Herbie run

Date:Sunday, December 22nd, 2024
Commit:24da1642 on main
Hostname:nightly with Racket 8.10
Seed:2024357
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:245 701.8 MB

Time bar (total: 4.5min)

sample2.1min (46.6%)

Memory
1 285.1MiB live, 119 447.9MiB allocated; 35.0s collecting garbage
Samples
28.8s43 608×2valid
23.6s96 647×1valid
23.5s145 850×0invalid
17.1s7 117×5exit
7.7s87 408×0valid
2.8s3 498×3valid
594.0ms4 103×0exit
8.0ms7×4valid
Precisions
Click to see histograms. Total time spent on operations: 1.4min
ival-pow: 16.4s (19% of total)
ival-tan: 12.7s (14.6% of total)
adjust: 8.4s (9.8% of total)
ival-mult: 6.0s (6.9% of total)
const: 4.8s (5.5% of total)
ival-sub: 4.7s (5.5% of total)
ival-div: 4.4s (5.1% of total)
ival-cos: 4.1s (4.7% of total)
ival-log: 3.6s (4.1% of total)
ival-add: 3.3s (3.9% of total)
ival-sin: 3.2s (3.8% of total)
ival-fabs: 2.2s (2.6% of total)
ival-expm1: 2.2s (2.5% of total)
ival-<=: 1.9s (2.3% of total)
ival-exp: 1.9s (2.2% of total)
ival-sqrt: 1.5s (1.7% of total)
ival-log1p: 1.2s (1.3% of total)
ival-<: 1.0s (1.2% of total)
ival-and: 627.0ms (0.7% of total)
ival-fmin: 506.0ms (0.6% of total)
exact: 362.0ms (0.4% of total)
ival->: 335.0ms (0.4% of total)
ival-atan: 325.0ms (0.4% of total)
ival-cbrt: 300.0ms (0.3% of total)
ival-neg: 281.0ms (0.3% of total)
ival-assert: 166.0ms (0.2% of total)
ival-true: 70.0ms (0.1% of total)
Bogosity

simplify35.3s (13.2%)

Memory
397.4MiB live, 29 434.9MiB allocated; 8.4s collecting garbage
Algorithm
246×egg-herbie
Stop Event
327×iter limit
214×node limit
32×saturated
Counts
9 122 → 9 020

localize25.6s (9.6%)

Memory
-174.8MiB live, 24 195.1MiB allocated; 5.8s collecting garbage
Samples
9.3s6 518×2valid
9.0s11 866×1valid
2.3s8 901×0valid
999.0ms436×3valid
135.0ms51×5exit
72.0ms130×0invalid
4.0ms2×4valid
Compiler

Compiled 25 692 to 3 668 computations (85.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.7s
adjust: 3.8s (21.4% of total)
ival-mult: 3.0s (16.9% of total)
ival-div: 1.9s (10.8% of total)
ival-tan: 1.7s (9.5% of total)
ival-add: 1.3s (7.6% of total)
ival-sub: 852.0ms (4.8% of total)
ival-pow: 795.0ms (4.5% of total)
const: 788.0ms (4.5% of total)
ival-sin: 698.0ms (3.9% of total)
ival-cos: 688.0ms (3.9% of total)
ival-log: 595.0ms (3.4% of total)
ival-sqrt: 307.0ms (1.7% of total)
ival-exp: 247.0ms (1.4% of total)
ival-pow2: 196.0ms (1.1% of total)
ival-log1p: 171.0ms (1% of total)
ival-cosh: 143.0ms (0.8% of total)
ival-neg: 141.0ms (0.8% of total)
ival-expm1: 111.0ms (0.6% of total)
ival-cbrt: 71.0ms (0.4% of total)
exact: 52.0ms (0.3% of total)
ival-fabs: 45.0ms (0.3% of total)
ival-true: 23.0ms (0.1% of total)
ival-pi: 21.0ms (0.1% of total)
ival-atan2: 14.0ms (0.1% of total)
ival-sinh: 13.0ms (0.1% of total)
ival-assert: 12.0ms (0.1% of total)
ival-atan: 9.0ms (0.1% of total)
ival-hypot: 8.0ms (0% of total)

derivations23.2s (8.7%)

Memory
251.8MiB live, 13 880.4MiB allocated; 3.3s collecting garbage
Stop Event
197×iter limit
134×node limit
25×fuel
3×done
Compiler

Compiled 9 222 to 2 033 computations (78% saved)

rewrite22.6s (8.5%)

Memory
-169.7MiB live, 20 523.1MiB allocated; 4.9s collecting garbage
Stop Event
221×iter limit
109×node limit
Counts
1 802 → 49 140

eval11.3s (4.2%)

Memory
-211.2MiB live, 12 542.7MiB allocated; 3.9s collecting garbage
Compiler

Compiled 2 481 853 to 268 880 computations (89.2% saved)

explain6.3s (2.3%)

Memory
-108.6MiB live, 5 773.7MiB allocated; 1.0s collecting garbage
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation416438
log.f64#fsensitivity7551
/.f64#fu/u4270
sqrt.f64#foflow-rescue3660
+.f64#fcancellation3400
/.f64#fu/n1060
pow.f64(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))sensitivity640
/.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/u290
↳(*.f64 b eps)underflow143
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow146
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow143
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow229
↳(*.f64 a eps)underflow146
sqrt.f64#fuflow-rescue280
-.f64#fnan-rescue280
/.f64#fn/o50
cos.f64(cos.f64 (+.f64 x eps))sensitivity20
exp.f64#fsensitivity20
tan.f64(tan.f64 (+.f64 x eps))cancellation10
tan.f64(tan.f64 (+.f64 x eps))sensitivity10
Confusion
Predicted +Predicted -
+517019
-1361843
Precision
0.974368639276291
Recall
0.9963384081711313
Confusion?
Predicted +Predicted MaybePredicted -
+5170145
-136261817
Precision?
0.9696969696969697
Recall?
0.9990364232029293
Freqs
test
numberfreq
01862
14504
2647
3100
455
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.6s2 670×2valid
1.2s6 024×1valid
592.0ms5 428×0valid
233.0ms214×3valid
Compiler

Compiled 2 154 to 763 computations (64.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.9s
ival-tan: 727.0ms (24.9% of total)
adjust: 470.0ms (16.1% of total)
ival-cos: 197.0ms (6.7% of total)
ival-sin: 193.0ms (6.6% of total)
ival-log: 178.0ms (6.1% of total)
ival-expm1: 162.0ms (5.5% of total)
ival-div: 155.0ms (5.3% of total)
ival-sub: 146.0ms (5% of total)
ival-mult: 133.0ms (4.6% of total)
ival-pow: 125.0ms (4.3% of total)
ival-exp: 116.0ms (4% of total)
ival-add: 105.0ms (3.6% of total)
ival-sqrt: 59.0ms (2% of total)
ival-log1p: 56.0ms (1.9% of total)
ival-atan: 44.0ms (1.5% of total)
ival-cbrt: 16.0ms (0.5% of total)
ival-neg: 13.0ms (0.4% of total)
ival-true: 12.0ms (0.4% of total)
exact: 9.0ms (0.3% of total)
ival-assert: 6.0ms (0.2% of total)

preprocess5.4s (2%)

Memory
438.6MiB live, 4 738.9MiB allocated; 1.5s collecting garbage
Algorithm
28×egg-herbie
Stop Event
56×iter limit
33×saturated
23×node limit
Compiler

Compiled 21 056 to 5 599 computations (73.4% saved)

prune3.4s (1.3%)

Memory
261.3MiB live, 5 078.2MiB allocated; 610ms collecting garbage
Counts
61 936 → 1 825
Compiler

Compiled 109 927 to 55 993 computations (49.1% saved)

series3.4s (1.3%)

Memory
177.9MiB live, 3 454.8MiB allocated; 823ms collecting garbage
Counts
1 802 → 9 122
Calls

507 calls:

TimeVariablePointExpression
80.0ms
x
@inf
((* (pow (cbrt x) -1) 1/3) (/ (* (pow (cbrt x) -1) 1/3) (cbrt x)) (- (cbrt (+ x 1)) (cbrt x)) (pow (cbrt x) -1) (- (cbrt (+ x 1)) (cbrt x)) (* (pow x -2/3) 1/3) (pow x -2/3) (- (cbrt (+ x 1)) (pow (sqrt x) 2/3)) (cbrt (+ x 1)) (+ x 1) (pow (sqrt x) 2/3) (- (cbrt (+ x 1)) (cbrt x)) (* (/ 1/3 (pow x 1/6)) (cbrt (pow x -3/2))) (/ 1/3 (pow x 1/6)) (pow x 1/6) (- (cbrt (+ x 1)) (cbrt x)) (* (* (cbrt (pow x -1)) (cbrt (pow x -1))) 1/3) (* (cbrt (pow x -1)) (cbrt (pow x -1))) (cbrt (pow x -1)) (cbrt x) (sqrt x) (cbrt (pow x -3/2)))
68.0ms
x
@0
((* (pow (cbrt x) -1) 1/3) (/ (* (pow (cbrt x) -1) 1/3) (cbrt x)) (- (cbrt (+ x 1)) (cbrt x)) (pow (cbrt x) -1) (- (cbrt (+ x 1)) (cbrt x)) (* (pow x -2/3) 1/3) (pow x -2/3) (- (cbrt (+ x 1)) (pow (sqrt x) 2/3)) (cbrt (+ x 1)) (+ x 1) (pow (sqrt x) 2/3) (- (cbrt (+ x 1)) (cbrt x)) (* (/ 1/3 (pow x 1/6)) (cbrt (pow x -3/2))) (/ 1/3 (pow x 1/6)) (pow x 1/6) (- (cbrt (+ x 1)) (cbrt x)) (* (* (cbrt (pow x -1)) (cbrt (pow x -1))) 1/3) (* (cbrt (pow x -1)) (cbrt (pow x -1))) (cbrt (pow x -1)) (cbrt x) (sqrt x) (cbrt (pow x -3/2)))
67.0ms
x
@inf
((+ (* (pow (/ (sin x) (cos x)) 3) -1/3) (+ (/ (* (/ (neg (pow (sin x) 4)) (pow (cos x) 4)) (sin x)) (cos x)) (* (pow (/ (sin x) (cos x)) 3) -1/3))) (/ (* (/ (neg (pow (sin x) 4)) (pow (cos x) 4)) (sin x)) (cos x)) (* (/ (neg (pow (sin x) 4)) (pow (cos x) 4)) (sin x)) (* (neg eps) (+ (* (pow (/ (sin x) (cos x)) 3) -1/3) (+ (/ (* (/ (neg (pow (sin x) 4)) (pow (cos x) 4)) (sin x)) (cos x)) (* (pow (/ (sin x) (cos x)) 3) -1/3)))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps eps) x) eps) (* (* eps eps) x) (* (+ (* (+ (* 17/45 (* x x)) 2/3) (* x x)) 1) x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (- (tan (+ (+ (+ (PI) x) (PI)) (+ (+ (PI) eps) (PI)))) (tan x)) (tan (+ (+ (+ (PI) x) (PI)) (+ (+ (PI) eps) (PI)))) (+ (+ (+ (PI) x) (PI)) (+ (+ (PI) eps) (PI))) (+ (* (PI) 4) (+ x eps)) (+ (/ (tan eps) (+ (* (neg (tan x)) (tan eps)) 1)) (- (/ (tan x) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x))) (/ (tan eps) (+ (* (neg (tan x)) (tan eps)) 1)) (tan eps) (+ (* (neg (tan x)) (tan eps)) 1) (- (/ (tan x) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (neg (pow (sin x) 4)) (pow (cos x) 4))) (* (pow (/ (sin x) (cos x)) 3) -1/3) (* (* (+ (* (+ (* 17/45 (* x x)) 2/3) (* x x)) 1) x) x) (- (/ (tan x) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (* (* x x) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))
61.0ms
n
@0
((/ (+ (- (neg (log (+ 1 x))) (/ (+ (* 1/6 (/ (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) n)) (* (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) 1/2)) n)) (log x)) (neg n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (+ (- (neg (log (+ 1 x))) (/ (+ (* 1/6 (/ (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) n)) (* (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) 1/2)) n)) (log x)) (- (neg (log (+ 1 x))) (/ (+ (* 1/6 (/ (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) n)) (* (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) 1/2)) n)) (- (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))) (- 1 (exp (/ (log x) n))) (exp (/ (log x) n)) (/ (log x) n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ (* (+ (* (+ (* (- (/ 1/6 (pow n 3)) (/ (+ -1/3 (/ 1/2 n)) n)) x) (/ (+ -1/2 (/ 1/2 n)) n)) x) (/ 1 n)) x) 1) (+ (* (+ (* (- (/ 1/6 (pow n 3)) (/ (+ -1/3 (/ 1/2 n)) n)) x) (/ (+ -1/2 (/ 1/2 n)) n)) x) (/ 1 n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (log x)) n) (- (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (log x)) (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) (+ (* (- (/ 1/6 (pow n 3)) (/ (+ -1/3 (/ 1/2 n)) n)) x) (/ (+ -1/2 (/ 1/2 n)) n)) (- (/ 1/6 (pow n 3)) (/ (+ -1/3 (/ 1/2 n)) n)) (pow (log x) 2))
50.0ms
x
@0
((- (cbrt (+ x 1)) (cbrt x)) (* (cbrt (/ (/ 1 x) x)) 1/3) (cbrt (/ (/ 1 x) x)) (/ (/ 1 x) x) (- (cbrt (+ x 1)) (cbrt x)) (cbrt (+ x 1)) (cbrt x) (+ (* (sqrt x) (sqrt x)) 1) (- (cbrt (+ (* (sqrt x) (sqrt x)) 1)) (cbrt x)) (cbrt (+ (* (sqrt x) (sqrt x)) 1)) (sqrt x) (- (cbrt (+ x 1)) (* (cbrt (neg (sqrt x))) (cbrt (neg (sqrt x))))) (cbrt (+ x 1)) (+ x 1) (* (cbrt (neg (sqrt x))) (cbrt (neg (sqrt x)))) (- (cbrt (+ (* (pow x 5/6) (pow x 1/6)) 1)) (cbrt x)) (cbrt (+ (* (pow x 5/6) (pow x 1/6)) 1)) (+ (* (pow x 5/6) (pow x 1/6)) 1) (pow x 5/6) (cbrt (neg (sqrt x))) (pow x 1/6))

regimes3.2s (1.2%)

Memory
-65.4MiB live, 3 436.2MiB allocated; 536ms collecting garbage
Counts
3 406 → 313
Calls

43 calls:

881.0ms
x
334.0ms
eps
170.0ms
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
141.0ms
a
103.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 2 127 to 1 976 computations (7.1% saved)

analyze2.1s (0.8%)

Memory
-21.4MiB live, 2 179.1MiB allocated; 1.1s collecting garbage
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)

bsearch1.0s (0.4%)

Memory
20.7MiB live, 1 014.5MiB allocated; 106ms collecting garbage
Algorithm
87×binary-search
8×left-value
Stop Event
82×narrow-enough
5×predicate-same
Samples
301.0ms3 851×0valid
167.0ms913×1valid
99.0ms334×2valid
60.0ms762×0invalid
6.0ms22×3valid
2.0ms31×0exit
Compiler

Compiled 35 950 to 23 914 computations (33.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 439.0ms
ival-mult: 90.0ms (20.5% of total)
ival-pow: 76.0ms (17.3% of total)
ival-sub: 72.0ms (16.4% of total)
ival-div: 46.0ms (10.5% of total)
adjust: 46.0ms (10.5% of total)
ival-sqrt: 28.0ms (6.4% of total)
ival-add: 21.0ms (4.8% of total)
ival-neg: 18.0ms (4.1% of total)
ival-cbrt: 11.0ms (2.5% of total)
ival-cos: 10.0ms (2.3% of total)
ival-expm1: 9.0ms (2.1% of total)
ival-true: 4.0ms (0.9% of total)
ival-exp: 3.0ms (0.7% of total)
exact: 3.0ms (0.7% of total)
ival-assert: 2.0ms (0.5% of total)

start28.0ms (0%)

Memory
2.0MiB live, 2.0MiB allocated; 19ms collecting garbage

end0.0ms (0%)

Memory
0.4MiB live, 0.3MiB allocated; 0ms collecting garbage

Profiling

Loading profile data...