Herbie run

Date:Thursday, August 1st, 2024
Commit:9d1b2398 on HEAD
Hostname:nightly with Racket 8.11.1
Seed:2024214
Parameters:256 points for 4 iterations
Flags:
localize:costslocalize:errorsreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs
default

Time bar (total: 5.5min)

sample1.8min (33.6%)

Memory
758.6MiB live, 128 393.5MiB allocated
Samples
28.3s41 301×2valid
23.4s144 356×0invalid
18.5s92 463×1valid
9.3s4 938×5exit
8.6s94 486×0valid
1.8s2 911×3valid
592.0ms4 311×0exit
517.0ms2 237×1exit
15.0ms7×4exit
8.0ms7×4valid
6.0ms2×3exit
3.0ms4×2exit
Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-tan: 12.9s (17.1% of total)
ival-pow: 9.2s (12.2% of total)
ival-mult: 5.9s (7.8% of total)
adjust: 5.8s (7.7% of total)
const: 5.0s (6.7% of total)
ival-cos: 4.1s (5.4% of total)
ival-sub: 3.9s (5.2% of total)
ival-div: 3.7s (5% of total)
ival-log: 3.5s (4.6% of total)
ival-add: 3.3s (4.3% of total)
ival-sin: 3.1s (4.1% of total)
ival-fabs: 2.6s (3.5% of total)
ival-exp: 2.2s (2.9% of total)
ival-<=: 2.2s (2.9% of total)
ival-expm1: 1.8s (2.4% of total)
ival-sqrt: 1.3s (1.7% of total)
ival-log1p: 1.1s (1.4% of total)
ival-<: 895.0ms (1.2% of total)
ival-and: 591.0ms (0.8% of total)
ival-fmin: 475.0ms (0.6% of total)
ival-atan: 387.0ms (0.5% of total)
ival-neg: 361.0ms (0.5% of total)
exact: 339.0ms (0.4% of total)
ival->: 295.0ms (0.4% of total)
ival-cbrt: 286.0ms (0.4% of total)
ival-assert: 158.0ms (0.2% of total)
ival-true: 69.0ms (0.1% of total)
Bogosity

simplify1.2min (21.1%)

Memory
-208.9MiB live, 84 967.9MiB allocated
Algorithm
246×egg-herbie
Rules
1 949 494×lower-fma.f32
1 948 904×lower-fma.f64
745 342×lower-*.f32
744 358×lower-*.f64
446 646×lower-+.f32
Stop Event
324×iter limit
167×node limit
82×saturated
Counts
24 252 → 23 739

rewrite39.2s (11.9%)

Memory
201.3MiB live, 50 336.5MiB allocated
Algorithm
109×batch-egg-rewrite
Rules
505 690×lower-fma.f32
505 094×lower-fma.f64
431 346×lower-*.f32
430 384×lower-*.f64
384 950×lower-/.f32
Stop Event
223×iter limit
107×node limit
4×saturated
Counts
1 484 → 76 996

soundness33.0s (10%)

Memory
-303.3MiB live, 19 505.7MiB allocated
Rules
1 116 788×lower-fma.f32
1 116 468×lower-fma.f64
592 872×lower-*.f32
592 274×lower-*.f64
329 584×lower-/.f32
Stop Event
210×iter limit
135×node limit
24×fuel
4×done
2×saturated
Compiler

Compiled 10 916 to 5 660 computations (48.1% saved)

eval19.8s (6%)

Memory
608.1MiB live, 28 915.2MiB allocated
Compiler

Compiled 3 480 180 to 294 747 computations (91.5% saved)

prune18.3s (5.6%)

Memory
-287.7MiB live, 28 763.3MiB allocated
Counts
119 428 → 2 197
Compiler

Compiled 79 893 to 38 094 computations (52.3% saved)

localize17.6s (5.4%)

Memory
140.7MiB live, 22 640.6MiB allocated
Samples
4.9s4 252×2valid
3.4s7 173×1valid
3.2s14 850×0valid
572.0ms330×3valid
266.0ms988×0invalid
154.0ms296×1exit
103.0ms15×5exit
Compiler

Compiled 19 704 to 2 905 computations (85.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.8s
ival-mult: 2.0s (20.6% of total)
ival-div: 1.3s (12.9% of total)
adjust: 960.0ms (9.8% of total)
ival-tan: 876.0ms (8.9% of total)
ival-add: 875.0ms (8.9% of total)
ival-sin: 746.0ms (7.6% of total)
const: 545.0ms (5.6% of total)
ival-log: 506.0ms (5.2% of total)
ival-cos: 480.0ms (4.9% of total)
ival-sub: 407.0ms (4.2% of total)
ival-pow: 205.0ms (2.1% of total)
ival-sqrt: 202.0ms (2.1% of total)
ival-neg: 191.0ms (2% of total)
ival-exp: 134.0ms (1.4% of total)
ival-log1p: 118.0ms (1.2% of total)
ival-pow2: 75.0ms (0.8% of total)
exact: 38.0ms (0.4% of total)
ival-cosh: 30.0ms (0.3% of total)
ival-cbrt: 27.0ms (0.3% of total)
ival-atan2: 26.0ms (0.3% of total)
ival-true: 23.0ms (0.2% of total)
ival-expm1: 20.0ms (0.2% of total)
ival-assert: 12.0ms (0.1% of total)
ival-atan: 12.0ms (0.1% of total)

explain5.7s (1.7%)

Memory
-71.2MiB live, 7 935.1MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation409225
log.f64#fsensitivity7612
/.f64#fu/u4330
sqrt.f64#foflow-rescue3940
+.f64#fcancellation3501
/.f64#fu/n980
pow.f64(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))sensitivity760
sqrt.f64#fuflow-rescue240
-.f64#fnan-rescue170
/.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/u140
↳(*.f64 b eps)underflow165
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow168
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow165
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow231
↳(*.f64 a eps)underflow168
exp.f64#fsensitivity42
/.f64(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))n/o30
↳(*.f64 x x)overflow60
sin.f64(sin.f64 (+.f64 x eps))sensitivity11
tan.f64(tan.f64 (+.f64 x eps))sensitivity11
Confusion
Predicted +Predicted -
+517722
-1521817
Precision
0.9714768249202477
Recall
0.9957684170032699
Confusion?
Predicted +Predicted MaybePredicted -
+5177157
-152151802
Precision?
0.9688374696771785
Recall?
0.9986535872283131
Freqs
test
numberfreq
01839
14551
2655
385
438
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.6s2 540×2valid
1.1s5 768×1valid
518.0ms5 810×0valid
107.0ms218×3valid
Compiler

Compiled 2 522 to 980 computations (61.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.7s
ival-tan: 792.0ms (29.2% of total)
ival-sub: 235.0ms (8.7% of total)
adjust: 232.0ms (8.5% of total)
ival-cos: 188.0ms (6.9% of total)
ival-log: 186.0ms (6.9% of total)
ival-div: 169.0ms (6.2% of total)
ival-add: 155.0ms (5.7% of total)
ival-sin: 144.0ms (5.3% of total)
ival-exp: 135.0ms (5% of total)
ival-mult: 125.0ms (4.6% of total)
ival-pow: 112.0ms (4.1% of total)
ival-log1p: 67.0ms (2.5% of total)
ival-sqrt: 61.0ms (2.2% of total)
ival-cbrt: 30.0ms (1.1% of total)
ival-expm1: 25.0ms (0.9% of total)
ival-atan: 19.0ms (0.7% of total)
ival-neg: 13.0ms (0.5% of total)
ival-true: 12.0ms (0.4% of total)
exact: 8.0ms (0.3% of total)
ival-assert: 6.0ms (0.2% of total)

preprocess5.0s (1.5%)

Memory
-106.9MiB live, 6 316.1MiB allocated
Algorithm
28×egg-herbie
Rules
27 478×lower-fma.f64
27 478×lower-fma.f32
10 768×div-sub
10 444×sub-neg
9 190×lower-*.f32
Stop Event
56×iter limit
50×saturated
6×node limit
Compiler

Compiled 11 046 to 3 866 computations (65% saved)

regimes4.7s (1.4%)

Memory
-101.7MiB live, 6 972.3MiB allocated
Counts
5 044 → 388
Calls

43 calls:

1.1s
x
336.0ms
(/.f64 #s(literal 1 binary64) n)
319.0ms
eps
219.0ms
b
210.0ms
n
Compiler

Compiled 3 336 to 2 221 computations (33.4% saved)

series3.1s (0.9%)

Memory
49.0MiB live, 4 171.0MiB allocated
Counts
1 484 → 24 252
Calls

4743 calls:

TimeVariablePointExpression
57.0ms
N
@-inf
(+ (* (pow (log (+ 1 N)) 3/2) (/ (pow (log (+ 1 N)) 3/2) (+ (* (log N) (log (+ (* N N) N))) (pow (log (+ 1 N)) 2)))) (neg (/ (pow (log N) 3) (+ (* (log N) (log (+ (* N N) N))) (pow (log (+ 1 N)) 2)))))
50.0ms
N
@inf
(log (/ 1 (atan2 1 (+ (* N N) (+ N 1)))))
49.0ms
N
@-inf
(+ (* (pow (neg (log (/ (- 1 N) (- 1 (* N N))))) 3/2) (/ (pow (log (+ 1 N)) 3/2) (+ (* (log N) (log (+ (* N N) N))) (pow (log (+ 1 N)) 2)))) (neg (/ (pow (log N) 3) (+ (* (log N) (log (+ (* N N) N))) (pow (log (+ 1 N)) 2)))))
45.0ms
eps
@-inf
(* 1/2 eps)
42.0ms
N
@0
(log (atan2 1 (+ N (+ (* N N) 1))))

analyze1.6s (0.5%)

Memory
185.1MiB live, 2 339.3MiB 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)

bsearch1.1s (0.3%)

Memory
56.9MiB live, 1 724.7MiB allocated
Algorithm
89×binary-search
50×left-value
Stop Event
81×narrow-enough
8×predicate-same
Samples
402.0ms4 068×0valid
154.0ms861×1valid
79.0ms280×2valid
72.0ms865×0invalid
7.0ms7×3valid
5.0ms55×0exit
2.0ms17×1exit
Compiler

Compiled 16 399 to 12 000 computations (26.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 499.0ms
ival-mult: 101.0ms (20.3% of total)
ival-pow: 100.0ms (20.1% of total)
ival-div: 53.0ms (10.6% of total)
ival-sqrt: 52.0ms (10.4% of total)
ival-sub: 50.0ms (10% of total)
ival-add: 39.0ms (7.8% of total)
adjust: 29.0ms (5.8% of total)
ival-neg: 28.0ms (5.6% of total)
ival-sin: 16.0ms (3.2% of total)
ival-cos: 15.0ms (3% of total)
ival-true: 5.0ms (1% of total)
ival-expm1: 4.0ms (0.8% of total)
exact: 4.0ms (0.8% of total)
ival-assert: 3.0ms (0.6% of total)
ival-cbrt: 3.0ms (0.6% of total)

end0.0ms (0%)

Memory
0.5MiB live, 0.4MiB allocated

Profiling

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