8%20.6%0%6.8%0%8
59%42.5%29.5%20.6%0%7.4%0%9
60.3%43.2%28.4%20.6%0%7.7%0%10
62.1%44.3%27%20.6%0%8.1%0%11
63.6%45.1%25.8%20.6%0%8.5%0%12
Compiler

Compiled 1 826 to 964 computations (47.2% saved)

eval1.7min (6.8%)

Memory
10 235.9MiB live, 42 538.7MiB allocated
Compiler

Compiled 6 329 507 to 521 598 computations (91.8% saved)

simplify1.1min (4.3%)

Memory
10 332.3MiB live, 21 056.7MiB allocated
Algorithm
357×egg-herbie
Stop Event
476×iter limit
248×node limit
109×saturated
Counts
17 410 → 17 298

rewrite55.1s (3.7%)

Memory
7 972.9MiB live, 21 186.4MiB allocated
Stop Event
319×iter limit
157×node limit
saturated
Counts
2 680 → 106 516

prune36.3s (2.4%)

Memory
10 247.7MiB live, 19 624.4MiB allocated
Counts
124 218 → 4 948
Compiler

Compiled 560 668 to 237 358 computations (57.7% saved)

localize27.5s (1.9%)

Memory
7 507.4MiB live, 10 640.3MiB allocated
Samples
9.6s11 575×1valid
5.8s22 882×0valid
3.4s3 042×2valid
917.0ms1 887×0invalid
416.0ms284×2exit
342.0ms218×1invalid
317.0ms198×3valid
147.0ms213×1exit
132.0ms52×2invalid
67.0ms3exit
47.0ms4exit
32.0ms3invalid
25.0ms75×0exit
7.0ms5exit
3.0ms4valid
Compiler

Compiled 129 755 to 13 538 computations (89.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.5s
ival-mult: 4.0s (24.6% of total)
ival-div: 1.8s (11.1% of total)
ival-add: 1.3s (8% of total)
adjust: 1.3s (8% of total)
ival-cos: 1.3s (7.7% of total)
ival-pow: 826.0ms (5% of total)
const: 727.0ms (4.4% of total)
ival-pow2: 633.0ms (3.8% of total)
ival-sub: 615.0ms (3.7% of total)
ival-exp: 546.0ms (3.3% of total)
ival-sqrt: 491.0ms (3% of total)
ival-sin: 490.0ms (3% of total)
ival-log: 489.0ms (3% of total)
ival-sinu: 452.0ms (2.7% of total)
ival-cosu: 276.0ms (1.7% of total)
ival-neg: 229.0ms (1.4% of total)
ival-log1p: 183.0ms (1.1% of total)
ival-hypot: 164.0ms (1% of total)
ival-cbrt: 133.0ms (0.8% of total)
ival-acos: 107.0ms (0.6% of total)
exact: 105.0ms (0.6% of total)
ival-true: 45.0ms (0.3% of total)
ival-pi: 42.0ms (0.3% of total)
ival-expm1: 34.0ms (0.2% of total)
ival-asin: 31.0ms (0.2% of total)
ival-assert: 25.0ms (0.2% of total)
ival-tan: 23.0ms (0.1% of total)
ival-fabs: 9.0ms (0.1% of total)
ival-cosh: 9.0ms (0.1% of total)
ival-sinh: 3.0ms (0% of total)
ival-copysign: 2.0ms (0% of total)
ival-tanh: 1.0ms (0% of total)

regimes16.1s (1.1%)

Memory
6 000.0MiB live, 7 530.3MiB allocated
Counts
12 021 → 684
Calls

121 calls:

1.5s
b
1.4s
a
658.0ms
(/.f64 angle #s(literal 180 binary64))
652.0ms
angle
480.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (-.f64 (pow.f64 B #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 4 binary64) A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))))) (-.f64 (pow.f64 B #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 4 binary64) A) C)))
Compiler

Compiled 9 623 to 9 172 computations (4.7% saved)

explain13.1s (0.9%)

Memory
5 082.1MiB live, 6 373.9MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
+.f64#fcancellation177829
cos.f64#fsensitivity9731
sqrt.f64#foflow-rescue9680
-.f64#fcancellation9050
sin.f64#fsensitivity6040
log.f64#fsensitivity5312
/.f64#fo/n3050
-.f64#fnan-rescue2530
/.f64#fo/o2120
*.f64#fn*o1840
exp.f64#fsensitivity16424
/.f64#fu/u1330
+.f64(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) y-scale) y-scale)) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (-.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))) (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) x-scale) y-scale) #s(literal 2 binary64)))nan-rescue1000
(/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) y-scale) y-scale)overflow99
(pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))overflow70
(pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))overflow69
(pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))overflow46
(+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)))overflow102
(pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))overflow44
(/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) x-scale)overflow85
(-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) y-scale) y-scale))overflow146
(/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) x-scale) x-scale)overflow95
(pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) y-scale) y-scale)) #s(literal 2 binary64))overflow181
(/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64))) y-scale)overflow92
(+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) #s(literal 2 binary64)))overflow104
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (-.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))) (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64))))overflow91
(-.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))overflow123
(/.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (-.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))) (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) x-scale) y-scale)overflow94
(*.f64 (*.f64 #s(literal 2 binary64) (-.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))) (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64))))overflow91
(pow.f64 b #s(literal 2 binary64))overflow69
(pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (-.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))) (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) x-scale) y-scale) #s(literal 2 binary64))overflow130
(pow.f64 a #s(literal 2 binary64))overflow70
(*.f64 #s(literal 2 binary64) (-.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))overflow123
(/.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (-.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))) (sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))) x-scale)overflow81
cbrt.f64#foflow-rescue760
/.f64#fn/o710
sqrt.f64#fuflow-rescue690
log.f64(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))uflow-rescue530
(*.f64 x x)underflow68
/.f64#fu/n530
*.f64#fo*u500
cbrt.f64#fuflow-rescue420
*.f64#fn*u420
*.f64#fu*o270
/.f64#fn/u240
acos.f64(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))sensitivity221
pow.f64#fsensitivity130
pow.f64#fuflow-rescue80
+.f64#foflow-left30
log.f64(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))oflow-rescue20
(+.f64 (exp.f64 a) (exp.f64 b))overflow2
(exp.f64 b)overflow2
Confusion
Predicted +Predicted -
+476860
-5605108
Precision
0.8948948948948949
Recall
0.9875724937862469
Confusion?
Predicted +Predicted MaybePredicted -
+47683327
-560265082
Precision?
0.8912196027473548
Recall?
0.9944076222038111
Freqs
test
numberfreq
05168
13926
2895
3264
4125
575
628
77
87
91
Total Confusion?
Predicted +Predicted MaybePredicted -
+3300
-107
Precision?
0.9705882352941176
Recall?
1.0
Samples
1.5s14 285×0valid
1.3s5 219×1valid
568.0ms1 377×2valid
53.0ms114×3valid
2.0ms4valid
Compiler

Compiled 24 724 to 6 789 computations (72.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.5s
ival-mult: 444.0ms (17.9% of total)
ival-div: 262.0ms (10.6% of total)
ival-exp: 221.0ms (8.9% of total)
adjust: 176.0ms (7.1% of total)
ival-add: 164.0ms (6.6% of total)
ival-sub: 159.0ms (6.4% of total)
ival-log: 157.0ms (6.3% of total)
ival-pow2: 150.0ms (6.1% of total)
ival-cos: 131.0ms (5.3% of total)
ival-sinu: 117.0ms (4.7% of total)
ival-cosu: 101.0ms (4.1% of total)
ival-sqrt: 97.0ms (3.9% of total)
ival-sin: 61.0ms (2.5% of total)
ival-neg: 52.0ms (2.1% of total)
ival-hypot: 32.0ms (1.3% of total)
ival-acos: 28.0ms (1.1% of total)
ival-pow: 23.0ms (0.9% of total)
ival-true: 22.0ms (0.9% of total)
ival-cbrt: 19.0ms (0.8% of total)
exact: 18.0ms (0.7% of total)
ival-assert: 12.0ms (0.5% of total)
ival-pi: 12.0ms (0.5% of total)
ival-tan: 11.0ms (0.4% of total)
ival-atan: 4.0ms (0.2% of total)
ival-fabs: 2.0ms (0.1% of total)

series11.4s (0.8%)

Memory
4 637.0MiB live, 5 541.7MiB allocated
Counts
2 680 → 17 410
Calls

1170 calls:

TimeVariablePointExpression
155.0ms
s
@inf
((pow (/ 1 (+ (exp (neg s)) 1)) c_p) (* (/ (pow (/ 1 (+ (exp (neg s)) 1)) c_p) (* (pow 1/2 c_p) (pow 1/2 c_n))) (pow (- 1 (/ 1 (+ (exp (neg s)) 1))) c_n)) (- 1 (/ 1 (+ (exp (neg s)) 1))) (/ (* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (/ (pow (- 1 (/ 1 (+ (exp (neg s)) 1))) c_n) (pow (- 1 (/ 1 (+ (exp (neg t)) 1))) c_n)) (- 1 (/ 1 (+ (exp (neg t)) 1))) (/ (* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (/ (pow (/ 1 (+ (exp (neg s)) 1)) c_p) (pow (/ 1 (+ (exp (neg t)) 1)) c_p)) (/ (* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (+ (exp (neg s)) 1) (- (neg (log (+ 1 (exp (neg s))))) (neg (log (+ 1 (exp (neg t)))))) (+ (* c_p (- (neg (log (+ 1 (exp (neg s))))) (neg (log (+ 1 (exp (neg t))))))) (* c_n (- (log (+ 1 (pow (- -1 (exp (neg s))) -1))) (log (+ 1 (pow (- -1 (exp (neg t))) -1)))))) (neg (log (+ 1 (exp (neg s))))) (log (+ 1 (exp (neg s)))) (/ (pow (/ 1 (+ (exp (neg s)) 1)) c_p) (* (pow 1/2 c_p) (pow 1/2 c_n))) (/ 1 (+ (exp (neg s)) 1)) (pow (/ 1 (+ (exp (neg t)) 1)) c_p) (- (log (+ 1 (pow (- -1 (exp (neg s))) -1))) (log (+ 1 (pow (- -1 (exp (neg t))) -1)))) (log (+ 1 (exp (neg t)))))
90.0ms
s
@inf
((* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (/ 1 (+ 1 (exp (neg s)))) (+ 1 (exp (neg s))) (/ (* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (- 1 (/ 1 (+ 1 (exp (neg t))))))
74.0ms
y-scale
@0
((/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (+ (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* 1/4 (* (sqrt 8) y-scale)) (sqrt (* 2 (+ (* (* a a) (pow (sin (* (* (PI) angle) 1/180)) 2)) (* (* b b) (pow (cos (* (* (PI) angle) 1/180)) 2)))))) (* 1/4 (* (sqrt 8) y-scale)) (* (sqrt 8) y-scale) (/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (+ (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* 1/4 b) (* (* y-scale (sqrt 2)) (sqrt 8))) (* 1/4 b) (* (* y-scale (sqrt 2)) (sqrt 8)) (/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (+ (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* 1/4 (* (* (* (sqrt 8) y-scale) x-scale) a)) (sqrt (+ (sqrt (+ (* (* (pow (cos (* (* (PI) angle) 1/180)) 2) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* (* y-scale x-scale) (* y-scale x-scale)))) 4) (pow (- (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* x-scale x-scale)) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) (* y-scale y-scale))) 2))) (+ (/ (pow (cos (* (* (PI) angle) 1/180)) 2) (* y-scale y-scale)) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* x-scale x-scale)))))) (* 1/4 (* (* (* (sqrt 8) y-scale) x-scale) a)) (* (* (* (sqrt 8) y-scale) x-scale) a) (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale) (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (+ (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (/ 1 (* 2 (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale))))) (/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (+ (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (+ (* (/ (* (* (* (sqrt 8) y-scale) (+ (* (/ (+ (* (/ 4 y-scale) (/ (* (* (pow (* (+ b a) (- b a)) 2) (pow (sin (* (* (PI) angle) 1/180)) 2)) (pow (cos (* (* (PI) angle) 1/180)) 2)) y-scale)) (* (* -2 (+ (* (* a a) (pow (sin (* (* (PI) angle) 1/180)) 2)) (* (* b b) (pow (cos (* (* (PI) angle) 1/180)) 2)))) (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale))))) (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale)))) 1/2) (+ (* (* a a) (pow (sin (* (* (PI) angle) 1/180)) 2)) (* (* b b) (pow (cos (* (* (PI) angle) 1/180)) 2))))) (sqrt (/ 1 (* 2 (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale))))))) (* x-scale x-scale)) 1/8) (* (* 1/4 (* (sqrt 8) y-scale)) (sqrt (* 2 (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale))))))) x-scale) (/ (* (* (* (sqrt 8) y-scale) (+ (* (/ (+ (* (/ 4 y-scale) (/ (* (* (pow (* (+ b a) (- b a)) 2) (pow (sin (* (* (PI) angle) 1/180)) 2)) (pow (cos (* (* (PI) angle) 1/180)) 2)) y-scale)) (* (* -2 (+ (* (* a a) (pow (sin (* (* (PI) angle) 1/180)) 2)) (* (* b b) (pow (cos (* (* (PI) angle) 1/180)) 2)))) (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale))))) (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale)))) 1/2) (+ (* (* a a) (pow (sin (* (* (PI) angle) 1/180)) 2)) (* (* b b) (pow (cos (* (* (PI) angle) 1/180)) 2))))) (sqrt (/ 1 (* 2 (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale))))))) (* x-scale x-scale)) (sqrt (* 2 (+ (* (* a a) (pow (sin (* (* (PI) angle) 1/180)) 2)) (* (* b b) (pow (cos (* (* (PI) angle) 1/180)) 2))))) (cos (* (* (PI) angle) 1/180)) (sin (* (* (PI) angle) 1/180)) (* y-scale (sqrt 2)) (sqrt 2) (sqrt (+ (sqrt (+ (* (* (pow (cos (* (* (PI) angle) 1/180)) 2) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* (* y-scale x-scale) (* y-scale x-scale)))) 4) (pow (- (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* x-scale x-scale)) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) (* y-scale y-scale))) 2))) (+ (/ (pow (cos (* (* (PI) angle) 1/180)) 2) (* y-scale y-scale)) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* x-scale x-scale))))) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))) (cos (* (/ angle 180) (PI))) (/ (+ (* (/ 4 y-scale) (/ (* (* (pow (* (+ b a) (- b a)) 2) (pow (sin (* (* (PI) angle) 1/180)) 2)) (pow (cos (* (* (PI) angle) 1/180)) 2)) y-scale)) (* (* -2 (+ (* (* a a) (pow (sin (* (* (PI) angle) 1/180)) 2)) (* (* b b) (pow (cos (* (* (PI) angle) 1/180)) 2)))) (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale))))) (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale)))) (+ (* (/ 4 y-scale) (/ (* (* (pow (* (+ b a) (- b a)) 2) (pow (sin (* (* (PI) angle) 1/180)) 2)) (pow (cos (* (* (PI) angle) 1/180)) 2)) y-scale)) (* (* -2 (+ (* (* a a) (pow (sin (* (* (PI) angle) 1/180)) 2)) (* (* b b) (pow (cos (* (* (PI) angle) 1/180)) 2)))) (+ (* (/ (* a a) y-scale) (/ (pow (cos (* (* (PI) angle) 1/180)) 2) y-scale)) (* (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale) (/ (* b b) y-scale))))))
73.0ms
F
@0
((/ (neg (sqrt (* (* 2 (* (- (pow B 2) (* (* 4 A) C)) F)) (+ (+ A C) (sqrt (+ (pow (- A C) 2) (pow B 2))))))) (- (pow B 2) (* (* 4 A) C))) (* (/ (sqrt (* (+ (sqrt (+ (* C C) (* B B))) C) 2)) (neg B)) (sqrt F)) (/ (sqrt (* (+ (sqrt (+ (* C C) (* B B))) C) 2)) (neg B)) (sqrt (* (+ (sqrt (+ (* C C) (* B B))) C) 2)) (/ (neg (sqrt (* (* 2 (* (- (pow B 2) (* (* 4 A) C)) F)) (+ (+ A C) (sqrt (+ (pow (- A C) 2) (pow B 2))))))) (- (pow B 2) (* (* 4 A) C))) (neg (sqrt (* (/ 2 B) F))) (sqrt (* (/ 2 B) F)) (* (/ 2 B) F) (* (/ (sqrt (+ (+ (sqrt (+ (* (- A C) (- A C)) (* B B))) A) C)) -1) (/ (sqrt (* (* 2 F) (+ (* -4 (* C A)) (* B B)))) (+ (* -4 (* C A)) (* B B)))) (/ (sqrt (+ (+ (sqrt (+ (* (- A C) (- A C)) (* B B))) A) C)) -1) (neg (* (sqrt C) (sqrt 2))) (* (sqrt C) (sqrt 2)) (/ (sqrt (* (* (+ (sqrt (+ (* (- A C) (- A C)) (* B B))) (+ C A)) (+ (* (* C A) -4) (* B B))) (* F 2))) (neg (+ (* (* C A) -4) (* B B)))) (sqrt (* (* (+ (sqrt (+ (* (- A C) (- A C)) (* B B))) (+ C A)) (+ (* (* C A) -4) (* B B))) (* F 2))) (* (* (+ (sqrt (+ (* (- A C) (- A C)) (* B B))) (+ C A)) (+ (* (* C A) -4) (* B B))) (* F 2)) (* (+ (sqrt (+ (* (- A C) (- A C)) (* B B))) (+ C A)) (+ (* (* C A) -4) (* B B))) (exp (log (* (/ F B) F))) (/ (neg (sqrt (* (* 2 (* (- (pow B 2) (* (* 4 A) C)) F)) (+ (+ A C) (sqrt (+ (pow (- A C) 2) (pow B 2))))))) (- (pow B 2) (* (* 4 A) C))) (* (neg (sqrt 2)) (pow (/ (exp (log (* (/ F B) F))) B) 1/4)) (neg (sqrt 2)) (+ (sqrt (+ (* C C) (* B B))) C) (sqrt (* (* 2 F) (+ (* -4 (* C A)) (* B B)))) (/ (sqrt (* (* 2 F) (+ (* -4 (* C A)) (* B B)))) (+ (* -4 (* C A)) (* B B))) (* (* 2 F) (+ (* -4 (* C A)) (* B B))) (+ (sqrt (+ (* (- A C) (- A C)) (* B B))) (+ C A)) (pow (/ (exp (log (* (/ F B) F))) B) 1/4) (log (* (/ F B) F)) (/ (exp (log (* (/ F B) F))) B))
73.0ms
angle
@inf
((* (* (* (sqrt (PI)) 1/180) angle) (sqrt (PI))) (* (sqrt (PI)) (sqrt (PI))) (+ (pow (* a (cos (* (* (* (sqrt (PI)) 1/180) angle) (sqrt (PI))))) 2) (pow (* b (sin (* (* (sqrt (PI)) (sqrt (PI))) (/ angle 180)))) 2)) (pow (* a (cos (* (* (* (sqrt (PI)) 1/180) angle) (sqrt (PI))))) 2) (+ (pow (* a (cos (* (* (* (sqrt (PI)) 1/180) angle) (sqrt (PI))))) 2) (pow (* b (sin (* (PI) (/ angle 180)))) 2)) (+ (* (* (* (PI) (PI)) (+ (* 1/32400 (* b b)) (* -1/32400 (* a a)))) (* angle angle)) (* a a)) (* (* (* angle angle) 1/32400) (* (* (* (PI) (PI)) b) b)) (* (* angle angle) 1/32400) (+ (* (* (* (cos (* -1/180 (* angle (PI)))) a) (cos (* -1/180 (* angle (PI))))) a) (pow (* (sin (* (* 1/180 (PI)) angle)) b) 2)) (* (* (cos (* -1/180 (* angle (PI)))) a) (cos (* -1/180 (* angle (PI))))) (* (cos (* -1/180 (* angle (PI)))) a) (cos (* -1/180 (* angle (PI)))) (exp (log (pow (* (cos (* -1/180 (* angle (PI)))) a) 2))) (+ (exp (log (pow (* (cos (* -1/180 (* angle (PI)))) a) 2))) (pow (* b (sin (* (PI) (/ angle 180)))) 2)) (log (pow (* (cos (* -1/180 (* angle (PI)))) a) 2)) (pow (* (cos (* -1/180 (* angle (PI)))) a) 2) (exp (+ (* (log (PI)) 1/2) (log angle))) (* (/ (sqrt (PI)) 180) (exp (+ (* (log (PI)) 1/2) (log angle)))) (+ (pow (* a (cos (* (/ (sqrt (PI)) 180) (exp (+ (* (log (PI)) 1/2) (log angle)))))) 2) (pow (* b (sin (* (PI) (/ angle 180)))) 2)) (pow (* a (cos (* (/ (sqrt (PI)) 180) (exp (+ (* (log (PI)) 1/2) (log angle)))))) 2) (sin (* (* (sqrt (PI)) (sqrt (PI))) (/ angle 180))) (cos (* (* (* (sqrt (PI)) 1/180) angle) (sqrt (PI)))) (sqrt (PI)) (sin (* (* 1/180 (PI)) angle)) (* -1/180 (* angle (PI))) (* angle (PI)) (sin (* (PI) (/ angle 180))) (cos (* (/ (sqrt (PI)) 180) (exp (+ (* (log (PI)) 1/2) (log angle))))))

preprocess8.4s (0.6%)

Memory
2 114.8MiB live, 2 699.1MiB allocated
Algorithm
41×egg-herbie
Stop Event
82×iter limit
51×saturated
31×node limit
Compiler

Compiled 104 412 to 21 488 computations (79.4% saved)

bsearch2.9s (0.2%)

Memory
756.6MiB live, 835.0MiB allocated
Algorithm
167×left-value
147×binary-search
Stop Event
141×narrow-enough
predicate-same
Samples
1.0s2 264×1valid
779.0ms6 853×0valid
125.0ms210×2valid
43.0ms502×0invalid
3.0ms48×0exit
1.0ms1invalid
0.0ms3valid
Compiler

Compiled 97 910 to 59 428 computations (39.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-mult: 299.0ms (18.7% of total)
ival-cos: 295.0ms (18.5% of total)
ival-sin: 169.0ms (10.6% of total)
ival-pow2: 117.0ms (7.3% of total)
ival-sinu: 104.0ms (6.5% of total)
ival-div: 95.0ms (5.9% of total)
adjust: 87.0ms (5.4% of total)
ival-cosu: 84.0ms (5.3% of total)
ival-add: 77.0ms (4.8% of total)
ival-sub: 72.0ms (4.5% of total)
ival-acos: 70.0ms (4.4% of total)
ival-sqrt: 33.0ms (2.1% of total)
ival-hypot: 23.0ms (1.4% of total)
ival-neg: 20.0ms (1.3% of total)
ival-exp: 17.0ms (1.1% of total)
ival-true: 11.0ms (0.7% of total)
ival-log: 7.0ms (0.4% of total)
ival-assert: 6.0ms (0.4% of total)
ival-pow: 6.0ms (0.4% of total)
exact: 6.0ms (0.4% of total)

start2.0ms (0%)

Memory
2.9MiB live, 2.9MiB allocated

end0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated

Profiling

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