Herbie run

Date:Friday, November 22nd, 2024
Commit:a938fc34 on zane-issue-1058
Hostname:nightly with Racket 8.10
Seed:2024327
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: 4.3min)

sample2.0min (45.4%)

Memory
-195.0MiB live, 103 217.5MiB allocated
Samples
28.0s41 168×2valid
25.2s145 546×0invalid
21.3s92 399×1valid
9.6s5 007×5exit
8.3s94 656×0valid
2.0s2 943×3valid
593.0ms2 372×1exit
357.0ms4 207×0exit
27.0ms2×4valid
13.0ms7×4exit
9.0ms4×2exit
0.0ms1×3exit
Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-tan: 12.8s (16.4% of total)
ival-pow: 9.4s (12% of total)
ival-mult: 6.5s (8.3% of total)
adjust: 6.0s (7.7% of total)
const: 5.8s (7.4% of total)
ival-cos: 4.4s (5.6% of total)
ival-div: 4.1s (5.2% of total)
ival-sub: 3.7s (4.7% of total)
ival-sin: 3.4s (4.4% of total)
ival-add: 3.4s (4.3% of total)
ival-log: 3.3s (4.2% of total)
ival-fabs: 2.4s (3% of total)
ival-exp: 2.3s (3% of total)
ival-<=: 2.3s (2.9% of total)
ival-expm1: 1.9s (2.4% of total)
ival-<: 1.3s (1.6% of total)
ival-log1p: 1.2s (1.5% of total)
ival-sqrt: 1.1s (1.4% of total)
ival-and: 656.0ms (0.8% of total)
ival-fmin: 608.0ms (0.8% of total)
ival-atan: 436.0ms (0.6% of total)
exact: 354.0ms (0.5% of total)
ival-cbrt: 350.0ms (0.4% of total)
ival-neg: 320.0ms (0.4% of total)
ival->: 227.0ms (0.3% of total)
ival-assert: 153.0ms (0.2% of total)
ival-true: 73.0ms (0.1% of total)
Bogosity

simplify35.4s (13.7%)

Memory
-54.9MiB live, 26 805.3MiB allocated
Algorithm
246×egg-herbie
Stop Event
327×iter limit
190×node limit
56×saturated
Counts
8 597 → 8 506

soundness26.2s (10.1%)

Memory
323.1MiB live, 13 653.2MiB allocated
Stop Event
192×iter limit
124×node limit
23×fuel
5×done
2×saturated
Compiler

Compiled 14 031 to 6 397 computations (54.4% saved)

rewrite23.0s (8.9%)

Memory
22.6MiB live, 19 612.1MiB allocated
Stop Event
223×iter limit
109×node limit
Counts
1 583 → 65 169

localize19.8s (7.6%)

Memory
347.0MiB live, 19 363.8MiB allocated
Samples
6.6s5 383×2valid
5.9s10 597×1valid
2.8s10 772×0valid
562.0ms347×3valid
223.0ms708×0invalid
83.0ms12×5exit
37.0ms82×0exit
3.0ms3×4valid
Compiler

Compiled 21 157 to 3 205 computations (84.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.8s
ival-mult: 2.0s (15.3% of total)
ival-div: 1.6s (12.3% of total)
adjust: 1.6s (12.3% of total)
ival-tan: 1.5s (11.5% of total)
ival-add: 968.0ms (7.6% of total)
ival-sub: 703.0ms (5.5% of total)
ival-pow: 607.0ms (4.7% of total)
ival-cos: 557.0ms (4.4% of total)
ival-cosh: 556.0ms (4.3% of total)
const: 546.0ms (4.3% of total)
ival-log: 429.0ms (3.4% of total)
ival-sin: 420.0ms (3.3% of total)
ival-exp: 290.0ms (2.3% of total)
ival-pow2: 283.0ms (2.2% of total)
ival-sqrt: 253.0ms (2% of total)
ival-log1p: 186.0ms (1.5% of total)
ival-neg: 128.0ms (1% of total)
ival-expm1: 99.0ms (0.8% of total)
ival-cbrt: 69.0ms (0.5% of total)
exact: 47.0ms (0.4% of total)
ival-true: 23.0ms (0.2% of total)
ival-atan2: 19.0ms (0.1% of total)
ival-atan: 18.0ms (0.1% of total)
ival-assert: 12.0ms (0.1% of total)

eval12.6s (4.9%)

Memory
169.4MiB live, 14 688.8MiB allocated
Compiler

Compiled 2 540 781 to 273 664 computations (89.2% saved)

explain6.4s (2.5%)

Memory
96.8MiB live, 5 541.7MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation415624
log.f64#fsensitivity7661
/.f64#fu/u4380
sqrt.f64#foflow-rescue3740
+.f64#fcancellation3422
/.f64#fu/n1060
pow.f64(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))sensitivity800
sqrt.f64#fuflow-rescue320
/.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/u250
↳(*.f64 b eps)underflow154
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow139
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow154
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow235
↳(*.f64 a eps)underflow139
-.f64#fnan-rescue180
cos.f64(cos.f64 (+.f64 x eps))sensitivity30
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o30
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow3
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow3
↳(exp.f64 x)overflow3
↳(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow3
tan.f64(tan.f64 (+.f64 x eps))sensitivity30
sin.f64(sin.f64 (+.f64 x eps))sensitivity21
*.f64#fn*u20
exp.f64(exp.f64 (neg.f64 x))sensitivity10
Confusion
Predicted +Predicted -
+519116
-1561805
Precision
0.9708247615485319
Recall
0.9969272133666218
Confusion?
Predicted +Predicted MaybePredicted -
+519188
-156181787
Precision?
0.9676158570630933
Recall?
0.9984636066833109
Freqs
test
numberfreq
01821
14549
2647
396
455
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.8s2 536×2valid
1.2s5 916×1valid
538.0ms5 732×0valid
105.0ms150×3valid
2.0ms2×4valid
Compiler

Compiled 2 154 to 763 computations (64.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.9s
ival-tan: 776.0ms (27% of total)
adjust: 275.0ms (9.6% of total)
ival-div: 221.0ms (7.7% of total)
ival-log: 208.0ms (7.2% of total)
ival-cos: 206.0ms (7.2% of total)
ival-exp: 188.0ms (6.5% of total)
ival-sub: 165.0ms (5.7% of total)
ival-add: 163.0ms (5.7% of total)
ival-pow: 158.0ms (5.5% of total)
ival-sin: 152.0ms (5.3% of total)
ival-mult: 133.0ms (4.6% of total)
ival-sqrt: 71.0ms (2.5% of total)
ival-log1p: 58.0ms (2% of total)
ival-expm1: 27.0ms (0.9% of total)
ival-atan: 18.0ms (0.6% of total)
ival-cbrt: 15.0ms (0.5% of total)
ival-true: 13.0ms (0.5% of total)
ival-neg: 12.0ms (0.4% of total)
exact: 8.0ms (0.3% of total)
ival-assert: 6.0ms (0.2% of total)

preprocess4.0s (1.6%)

Memory
-55.6MiB live, 3 483.4MiB allocated
Algorithm
28×egg-herbie
Stop Event
56×iter limit
50×saturated
6×node limit
Compiler

Compiled 17 614 to 4 951 computations (71.9% saved)

prune3.8s (1.5%)

Memory
-421.9MiB live, 6 100.4MiB allocated
Counts
71 087 → 1 986
Compiler

Compiled 110 055 to 56 938 computations (48.3% saved)

regimes3.8s (1.5%)

Memory
90.9MiB live, 4 279.6MiB allocated
Counts
3 955 → 306
Calls

43 calls:

927.0ms
x
296.0ms
eps
196.0ms
b
183.0ms
(/.f64 #s(literal 1 binary64) n)
148.0ms
a
Compiler

Compiled 2 083 to 1 958 computations (6% saved)

series3.4s (1.3%)

Memory
-2.9MiB live, 3 727.6MiB allocated
Counts
1 583 → 8 597
Calls

507 calls:

TimeVariablePointExpression
158.0ms
n
@0
((- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (+ (/ 1/2 n) (log n)) (/ 1/2 n) (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log n))
78.0ms
b_2
@-inf
((/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* -2 b_2) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (* -1/2 (/ c b_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)))) (neg b_2) (sqrt (- (* b_2 b_2) (* a c))) (/ (- (* a b_2) (* (sqrt (neg (+ (* c a) (* b_2 b_2)))) a)) (* a a)) (- (* a b_2) (* (sqrt (neg (+ (* c a) (* b_2 b_2)))) a)) (* a b_2) (* (sqrt (neg (+ (* c a) (* b_2 b_2)))) a) (/ 1 (/ a (+ (* b_2 b_2) (+ (* c a) (* b_2 b_2))))) (+ (* b_2 b_2) (+ (* c a) (* b_2 b_2))) (/ (/ 1 (/ a (+ (* b_2 b_2) (+ (* c a) (* b_2 b_2))))) (- (sqrt (neg (+ (* c a) (* b_2 b_2)))) b_2)) (/ a (+ (* b_2 b_2) (+ (* c a) (* b_2 b_2)))) (- (* b_2 b_2) (* a c)) (neg a) (sqrt (neg (+ (* c a) (* b_2 b_2)))) (+ (* c a) (* b_2 b_2)))
56.0ms
x
@-inf
((- (cbrt (+ x 1)) (cbrt x)) (* (/ (cbrt (/ -1 x)) (cbrt (neg x))) 1/3) (/ (cbrt (/ -1 x)) (cbrt (neg x))) (cbrt (/ -1 x)) (pow x 1/3) (- (cbrt (+ x 1)) (pow x 1/3)) (cbrt (+ x 1)) (- (cbrt (+ x 1)) (cbrt x)) (* (cbrt (pow (sqrt x) -4)) 1/3) (cbrt (pow (sqrt x) -4)) (pow (sqrt x) -4) (pow (pow x 1/6) 2) (- (cbrt (+ x 1)) (pow (pow x 1/6) 2)) (cbrt (+ x 1)) (+ x 1) (+ (* -1/9 (cbrt x)) (* (* (cbrt x) x) 1/3)) (/ 1 (/ (* x x) (+ (* 5/81 (pow (cbrt x) -2)) (+ (* -1/9 (cbrt x)) (* (* (cbrt x) x) 1/3))))) (- (cbrt (+ x 1)) (cbrt x)) (/ (* x x) (+ (* 5/81 (pow (cbrt x) -2)) (+ (* -1/9 (cbrt x)) (* (* (cbrt x) x) 1/3)))) (cbrt (neg x)) (pow x 1/6) (pow (cbrt x) -2) (cbrt x) (* (* (cbrt x) x) 1/3))
53.0ms
n
@-inf
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (pow x (+ (* 2 (/ 1/2 n)) -1)) n) (pow x (+ (* 2 (/ 1/2 n)) -1)) (+ (* 2 (/ 1/2 n)) -1) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (pow x (pow n -1)) (* n x)) (pow x (pow n -1)) (* n x) (/ (+ (* -1/2 (/ x n)) (/ 1/3 n)) x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (/ (+ (/ (- (/ (/ 1/3 n) x) (/ 1/2 n)) x) (/ 1 n)) 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 (/ n (- (log (+ 1 x)) (log x)))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ n (- (log (+ 1 x)) (log x))) (- (log (+ 1 x)) (log x)) (+ (/ (- (/ (/ 1/3 n) x) (/ 1/2 n)) x) (/ 1 n)) (log x))
45.0ms
n
@0
((- (exp (/ (log (+ 1 x)) n)) (pow x (/ 1 n))) (exp (/ (log (+ 1 x)) n)) (/ (log (+ 1 x)) n) (log (+ 1 x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)) (/ 1 n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (/ (pow x (/ 1 n)) x) n) (/ (pow x (/ 1 n)) x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (+ (* (/ (pow x (/ 1 n)) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (/ (pow x (/ 1 n)) n)) (- (/ 1/2 (* n n)) (/ 1/2 n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (+ (* (/ (pow x (/ 1 n)) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (/ (pow x (/ 1 n)) n)) x) (log x) (/ 1/2 (* n n)))

analyze1.9s (0.8%)

Memory
53.4MiB live, 1 948.0MiB 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)

bsearch1.2s (0.5%)

Memory
-61.1MiB live, 1 174.3MiB allocated
Algorithm
69×binary-search
32×left-value
Stop Event
62×narrow-enough
7×predicate-same
Samples
320.0ms3 296×0valid
185.0ms458×2valid
185.0ms847×1valid
51.0ms657×0invalid
13.0ms142×0exit
2.0ms7×3valid
Compiler

Compiled 24 345 to 18 825 computations (22.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 543.0ms
ival-pow: 149.0ms (27.4% of total)
ival-mult: 85.0ms (15.7% of total)
ival-div: 83.0ms (15.3% of total)
ival-add: 46.0ms (8.5% of total)
ival-sub: 44.0ms (8.1% of total)
adjust: 38.0ms (7% of total)
ival-sqrt: 32.0ms (5.9% of total)
ival-neg: 19.0ms (3.5% of total)
ival-cos: 18.0ms (3.3% of total)
ival-sin: 9.0ms (1.7% of total)
ival-cbrt: 7.0ms (1.3% of total)
ival-true: 4.0ms (0.7% of total)
exact: 3.0ms (0.6% of total)
ival-assert: 2.0ms (0.4% of total)
ival-expm1: 2.0ms (0.4% of total)
ival-log1p: 1.0ms (0.2% of total)
ival-log: 1.0ms (0.2% of total)

start4.0ms (0%)

Memory
-31.0MiB live, 1.5MiB allocated

end0.0ms (0%)

Memory
0.3MiB live, 0.2MiB allocated

Profiling

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