Herbie run

Date:Wednesday, September 11th, 2024
Commit:b5881a3c on zane-concrete-values
Hostname:nightly with Racket 8.11.1
Seed:2024255
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: 4.6min)

sample2.0min (43.1%)

Memory
426.9MiB live, 115 798.9MiB allocated
Samples
30.3s41 513×2valid
25.4s147 415×0invalid
19.7s92 168×1valid
9.5s94 516×0valid
9.5s4 847×5exit
1.9s2 964×3valid
499.0ms2 261×1exit
467.0ms4 244×0exit
14.0ms5×4exit
8.0ms7×4valid
8.0ms7×2exit
0.0ms1×3exit
Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-tan: 14.2s (17.7% of total)
ival-pow: 9.8s (12.3% of total)
ival-mult: 5.7s (7.2% of total)
const: 5.6s (7% of total)
adjust: 5.4s (6.7% of total)
ival-cos: 4.7s (5.9% of total)
ival-add: 4.2s (5.2% of total)
ival-sub: 3.9s (4.8% of total)
ival-div: 3.8s (4.8% of total)
ival-log: 3.5s (4.4% of total)
ival-sin: 3.3s (4.2% of total)
ival-fabs: 2.9s (3.6% of total)
ival-<=: 2.4s (2.9% of total)
ival-exp: 2.2s (2.8% of total)
ival-expm1: 2.1s (2.6% of total)
ival-sqrt: 1.2s (1.5% of total)
ival-log1p: 1.1s (1.4% of total)
ival-<: 994.0ms (1.2% of total)
ival-and: 649.0ms (0.8% of total)
ival-fmin: 464.0ms (0.6% of total)
ival-atan: 372.0ms (0.5% of total)
exact: 366.0ms (0.5% of total)
ival->: 327.0ms (0.4% of total)
ival-neg: 315.0ms (0.4% of total)
ival-cbrt: 279.0ms (0.3% of total)
ival-assert: 159.0ms (0.2% of total)
ival-true: 76.0ms (0.1% of total)
Bogosity

simplify35.9s (13%)

Memory
672.3MiB live, 29 654.2MiB allocated
Algorithm
240×egg-herbie
Rules
2 038 906×lower-fma.f32
2 038 338×lower-fma.f64
718 514×lower-*.f32
717 750×lower-*.f64
451 508×lower-+.f32
Stop Event
315×iter limit
160×node limit
83×saturated
Counts
28 164 → 27 817

soundness29.8s (10.8%)

Memory
78.1MiB live, 16 471.5MiB allocated
Rules
1 105 196×lower-fma.f32
1 104 892×lower-fma.f64
577 816×lower-*.f32
577 454×lower-*.f64
318 306×lower-+.f32
Stop Event
193×iter limit
127×node limit
20×fuel
8×done
2×saturated
Compiler

Compiled 8 344 to 4 907 computations (41.2% saved)

eval21.2s (7.6%)

Memory
379.6MiB live, 24 793.2MiB allocated
Compiler

Compiled 2 713 292 to 287 028 computations (89.4% saved)

rewrite21.1s (7.6%)

Memory
-33.7MiB live, 20 661.9MiB allocated
Rules
488 946×lower-fma.f32
488 382×lower-fma.f64
433 768×lower-*.f32
433 014×lower-*.f64
391 134×lower-/.f32
Stop Event
213×iter limit
105×node limit
3×saturated
Counts
1 583 → 60 933

localize20.2s (7.3%)

Memory
70.8MiB live, 20 508.4MiB allocated
Samples
6.6s5 361×2valid
6.2s9 632×1valid
3.0s10 886×0valid
335.0ms835×0invalid
278.0ms305×3valid
82.0ms104×0exit
7.0ms10×1exit
4.0ms3×5exit
Compiler

Compiled 21 697 to 3 162 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.2s
ival-mult: 2.4s (18% of total)
ival-div: 1.6s (12.4% of total)
adjust: 1.5s (11.7% of total)
ival-add: 1.3s (9.6% of total)
ival-tan: 1.3s (9.5% of total)
ival-sub: 1.1s (8% of total)
ival-pow: 859.0ms (6.5% of total)
const: 648.0ms (4.9% of total)
ival-cos: 541.0ms (4.1% of total)
ival-exp: 425.0ms (3.2% of total)
ival-log: 345.0ms (2.6% of total)
ival-sin: 235.0ms (1.8% of total)
ival-log1p: 202.0ms (1.5% of total)
ival-sqrt: 198.0ms (1.5% of total)
ival-neg: 133.0ms (1% of total)
ival-pow2: 100.0ms (0.8% of total)
ival-cosh: 95.0ms (0.7% of total)
exact: 71.0ms (0.5% of total)
ival-cbrt: 60.0ms (0.5% of total)
ival-expm1: 58.0ms (0.4% of total)
ival-true: 24.0ms (0.2% of total)
ival-atan2: 17.0ms (0.1% of total)
ival-assert: 12.0ms (0.1% of total)
ival-copysign: 10.0ms (0.1% of total)
ival-atan: 9.0ms (0.1% of total)
ival-fabs: 7.0ms (0.1% of total)
ival-sinh: 1.0ms (0% of total)

prune6.7s (2.4%)

Memory
-863.7MiB live, 9 323.7MiB allocated
Counts
103 397 → 1 771
Compiler

Compiled 59 445 to 33 848 computations (43.1% saved)

explain5.7s (2.1%)

Memory
164.4MiB live, 6 589.6MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation416832
log.f64#fsensitivity7642
/.f64#fu/u4280
sqrt.f64#foflow-rescue3380
+.f64#fcancellation3281
/.f64#fu/n1190
pow.f64(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))sensitivity651
sqrt.f64#fuflow-rescue280
/.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/u180
↳(*.f64 b eps)underflow153
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow138
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow153
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow230
↳(*.f64 a eps)underflow138
-.f64#fnan-rescue180
cos.f64(cos.f64 (+.f64 x eps))sensitivity20
/.f64(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))n/o20
↳(*.f64 x x)overflow63
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o20
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow2
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow2
↳(exp.f64 x)overflow2
↳(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow2
sin.f64(sin.f64 (+.f64 x eps))sensitivity20
tan.f64(tan.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+515919
-1371853
Precision
0.9741314199395771
Recall
0.996330629586713
Confusion?
Predicted +Predicted MaybePredicted -
+5159127
-137231830
Precision?
0.9699868692552992
Recall?
0.9986481266898416
Freqs
test
numberfreq
01872
14511
2625
3117
443
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.6s2 586×2valid
1.0s5 808×1valid
561.0ms5 770×0valid
103.0ms172×3valid
Compiler

Compiled 2 154 to 763 computations (64.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-tan: 673.0ms (26.3% of total)
ival-cos: 250.0ms (9.8% of total)
adjust: 241.0ms (9.4% of total)
ival-log: 201.0ms (7.9% of total)
ival-div: 166.0ms (6.5% of total)
ival-mult: 155.0ms (6.1% of total)
ival-sub: 148.0ms (5.8% of total)
ival-sin: 129.0ms (5% of total)
ival-exp: 128.0ms (5% of total)
ival-pow: 121.0ms (4.7% of total)
ival-add: 97.0ms (3.8% of total)
ival-sqrt: 74.0ms (2.9% of total)
ival-log1p: 62.0ms (2.4% of total)
ival-cbrt: 27.0ms (1.1% of total)
ival-expm1: 23.0ms (0.9% of total)
ival-atan: 19.0ms (0.7% of total)
ival-neg: 18.0ms (0.7% of total)
ival-true: 13.0ms (0.5% of total)
exact: 8.0ms (0.3% of total)
ival-assert: 6.0ms (0.2% of total)

series5.1s (1.8%)

Memory
-1.4MiB live, 4 993.1MiB allocated
Counts
1 583 → 28 164
Calls

489 calls:

TimeVariablePointExpression
229.0ms
c
@0
((- (/ (sqrt (+ (* a (neg c)) (* b_2 b_2))) a) (/ b_2 a)) (/ (sqrt (+ (* a (neg c)) (* b_2 b_2))) a) (sqrt (+ (* a (neg c)) (* b_2 b_2))) (+ (* a (neg c)) (* b_2 b_2)) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (* (/ -1/2 b_2) c) (/ -1/2 b_2) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (sqrt (- (* b_2 b_2) (* a c))) (- (* b_2 b_2) (* a c)) (/ (- (* b_2 b_2) (+ (* (neg c) a) (* b_2 b_2))) (* a (- (neg b_2) (sqrt (+ (* (neg c) a) (* b_2 b_2)))))) (- (* b_2 b_2) (+ (* (neg c) a) (* b_2 b_2))) (* a c) (* a (- (neg b_2) (sqrt (+ (* (neg c) a) (* b_2 b_2))))) (/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (- (* b_2 b_2) (- (* b_2 b_2) (* a c))))) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (- (* b_2 b_2) (- (* b_2 b_2) (* a c)))) (/ (/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (- (* b_2 b_2) (- (* b_2 b_2) (* a c))))) a) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (+ (* (neg c) a) (* b_2 b_2))) (- (neg b_2) (sqrt (+ (* (neg c) a) (* b_2 b_2)))) (- (* b_2 b_2) (- (* b_2 b_2) (* a c))))
125.0ms
n
@0
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (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 n)) x) n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (pow x (/ 1 n)) x) (+ (* (/ (pow x (/ 1 n)) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (/ (pow x (/ 1 n)) 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) (+ (/ (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (+ (* (/ (pow x (/ 1 n)) x) (+ (/ (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n)))) (/ (pow x (/ 1 n)) n)) x) (+ (* (/ (pow x (/ 1 n)) x) (+ (/ (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n)))) (/ (pow x (/ 1 n)) n)) (log x) (/ 1/2 (* n n)) (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))))
123.0ms
x
@inf
((/ x (/ 1 (+ (* (+ (* (+ (* 1/24 x) -1/6) x) 1/2) x) -1))) (/ -1 (- (exp (neg x)) 1)) (- (exp (neg x)) 1) (/ 1 (+ (* (+ (* (+ (* 1/24 x) -1/6) x) 1/2) x) -1)) (/ -1 (- (exp (neg x)) 1)) (- (exp (neg x)) 1) (* (+ (* 1/2 x) -1) x) (+ (* 1/2 x) -1) (/ -1 (- (exp (neg x)) 1)) (- (exp (neg x)) 1) (* (+ (* (+ (* (+ (* 1/24 x) -1/6) x) 1/2) x) -1) x) (+ (* (+ (* (+ (* 1/24 x) -1/6) x) 1/2) x) -1) (/ -1 (- (exp (neg x)) 1)) (- (exp (neg x)) 1) (* (+ (* (+ (* (/ (+ (* 1/576 (* x x)) -1/36) (+ (* 1/24 x) 1/6)) x) 1/2) x) -1) x) (+ (* (+ (* (/ (+ (* 1/576 (* x x)) -1/36) (+ (* 1/24 x) 1/6)) x) 1/2) x) -1) (/ (- (* (* (* 1/2 x) x) (* (* 1/2 x) x)) (* x x)) (- (* (* 1/2 x) x) (neg x))) (- (* (* 1/2 x) x) (neg x)) (/ -1 (- (exp (neg x)) 1)) (- (exp (neg x)) 1) (+ (* 1/24 x) -1/6) (+ (* (+ (* 1/24 x) -1/6) x) 1/2) (* (+ (* 1/24 x) -1/6) x) (* (* (+ (* 1/24 x) -1/6) x) x) (/ (+ (* 1/576 (* x x)) -1/36) (+ (* 1/24 x) 1/6)) (+ (* 1/24 x) 1/6) (+ (* 1/576 (* x x)) -1/36) (- (* (* (* 1/2 x) x) (* (* 1/2 x) x)) (* x x)) (* (* (* 1/2 x) x) (* (* 1/2 x) x)))
108.0ms
n
@inf
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (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 n)) x) n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (pow x (/ 1 n)) x) (+ (* (/ (pow x (/ 1 n)) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (/ (pow x (/ 1 n)) 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) (+ (/ (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (+ (* (/ (pow x (/ 1 n)) x) (+ (/ (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n)))) (/ (pow x (/ 1 n)) n)) x) (+ (* (/ (pow x (/ 1 n)) x) (+ (/ (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))) x) (- (/ 1/2 (* n n)) (/ 1/2 n)))) (/ (pow x (/ 1 n)) n)) (log x) (/ 1/2 (* n n)) (- (+ (/ 1/3 n) (/ 1/6 (pow n 3))) (/ 1/2 (* n n))))
69.0ms
n
@-inf
((* (pow n -1) (- (log (+ 1 x)) (log x))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow n -1) (- (log (+ 1 x)) (log x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (neg (log x)) (/ 1 (/ n (- (log (+ 1 x)) (log x)))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ n (- (log (+ 1 x)) (log x))) (/ (- (pow (+ 1 x) (/ 2 n)) (pow x (/ 2 n))) (+ (pow x (pow n -1)) (exp (/ (log (+ 1 x)) n)))) (- (pow (+ 1 x) (/ 2 n)) (pow x (/ 2 n))) (pow (+ 1 x) (/ 2 n)) (+ 1 x) (log x) (/ (log (+ 1 x)) n))

preprocess4.8s (1.7%)

Memory
-150.4MiB live, 4 674.3MiB 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 10 216 to 4 223 computations (58.7% saved)

regimes3.7s (1.4%)

Memory
38.4MiB live, 4 783.5MiB allocated
Counts
3 508 → 328
Calls

43 calls:

1.0s
x
308.0ms
eps
157.0ms
b
148.0ms
b_2
131.0ms
a
Compiler

Compiled 2 110 to 2 011 computations (4.7% saved)

analyze2.1s (0.8%)

Memory
-246.0MiB live, 2 134.2MiB 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)

bsearch1.3s (0.5%)

Memory
-93.1MiB live, 1 383.0MiB allocated
Algorithm
74×binary-search
36×left-value
Stop Event
69×narrow-enough
5×predicate-same
Samples
372.0ms3 634×0valid
223.0ms713×1valid
174.0ms381×2valid
106.0ms788×0invalid
6.0ms73×0exit
2.0ms8×3valid
Compiler

Compiled 11 064 to 10 988 computations (0.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 592.0ms
ival-pow: 112.0ms (18.9% of total)
ival-mult: 108.0ms (18.3% of total)
adjust: 82.0ms (13.9% of total)
ival-div: 74.0ms (12.5% of total)
ival-sub: 52.0ms (8.8% of total)
ival-neg: 42.0ms (7.1% of total)
ival-expm1: 34.0ms (5.7% of total)
ival-sqrt: 30.0ms (5.1% of total)
ival-add: 20.0ms (3.4% of total)
ival-cos: 20.0ms (3.4% of total)
ival-true: 5.0ms (0.8% of total)
ival-cbrt: 3.0ms (0.5% of total)
ival-sin: 3.0ms (0.5% of total)
exact: 3.0ms (0.5% of total)
ival-exp: 2.0ms (0.3% of total)
ival-assert: 2.0ms (0.3% of total)

start1.0ms (0%)

Memory
1.8MiB live, 1.7MiB allocated

end0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated

Profiling

Loading profile data...