Herbie run

Date:Thursday, November 21st, 2024
Commit:d1b0bfd6 on main
Hostname:nightly with Racket 8.10
Seed:2024326
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: 4.6min)

sample1.1min (23.9%)

Memory
330.4MiB live, 66 927.3MiB allocated
Samples
28.7s285 570×0valid
12.1s44 015×1valid
7.1s16 745×2valid
436.0ms4 233×0invalid
175.0ms422×3valid
151.0ms972×0exit
64.0ms101×3exit
60.0ms101×4exit
5.0ms32×1exit
Precisions
Click to see histograms. Total time spent on operations: 36.5s
ival-mult: 7.8s (21.3% of total)
ival-add: 4.2s (11.4% of total)
ival-div: 3.6s (9.8% of total)
ival-pow: 3.3s (9% of total)
const: 3.3s (9% of total)
ival-sub: 3.3s (9% of total)
adjust: 2.4s (6.5% of total)
ival-sin: 2.1s (5.8% of total)
ival-<=: 1.9s (5.3% of total)
ival-cos: 1.4s (3.7% of total)
ival-exp: 606.0ms (1.7% of total)
ival-sqrt: 449.0ms (1.2% of total)
exact: 422.0ms (1.2% of total)
ival-neg: 387.0ms (1.1% of total)
ival-and: 353.0ms (1% of total)
ival-pow2: 278.0ms (0.8% of total)
ival-==: 190.0ms (0.5% of total)
ival-assert: 138.0ms (0.4% of total)
ival-true: 137.0ms (0.4% of total)
ival-expm1: 89.0ms (0.2% of total)
ival-log1p: 88.0ms (0.2% of total)
ival-atan: 88.0ms (0.2% of total)
ival-tan: 62.0ms (0.2% of total)
ival-<: 59.0ms (0.2% of total)
ival-pi: 32.0ms (0.1% of total)
ival-hypot: 17.0ms (0% of total)
ival-if: 4.0ms (0% of total)
ival-fabs: 4.0ms (0% of total)
Bogosity

simplify50.5s (18.2%)

Memory
203.9MiB live, 44 181.7MiB allocated
Algorithm
350×egg-herbie
Stop Event
450×iter limit
269×node limit
93×saturated
Counts
10 333 → 10 203

soundness40.4s (14.6%)

Memory
-32.9MiB live, 22 640.3MiB allocated
Stop Event
272×iter limit
181×node limit
28×fuel
14×done
6×saturated
Compiler

Compiled 42 462 to 12 455 computations (70.7% saved)

rewrite35.7s (12.9%)

Memory
-91.2MiB live, 32 509.5MiB allocated
Stop Event
307×iter limit
150×node limit
11×saturated
Counts
2 029 → 71 840

localize22.2s (8%)

Memory
-211.7MiB live, 21 632.9MiB allocated
Samples
7.8s30 159×0valid
3.9s3 198×2valid
3.7s5 458×1valid
742.0ms120×3valid
195.0ms139×5exit
66.0ms167×0invalid
40.0ms124×0exit
30.0ms9×4valid
21.0ms50×1exit
Compiler

Compiled 38 339 to 4 296 computations (88.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.4s
ival-mult: 3.5s (28.2% of total)
ival-add: 2.1s (16.8% of total)
ival-div: 1.6s (13.3% of total)
adjust: 1.3s (10.7% of total)
ival-pow: 1.1s (9% of total)
ival-sub: 912.0ms (7.4% of total)
const: 569.0ms (4.6% of total)
ival-neg: 298.0ms (2.4% of total)
ival-cos: 198.0ms (1.6% of total)
ival-sin: 192.0ms (1.6% of total)
ival-exp: 150.0ms (1.2% of total)
ival-pow2: 122.0ms (1% of total)
ival-sqrt: 100.0ms (0.8% of total)
exact: 56.0ms (0.5% of total)
ival-true: 30.0ms (0.2% of total)
ival-expm1: 22.0ms (0.2% of total)
ival-assert: 17.0ms (0.1% of total)
ival-log1p: 16.0ms (0.1% of total)
ival-atan: 13.0ms (0.1% of total)
ival-log: 9.0ms (0.1% of total)
ival-tan: 8.0ms (0.1% of total)
ival-cosh: 4.0ms (0% of total)
ival-pi: 4.0ms (0% of total)
ival-sinh: 2.0ms (0% of total)
ival-cbrt: 2.0ms (0% of total)

eval18.3s (6.6%)

Memory
-105.4MiB live, 20 398.9MiB allocated
Compiler

Compiled 4 058 879 to 313 470 computations (92.3% saved)

explain9.5s (3.4%)

Memory
-98.6MiB live, 10 741.1MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation12954
+.f64#fcancellation39293
-.f64(-.f64 (*.f64 #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) t) #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64))oflow-left2260
sqrt.f64#foflow-rescue1800
log.f64(log.f64 (+.f64 #s(literal 1 binary64) x))sensitivity1732
/.f64#fn/o1680
/.f64#fo/o1640
pow.f64(pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n)sensitivity1051
-.f64#fnan-rescue970
/.f64#fu/n890
/.f64#fu/u570
/.f64#fn/u550
*.f64#fn*u530
+.f64#fnan-rescue500
/.f64#fo/n410
*.f64#fn*o240
pow.f64(pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n)oflow-rescue210
↳(pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n)overflow34
↳(/.f64 i n)overflow21
↳(+.f64 #s(literal 1 binary64) (/.f64 i n))overflow21
sqrt.f64#fuflow-rescue140
Confusion
Predicted +Predicted -
+3913214
-1126513
Precision
0.9721739130434782
Recall
0.9481463532832566
Confusion?
Predicted +Predicted MaybePredicted -
+391316054
-1121956318
Precision?
0.9299086757990868
Recall?
0.9869154349406348
Freqs
test
numberfreq
06727
13605
2386
334
Total Confusion?
Predicted +Predicted MaybePredicted -
+3010
-209
Precision?
0.9393939393939394
Recall?
1.0
Samples
1.8s16 366×0valid
1.2s3 726×1valid
614.0ms1 390×2valid
10.0ms20×3valid
2.0ms2×4valid
Compiler

Compiled 7 535 to 1 486 computations (80.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.4s
ival-mult: 713.0ms (29.3% of total)
ival-add: 319.0ms (13.1% of total)
ival-div: 249.0ms (10.2% of total)
ival-sub: 245.0ms (10.1% of total)
adjust: 220.0ms (9% of total)
ival-pow: 178.0ms (7.3% of total)
ival-cos: 138.0ms (5.7% of total)
ival-sin: 120.0ms (4.9% of total)
ival-sqrt: 78.0ms (3.2% of total)
const: 42.0ms (1.7% of total)
ival-exp: 28.0ms (1.2% of total)
ival-neg: 20.0ms (0.8% of total)
ival-true: 19.0ms (0.8% of total)
exact: 19.0ms (0.8% of total)
ival-pow2: 15.0ms (0.6% of total)
ival-assert: 9.0ms (0.4% of total)
ival-log1p: 6.0ms (0.2% of total)
ival-atan: 5.0ms (0.2% of total)
ival-tan: 4.0ms (0.2% of total)
ival-expm1: 3.0ms (0.1% of total)
ival-pi: 2.0ms (0.1% of total)

preprocess9.3s (3.4%)

Memory
94.0MiB live, 7 814.3MiB allocated
Algorithm
42×egg-herbie
Stop Event
82×iter limit
53×saturated
33×node limit
Compiler

Compiled 56 431 to 8 524 computations (84.9% saved)

regimes7.5s (2.7%)

Memory
-137.7MiB live, 8 324.8MiB allocated
Counts
4 829 → 551
Calls

96 calls:

748.0ms
x
467.0ms
x2
408.0ms
a
353.0ms
c
345.0ms
b
Compiler

Compiled 9 135 to 5 843 computations (36% saved)

prune6.5s (2.3%)

Memory
-154.1MiB live, 7 908.4MiB allocated
Counts
81 514 → 2 032
Compiler

Compiled 161 940 to 68 087 computations (58% saved)

series4.6s (1.6%)

Memory
122.3MiB live, 5 018.7MiB allocated
Counts
2 029 → 10 333
Calls

897 calls:

TimeVariablePointExpression
153.0ms
x
@inf
((* (* x x) x) (/ x (+ (* x x) 1)) (- x (* (* x x) x)) (* x x) (* x (+ (* x x) -1)) (/ (* x (+ (* x x) -1)) (- (pow x 4) 1)) (+ (* x x) -1) (- (pow x 4) 1) (pow x 4))
120.0ms
x
@0
((* (+ y x) (/ (- x y) (+ (* y y) (* x x)))) (+ y x) (/ (- x y) (+ (* y y) (* x x))) (/ (+ (* (/ x y) (+ (/ x y) 1)) -1) y) (* (+ y x) (/ (- x y) (+ (* y y) (* x x)))) (/ (- x y) (+ (* y y) (* x x))) (/ (- (/ x y) 1) y) (- (- (/ x y) (pow (/ x y) 3)) (+ (* (/ x (neg y)) (/ x y)) 1)) (* (+ y x) (/ (- x y) (+ (* y y) (* x x)))) (/ (- x y) (+ (* y y) (* x x))) (/ (- (pow (* (* (pow (/ y x) 4) 4) (- (* (pow (/ y x) 2) -2) 1)) 3) (pow (- (* (pow (/ y x) 2) -2) 1) 3)) (* (+ (* (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) 16) (+ (pow (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) 2) (pow (+ (* (pow (/ y x) 2) 2) 1) 2))) (pow (+ (* (pow (/ y x) 2) 2) 1) 2))) (* (+ (* (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) 16) (+ (pow (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) 2) (pow (+ (* (pow (/ y x) 2) 2) 1) 2))) (pow (+ (* (pow (/ y x) 2) 2) 1) 2)) (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- (/ (pow (* (* (pow (/ y x) 4) 4) (- (* (pow (/ y x) 2) -2) 1)) 3) (+ (* (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) 16) (+ (pow (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) 2) (pow (+ (* (pow (/ y x) 2) 2) 1) 2)))) (/ (pow (- (* (pow (/ y x) 2) -2) 1) 3) (+ (* (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) 16) (+ (pow (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) 2) (pow (+ (* (pow (/ y x) 2) 2) 1) 2))))) (/ (- (/ (pow (* (* (pow (/ y x) 4) 4) (- (* (pow (/ y x) 2) -2) 1)) 3) (+ (* (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) 16) (+ (pow (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) 2) (pow (+ (* (pow (/ y x) 2) 2) 1) 2)))) (/ (pow (- (* (pow (/ y x) 2) -2) 1) 3) (+ (* (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) 16) (+ (pow (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) 2) (pow (+ (* (pow (/ y x) 2) 2) 1) 2))))) (* (- (* -2 (pow (/ y x) 2)) 1) (- (* -2 (pow (/ y x) 2)) 1))) (* (- (* -2 (pow (/ y x) 2)) 1) (- (* -2 (pow (/ y x) 2)) 1)) (+ (* (/ x y) (+ (/ x y) 1)) -1) (- (/ x y) 1) (pow (/ x y) 3) (- (pow (* (* (pow (/ y x) 4) 4) (- (* (pow (/ y x) 2) -2) 1)) 3) (pow (- (* (pow (/ y x) 2) -2) 1) 3)) (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (pow (* (* (pow (/ y x) 4) 4) (- (* (pow (/ y x) 2) -2) 1)) 3) (+ (* (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) 16) (+ (pow (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) 2) (pow (+ (* (pow (/ y x) 2) 2) 1) 2)))) (/ (pow (- (* (pow (/ y x) 2) -2) 1) 3) (+ (* (pow (* (- (* (pow (/ y x) 2) -2) 1) (pow (/ y x) 4)) 2) 16) (+ (pow (+ (* (pow (/ y x) 4) 4) (* (pow (/ y x) 2) -2)) 2) (pow (+ (* (pow (/ y x) 2) 2) 1) 2)))))
93.0ms
y
@0
((+ (* (* (neg (/ (* -2 y) x)) (/ y x)) (* (neg (/ (* -2 y) x)) (/ y x))) (* 1 (* (neg (/ (* -2 y) x)) (/ y x)))) (* (neg (/ (* -2 y) x)) (/ y x)) (* 1 (* (neg (/ (* -2 y) x)) (/ y x))) (- 1 (pow (* (neg (/ (* -2 y) x)) (/ y x)) 3)) (/ (- (* (* 4 (pow (pow (/ y x) 2) 2)) (- (* -2 (pow (/ y x) 2)) 1)) (* (- (* -2 (pow (/ y x) 2)) 1) 1)) (* (- (* -2 (pow (/ y x) 2)) 1) (- (* -2 (pow (/ y x) 2)) 1))) (- (* (* 4 (pow (pow (/ y x) 2) 2)) (- (* -2 (pow (/ y x) 2)) 1)) (* (- (* -2 (pow (/ y x) 2)) 1) 1)) (pow (pow (/ y x) 2) 2) (* (- (* -2 (pow (/ y x) 2)) 1) 1) (+ (* (* -2 y) (/ y (* x x))) 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (* -2 y) (/ y (* x x)) (* (+ y x) (/ (- x y) (+ (* y y) (* x x)))) (+ y x) (/ (- x y) (+ (* y y) (* x x))) (- x y) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (- 1 (pow (* (neg (/ (* -2 y) x)) (/ y x)) 3)) (+ 1 (+ (* (* (neg (/ (* -2 y) x)) (/ y x)) (* (neg (/ (* -2 y) x)) (/ y x))) (* 1 (* (neg (/ (* -2 y) x)) (/ y x)))))) (pow (* (neg (/ (* -2 y) x)) (/ y x)) 3) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (pow (/ y x) 2) (* x x))
90.0ms
a
@0
((/ (+ (neg b) (sqrt (+ (* (* c a) -4) (* b b)))) (* 2 a)) (+ (neg b) (sqrt (+ (* (* c a) -4) (* b b)))) (neg b) (sqrt (+ (* (* c a) -4) (* b b))) (/ (+ (neg b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (neg b) a) (+ (* (/ (neg c) (* b b)) b) (/ b a)) (/ (+ (neg b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (neg (+ (* (/ (neg c) (* b b)) b) (/ b a))) (/ (neg c) (* b b)) (/ (+ (neg b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (neg (+ (* (/ (* c c) b) (/ a b)) c)) b) (neg (+ (* (/ (* c c) b) (/ a b)) c)) (+ (* (/ (* c c) b) (/ a b)) c) (/ (+ (neg b) (pow (pow (+ (* c (* a 4)) (* b b)) 2) 1/4)) (* 2 a)) (+ (neg b) (pow (pow (+ (* c (* a 4)) (* b b)) 2) 1/4)) (pow (pow (+ (* c (* a 4)) (* b b)) 2) 1/4) (+ (* (* c a) -4) (* b b)) (neg c) (/ (* c c) b) (pow (+ (* c (* a 4)) (* b b)) 2))
82.0ms
x
@inf
((- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (sqrt (- (* x x) eps)) (/ eps (pow x 5)))

analyze3.7s (1.3%)

Memory
26.5MiB live, 4 168.6MiB allocated
Algorithm
43×search
2×random
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%54.5%45.5%0%0%0%0
21.4%11.7%42.9%45.5%0%0%0%1
37.4%20.4%34.1%45.5%0%0%0%2
48.7%26.2%27.7%45.5%0%0.6%0%3
57.7%30.7%22.6%45.5%0%1.2%0%4
71.2%37.7%15.3%45.5%0%1.6%0%5
72.9%38.4%14.3%45.5%0%1.8%0%6
77.9%40.7%11.6%45.5%0%2.2%0%7
81.5%42.6%9.7%45.5%0%2.3%0%8
84.1%43.8%8.3%45.5%0%2.5%0%9
86.2%44.6%7.2%45.5%0%2.7%0%10
88.2%45.6%6.1%45.5%0%2.8%0%11
89.1%45.9%5.6%45.5%0%2.9%0%12
Compiler

Compiled 1 402 to 721 computations (48.6% saved)

bsearch2.6s (0.9%)

Memory
63.3MiB live, 3 225.6MiB allocated
Algorithm
149×binary-search
108×left-value
Stop Event
144×narrow-enough
4×predicate-same
1×predicate-failed
Samples
1.1s10 373×0valid
205.0ms918×1valid
149.0ms413×2valid
57.0ms934×0invalid
22.0ms152×0exit
6.0ms8×3valid
Compiler

Compiled 129 165 to 65 066 computations (49.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.2s
ival-mult: 408.0ms (35.1% of total)
ival-div: 162.0ms (13.9% of total)
ival-pow: 160.0ms (13.8% of total)
ival-add: 126.0ms (10.8% of total)
ival-sub: 123.0ms (10.6% of total)
adjust: 41.0ms (3.5% of total)
ival-pi: 37.0ms (3.2% of total)
ival-neg: 29.0ms (2.5% of total)
ival-exp: 24.0ms (2.1% of total)
ival-expm1: 20.0ms (1.7% of total)
ival-sqrt: 10.0ms (0.9% of total)
ival-true: 9.0ms (0.8% of total)
exact: 9.0ms (0.8% of total)
ival-assert: 5.0ms (0.4% of total)

start2.0ms (0%)

Memory
3.9MiB live, 3.7MiB allocated

end0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated

Profiling

Loading profile data...