Herbie run

Date:Sunday, November 3rd, 2024
Commit:3e00ba3f on bhargav-double-double
Hostname:nightly with Racket 8.10
Seed:2024308
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: 4.5min)

sample2.0min (43.9%)

Memory
425.4MiB live, 101 061.1MiB allocated
Samples
29.8s41 467×2valid
25.4s144 746×0invalid
18.6s91 774×1valid
9.9s4 937×5exit
9.7s94 904×0valid
2.3s3 019×3valid
461.0ms2 180×1exit
407.0ms4 411×0exit
26.0ms10×4exit
6.0ms4×4valid
4.0ms2×3exit
2.0ms3×2exit
Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-tan: 13.7s (17.2% of total)
ival-pow: 9.3s (11.7% of total)
ival-mult: 6.5s (8.1% of total)
adjust: 5.5s (6.9% of total)
const: 5.2s (6.5% of total)
ival-cos: 4.5s (5.7% of total)
ival-div: 4.3s (5.5% of total)
ival-add: 4.1s (5.1% of total)
ival-sub: 3.8s (4.8% of total)
ival-log: 3.6s (4.6% of total)
ival-sin: 3.5s (4.4% of total)
ival-fabs: 2.5s (3.1% of total)
ival-exp: 2.4s (3.1% of total)
ival-expm1: 2.2s (2.8% of total)
ival-<=: 2.2s (2.7% of total)
ival-sqrt: 1.4s (1.8% of total)
ival-log1p: 996.0ms (1.3% of total)
ival-<: 869.0ms (1.1% of total)
ival-and: 604.0ms (0.8% of total)
ival-fmin: 490.0ms (0.6% of total)
ival-atan: 373.0ms (0.5% of total)
exact: 358.0ms (0.5% of total)
ival-cbrt: 302.0ms (0.4% of total)
ival-neg: 266.0ms (0.3% of total)
ival->: 263.0ms (0.3% of total)
ival-assert: 155.0ms (0.2% of total)
ival-true: 72.0ms (0.1% of total)
Bogosity

simplify36.0s (13.5%)

Memory
781.0MiB live, 27 604.9MiB allocated
Algorithm
246×egg-herbie
Stop Event
327×iter limit
169×node limit
77×saturated
Counts
8 557 → 8 466

soundness30.5s (11.4%)

Memory
315.1MiB live, 14 920.2MiB allocated
Stop Event
213×iter limit
141×node limit
24×fuel
4×done
2×saturated
Compiler

Compiled 14 455 to 6 729 computations (53.4% saved)

rewrite23.4s (8.8%)

Memory
32.5MiB live, 20 104.7MiB allocated
Stop Event
222×iter limit
109×node limit
Counts
1 629 → 60 028

localize21.2s (7.9%)

Memory
-778.2MiB live, 19 191.6MiB allocated
Samples
6.6s5 626×2valid
6.4s10 263×1valid
3.0s10 898×0valid
352.0ms781×0invalid
350.0ms299×3valid
45.0ms37×5exit
Compiler

Compiled 47 623 to 6 937 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.3s
ival-mult: 2.2s (16.9% of total)
adjust: 1.7s (13.2% of total)
ival-div: 1.6s (12.2% of total)
ival-add: 1.3s (9.6% of total)
ival-tan: 1.1s (8.5% of total)
ival-sub: 840.0ms (6.3% of total)
ival-pow: 724.0ms (5.4% of total)
ival-log: 717.0ms (5.4% of total)
const: 682.0ms (5.1% of total)
ival-cos: 511.0ms (3.8% of total)
ival-sin: 330.0ms (2.5% of total)
ival-exp: 317.0ms (2.4% of total)
ival-sqrt: 223.0ms (1.7% of total)
ival-log1p: 223.0ms (1.7% of total)
ival-pow2: 203.0ms (1.5% of total)
ival-cosh: 107.0ms (0.8% of total)
ival-expm1: 102.0ms (0.8% of total)
ival-neg: 99.0ms (0.7% of total)
ival-cbrt: 52.0ms (0.4% of total)
exact: 49.0ms (0.4% of total)
ival-true: 25.0ms (0.2% of total)
ival-hypot: 22.0ms (0.2% of total)
ival-atan2: 15.0ms (0.1% of total)
ival-assert: 14.0ms (0.1% of total)
ival-atan: 9.0ms (0.1% of total)
ival-fabs: 1.0ms (0% of total)

eval12.5s (4.7%)

Memory
-9.2MiB live, 14 403.1MiB allocated
Compiler

Compiled 2 391 835 to 264 864 computations (88.9% saved)

explain7.5s (2.8%)

Memory
-54.0MiB live, 7 379.2MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation536630
log.f64#fsensitivity7613
+.f64#fcancellation6750
sqrt.f64#foflow-rescue4240
/.f64#fu/n2920
/.f64#fu/u2110
pow.f64#fsensitivity310
sqrt.f64#fuflow-rescue240
/.f64(/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))n/u210
↳(*.f64 b eps)underflow150
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow141
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow150
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow225
↳(*.f64 a eps)underflow141
*.f64#fn*u130
-.f64#fnan-rescue80
/.f64(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))n/o40
↳(*.f64 x x)overflow66
sin.f64(sin.f64 (+.f64 x eps))sensitivity20
tan.f64(tan.f64 (+.f64 x eps))sensitivity20
cos.f64(cos.f64 (+.f64 x eps))sensitivity20
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o10
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow1
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow1
↳(exp.f64 x)overflow1
↳(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow1
exp.f64(exp.f64 (*.f64 a x))sensitivity10
-.f64(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n)) (pow.f64 x (/.f64 #s(literal 1 binary64) n)))oflow-left10
Confusion
Predicted +Predicted -
+522251
-7341161
Precision
0.876762928139691
Recall
0.9903280864782856
Confusion?
Predicted +Predicted MaybePredicted -
+52221338
-734191142
Precision?
0.874248496993988
Recall?
0.992793476199507
Freqs
test
numberfreq
01212
14783
2675
3287
4210
51
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.6s2 562×2valid
1.0s5 818×1valid
519.0ms5 778×0valid
85.0ms178×3valid
Compiler

Compiled 3 914 to 1 430 computations (63.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-tan: 511.0ms (19.9% of total)
ival-cos: 357.0ms (13.9% of total)
adjust: 256.0ms (10% of total)
ival-log: 224.0ms (8.7% of total)
ival-sin: 188.0ms (7.3% of total)
ival-div: 163.0ms (6.4% of total)
ival-sub: 158.0ms (6.2% of total)
ival-mult: 155.0ms (6% of total)
ival-exp: 137.0ms (5.3% of total)
ival-add: 101.0ms (3.9% of total)
ival-pow: 82.0ms (3.2% of total)
ival-log1p: 60.0ms (2.3% of total)
ival-sqrt: 58.0ms (2.3% of total)
ival-cbrt: 33.0ms (1.3% of total)
ival-expm1: 23.0ms (0.9% of total)
ival-atan: 19.0ms (0.7% of total)
ival-true: 14.0ms (0.5% of total)
ival-neg: 12.0ms (0.5% of total)
exact: 9.0ms (0.4% of total)
ival-assert: 6.0ms (0.2% of total)

prune4.7s (1.8%)

Memory
-208.0MiB live, 5 694.6MiB allocated
Counts
67 802 → 1 814
Compiler

Compiled 93 831 to 50 303 computations (46.4% saved)

series4.0s (1.5%)

Memory
276.2MiB live, 4 808.8MiB allocated
Counts
1 629 → 8 557
Calls

507 calls:

TimeVariablePointExpression
75.0ms
n
@0
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (log (/ (+ 1 x) x)) n) (log (/ (+ 1 x) x)) (/ (+ 1 x) x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (/ 1 x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (- x (log x)) (+ (* 1/6 (/ x n)) (+ (* -1/2 x) 1/2)) (/ (+ (* -1/3 x) (- 1/2 (/ (+ (* 1/6 (/ x n)) (+ (* -1/2 x) 1/2)) n))) (neg n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (exp (neg (log x))) (- (pow (+ x 1) (/ 1 n)) (pow (exp (neg (log x))) (/ -1 n))) (pow (+ x 1) (/ 1 n)) (pow (exp (neg (log x))) (/ -1 n)) (+ (* (+ (* (+ (* (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) x) (/ 1 n)) x) 1) (+ (* (+ (* (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) x) (/ 1 n)))
71.0ms
x
@inf
((+ (- (exp x) 2) (exp (neg x))) (+ (* (* 1/12 x) x) 1) (* 1/12 x) (* x x) (+ (- (exp x) 2) (exp (neg x))) (+ (* (pow x 4) (+ (* 1/360 (* x x)) 1/12)) (* x x)) (pow x 4) (+ (* 1/360 (* x x)) 1/12) (+ (* 2 (cosh x)) -2) (cosh x) (+ (* (+ (* (+ (* 1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (+ (* (+ (* 1/720 (* x x)) 1/24) (* x x)) 1/2) (+ (* 2 (cosh x)) -2) (cosh x) (+ (* (* (+ (* (+ (* 1/720 (* x x)) 1/24) (* x x)) 1/2) x) x) 1) (* (+ (* (+ (* 1/720 (* x x)) 1/24) (* x x)) 1/2) x) (* (+ (* (* 1/12 x) x) 1) (* x x)) (* (+ (* 1/720 (* x x)) 1/24) x) (+ (* 1/720 (* x x)) 1/24))
70.0ms
x
@0
((* (cbrt (/ (/ 1 x) x)) 1/3) (- (cbrt (+ x 1)) (cbrt x)) (/ (/ 1 x) x) (/ 1 x) (- (cbrt (+ x 1)) (cbrt x)) (cbrt (+ x 1)) (cbrt x) (pow (pow x 1/6) 2) (- (cbrt (+ x 1)) (pow (pow x 1/6) 2)) (cbrt (+ x 1)) (+ x 1) (- (pow (exp 1/3) (log (+ 1 x))) (cbrt x)) (pow (exp 1/3) (log (+ 1 x))) (exp 1/3) (log (+ 1 x)) (+ (* (pow (cbrt x) 2) (cbrt x)) 1) (- (cbrt (+ (* (pow (cbrt x) 2) (cbrt x)) 1)) (cbrt x)) (cbrt (+ (* (pow (cbrt x) 2) (cbrt x)) 1)) (pow (cbrt x) 2) (cbrt (/ (/ 1 x) x)) (pow x 1/6))
67.0ms
x
@-inf
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (log (/ (+ 1 x) x)) n) (log (/ (+ 1 x) x)) (/ (+ 1 x) x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (/ 1 x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (- x (log x)) (+ (* 1/6 (/ x n)) (+ (* -1/2 x) 1/2)) (/ (+ (* -1/3 x) (- 1/2 (/ (+ (* 1/6 (/ x n)) (+ (* -1/2 x) 1/2)) n))) (neg n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (exp (neg (log x))) (- (pow (+ x 1) (/ 1 n)) (pow (exp (neg (log x))) (/ -1 n))) (pow (+ x 1) (/ 1 n)) (pow (exp (neg (log x))) (/ -1 n)) (+ (* (+ (* (+ (* (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) x) (/ 1 n)) x) 1) (+ (* (+ (* (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) x) (/ 1 n)))
56.0ms
a
@0
((+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (neg b_2) (sqrt (- (* b_2 b_2) (* a c))) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (* (/ c b_2) -1/2) (/ c b_2) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* (* (/ a b_2) -1/2) c) (* (/ a b_2) -1/2) (+ (* (/ -1/8 b_2) (/ (* (* c c) a) b_2)) (* -1/2 c)) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (/ (+ (* (/ -1/8 b_2) (/ (* (* c c) a) b_2)) (* -1/2 c)) b_2) (/ -1/8 b_2) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4)) (+ (neg b_2) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4))) (/ (+ (neg b_2) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4))) a) (- (* b_2 b_2) (* a c)) (/ (* (* c c) a) b_2) (* (* c c) a) (log (pow (+ (* c a) (* b_2 b_2)) 2)))

preprocess3.9s (1.5%)

Memory
61.2MiB live, 3 795.8MiB allocated
Algorithm
28×egg-herbie
Stop Event
56×iter limit
50×saturated
6×node limit
Compiler

Compiled 17 790 to 5 239 computations (70.6% saved)

regimes3.5s (1.3%)

Memory
-72.0MiB live, 4 031.2MiB allocated
Counts
3 248 → 313
Calls

43 calls:

741.0ms
x
278.0ms
eps
217.0ms
n
194.0ms
b
166.0ms
(/.f64 #s(literal 1 binary64) n)
Compiler

Compiled 2 256 to 2 089 computations (7.4% saved)

analyze1.7s (0.7%)

Memory
-59.0MiB live, 1 878.8MiB allocated
Algorithm
28×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%61.1%38.9%0%0%0%0
7.4%4.5%56.6%38.9%0%0%0%1
22.3%13.6%47.5%38.9%0%0%0%2
40.2%23.5%34.9%38.9%0%2.7%0%3
53.4%31.1%27.2%38.9%0%2.8%0%4
63%36.3%21.3%38.9%0%3.6%0%5
65.9%37.5%19.4%38.9%0%4.2%0%6
70.4%38.8%16.3%38.9%0%6%0%7
73.6%40.2%14.4%38.9%0%6.5%0%8
76.3%40.9%12.7%38.9%0%7.5%0%9
78.4%41.4%11.4%38.9%0%8.3%0%10
81.1%42.4%9.9%38.9%0%8.8%0%11
82.3%42.7%9.2%38.9%0%9.3%0%12
Compiler

Compiled 483 to 337 computations (30.2% saved)

bsearch949.0ms (0.4%)

Memory
57.2MiB live, 854.8MiB allocated
Algorithm
64×binary-search
37×left-value
Stop Event
64×narrow-enough
Samples
310.0ms3 536×0valid
86.0ms258×2valid
66.0ms525×0invalid
57.0ms411×1valid
3.0ms36×0exit
1.0ms3×3valid
0.0ms2×1exit
Compiler

Compiled 20 140 to 15 770 computations (21.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 376.0ms
ival-sub: 86.0ms (22.9% of total)
ival-mult: 68.0ms (18.1% of total)
ival-pow: 52.0ms (13.8% of total)
ival-div: 37.0ms (9.8% of total)
ival-sqrt: 25.0ms (6.7% of total)
ival-cos: 22.0ms (5.9% of total)
ival-neg: 22.0ms (5.9% of total)
adjust: 17.0ms (4.5% of total)
ival-add: 14.0ms (3.7% of total)
ival-sin: 11.0ms (2.9% of total)
ival-cbrt: 7.0ms (1.9% of total)
ival-expm1: 4.0ms (1.1% of total)
ival-true: 4.0ms (1.1% of total)
exact: 3.0ms (0.8% of total)
ival-exp: 2.0ms (0.5% of total)
ival-assert: 2.0ms (0.5% of total)

start1.0ms (0%)

Memory
1.6MiB live, 1.7MiB allocated

end0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated

Profiling

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