Herbie run

Date:Friday, November 8th, 2024
Commit:e1f2a9b8 on fix-1030
Hostname:nightly with Racket 8.10
Seed:2024313
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: 4.4min)

sample2.0min (44.4%)

Memory
379.9MiB live, 103 751.2MiB allocated
Samples
29.5s41 559×2valid
26.2s145 403×0invalid
19.2s92 266×1valid
9.9s4 852×5exit
9.2s94 385×0valid
2.5s2 950×3valid
558.0ms2 353×1exit
300.0ms4 177×0exit
15.0ms4exit
9.0ms4valid
6.0ms2exit
1.0ms3exit
Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-tan: 13.3s (16.5% of total)
ival-pow: 9.9s (12.3% of total)
ival-mult: 7.2s (8.9% of total)
adjust: 6.5s (8% of total)
const: 5.4s (6.7% of total)
ival-cos: 4.4s (5.4% of total)
ival-div: 4.0s (5% of total)
ival-sub: 4.0s (5% of total)
ival-sin: 3.6s (4.4% of total)
ival-add: 3.2s (4% of total)
ival-log: 3.1s (3.9% of total)
ival-exp: 2.6s (3.3% of total)
ival-<=: 2.4s (3% of total)
ival-fabs: 2.3s (2.9% of total)
ival-expm1: 2.0s (2.4% of total)
ival-sqrt: 1.4s (1.7% of total)
ival-<: 1.1s (1.4% of total)
ival-log1p: 1.1s (1.4% of total)
ival-fmin: 690.0ms (0.9% of total)
ival-and: 638.0ms (0.8% of total)
ival-atan: 390.0ms (0.5% of total)
ival->: 387.0ms (0.5% of total)
exact: 355.0ms (0.4% of total)
ival-cbrt: 281.0ms (0.3% of total)
ival-neg: 263.0ms (0.3% of total)
ival-assert: 158.0ms (0.2% of total)
ival-true: 71.0ms (0.1% of total)
Bogosity

simplify36.2s (13.6%)

Memory
598.4MiB live, 26 951.9MiB allocated
Algorithm
248×egg-herbie
Stop Event
327×iter limit
191×node limit
60×saturated
Counts
8 693 → 8 592

soundness28.2s (10.6%)

Memory
225.2MiB live, 15 384.8MiB allocated
Stop Event
208×iter limit
134×node limit
22×fuel
done
saturated
Compiler

Compiled 15 483 to 7 143 computations (53.9% saved)

rewrite23.9s (9%)

Memory
-168.7MiB live, 19 811.8MiB allocated
Stop Event
225×iter limit
108×node limit
saturated
unsound
Counts
1 607 → 64 459

localize20.7s (7.8%)

Memory
29.9MiB live, 20 200.0MiB allocated
Samples
6.9s5 803×2valid
5.3s10 002×1valid
2.8s10 998×0valid
1.1s530×3valid
346.0ms769×0invalid
21.0ms16×1invalid
15.0ms12×5exit
8.0ms27×0exit
2.0ms2invalid
1.0ms4valid
Compiler

Compiled 45 223 to 6 643 computations (85.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.8s
ival-mult: 2.1s (16.1% of total)
ival-tan: 1.8s (14.2% of total)
ival-div: 1.5s (12% of total)
adjust: 1.5s (11.6% of total)
ival-add: 1.1s (8.3% of total)
ival-log: 667.0ms (5.2% of total)
ival-sub: 586.0ms (4.6% of total)
ival-sin: 576.0ms (4.5% of total)
const: 571.0ms (4.4% of total)
ival-pow: 545.0ms (4.2% of total)
ival-cos: 473.0ms (3.7% of total)
ival-exp: 348.0ms (2.7% of total)
ival-neg: 231.0ms (1.8% of total)
ival-sqrt: 211.0ms (1.6% of total)
ival-log1p: 198.0ms (1.5% of total)
ival-cosh: 101.0ms (0.8% of total)
ival-pow2: 91.0ms (0.7% of total)
ival-expm1: 90.0ms (0.7% of total)
ival-cbrt: 65.0ms (0.5% of total)
exact: 45.0ms (0.4% of total)
ival-true: 25.0ms (0.2% of total)
ival-atan2: 14.0ms (0.1% of total)
ival-assert: 13.0ms (0.1% of total)
ival-atan: 10.0ms (0.1% of total)
ival-fabs: 1.0ms (0% of total)

eval12.4s (4.7%)

Memory
233.8MiB live, 15 293.0MiB allocated
Compiler

Compiled 2 698 237 to 282 757 computations (89.5% saved)

explain5.6s (2.1%)

Memory
63.3MiB live, 6 074.6MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation413622
log.f64#fsensitivity7640
/.f64#fu/u4470
sqrt.f64#foflow-rescue4220
+.f64#fcancellation3630
/.f64#fu/n1050
pow.f64(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))sensitivity630
/.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/u220
(*.f64 b eps)underflow150
(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow142
(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow150
(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow236
(*.f64 a eps)underflow142
sqrt.f64#fuflow-rescue200
-.f64#fnan-rescue140
/.f64(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))n/o40
(*.f64 x x)overflow59
/.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
exp.f64#fsensitivity20
cos.f64(cos.f64 (+.f64 x eps))sensitivity10
tan.f64(tan.f64 (+.f64 x eps))sensitivity10
Confusion
Predicted +Predicted -
+52278
-1381795
Precision
0.9742777260018639
Recall
0.9984718242597899
Confusion?
Predicted +Predicted MaybePredicted -
+522771
-138131782
Precision?
0.9719591457753017
Recall?
0.9998089780324737
Freqs
test
numberfreq
01803
14569
2640
3106
450
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.7s2 650×2valid
1.1s5 672×1valid
506.0ms5 798×0valid
150.0ms216×3valid
Compiler

Compiled 3 034 to 980 computations (67.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.7s
ival-tan: 745.0ms (27.2% of total)
ival-sin: 246.0ms (9% of total)
adjust: 243.0ms (8.9% of total)
ival-div: 215.0ms (7.8% of total)
ival-cos: 208.0ms (7.6% of total)
ival-log: 201.0ms (7.3% of total)
ival-sub: 182.0ms (6.6% of total)
ival-exp: 138.0ms (5% of total)
ival-mult: 109.0ms (4% of total)
ival-add: 90.0ms (3.3% of total)
ival-pow: 89.0ms (3.2% of total)
ival-log1p: 62.0ms (2.3% of total)
ival-sqrt: 58.0ms (2.1% of total)
ival-cbrt: 49.0ms (1.8% of total)
ival-atan: 38.0ms (1.4% of total)
ival-expm1: 28.0ms (1% 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)

series4.7s (1.8%)

Memory
6.2MiB live, 4 475.7MiB allocated
Counts
1 607 → 8 693
Calls

504 calls:

TimeVariablePointExpression
249.0ms
c
@0
((/ (- (neg (sqrt (+ (* -4 (* c a)) (* b b)))) b) (* 2 a)) (- (neg (sqrt (+ (* -4 (* c a)) (* b b)))) b) (neg (sqrt (+ (* -4 (* c a)) (* b b)))) (sqrt (+ (* -4 (* c a)) (* b b))) (/ (- (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (/ c (neg b)) (neg b) (/ (- (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (- (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (* (* (/ a b) -2) c) (* (/ a b) -2) (/ 1/2 (/ a (- b (sqrt (+ (* -4 (* c a)) (* b b)))))) (/ a (- b (sqrt (+ (* -4 (* c a)) (* b b))))) (- b (sqrt (+ (* -4 (* c a)) (* b b)))) (/ (- (neg b) (/ (+ (* -4 (* c a)) (* b b)) (sqrt (+ (* -4 (* c a)) (* b b))))) (* 2 a)) (- (neg b) (/ (+ (* -4 (* c a)) (* b b)) (sqrt (+ (* -4 (* c a)) (* b b))))) (/ (+ (* -4 (* c a)) (* b b)) (sqrt (+ (* -4 (* c a)) (* b b)))) (+ (* -4 (* c a)) (* b b)) (* 2 a))
98.0ms
x
@inf
((+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x))) (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (exp (* (log (tan (+ eps x))) 1)) (* (log (tan (+ eps x))) 1) (- (exp (* (log (tan (+ eps x))) 1)) (tan x)) (log (tan (+ eps x))) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* 1 (/ 1 (tan x))) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin (+ eps x)) (+ eps x) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (sin x) 4) (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (tan (+ eps x)) (/ 1 (tan (+ eps x))) (* (cos (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x))))
96.0ms
c
@-inf
((/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (/ (+ (* (/ -1/8 b_2) (/ (* (* c c) a) b_2)) (* -1/2 c)) b_2) (+ (* (/ -1/8 b_2) (/ (* (* c c) a) b_2)) (* -1/2 c)) (* (+ (* (/ -1/8 b_2) (* a (/ c b_2))) -1/2) c) (/ -1/2 (/ b_2 c)) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (/ b_2 c) (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (neg b_2) (sqrt (- (* b_2 b_2) (* a c))) (exp (* (log (/ a (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) -1)) (* (log (/ a (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) -1) (log (/ a (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ a (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (+ (neg b_2) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4))) (+ (* (neg (log a)) -2) (log (* c c))) (/ (+ (neg b_2) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4))) a) (* a (/ c b_2)) (- (* b_2 b_2) (* a c)) (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (log (pow (+ (* c a) (* b_2 b_2)) 2)) (log (* c c)) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4)))
91.0ms
N
@inf
((- (log (+ N 1)) (log N)) (/ (- (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) -1) N) (- (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) -1) (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) (- (log (+ N 1)) (log N)) (/ 1 N) (- (log (+ 1 N)) (log N)) (log (+ 1 N)) (log N) (+ (* (pow (log (+ 1 N)) 3) (pow (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) -1)) (neg (/ (pow (log N) 3) (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2))))) (pow (log (+ 1 N)) 3) (pow (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) -1) (/ (- (* 1 (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2))) (* (/ (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) (pow (log (+ 1 N)) 3)) (pow (log N) 3))) (* (/ (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) (pow (log (+ 1 N)) 3)) (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)))) (- (* 1 (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2))) (* (/ (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) (pow (log (+ 1 N)) 3)) (pow (log N) 3))) (* 1 (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2))) (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) (/ (- (/ 1/4 N) 1/3) N) (- (/ 1/4 N) 1/3) (pow (log N) 3) (pow (log (+ 1 N)) 2))
86.0ms
c
@0
((/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (/ (+ (* (/ -1/8 b_2) (/ (* (* c c) a) b_2)) (* -1/2 c)) b_2) (+ (* (/ -1/8 b_2) (/ (* (* c c) a) b_2)) (* -1/2 c)) (* (+ (* (/ -1/8 b_2) (* a (/ c b_2))) -1/2) c) (/ -1/2 (/ b_2 c)) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (/ b_2 c) (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) (neg b_2) (sqrt (- (* b_2 b_2) (* a c))) (exp (* (log (/ a (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) -1)) (* (log (/ a (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) -1) (log (/ a (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ a (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (+ (neg b_2) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4))) (+ (* (neg (log a)) -2) (log (* c c))) (/ (+ (neg b_2) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4))) a) (* a (/ c b_2)) (- (* b_2 b_2) (* a c)) (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (log (pow (+ (* c a) (* b_2 b_2)) 2)) (log (* c c)) (exp (* (log (pow (+ (* c a) (* b_2 b_2)) 2)) 1/4)))

prune4.5s (1.7%)

Memory
-494.6MiB live, 6 099.2MiB allocated
Counts
74 285 → 1 964
Compiler

Compiled 110 015 to 55 023 computations (50% saved)

regimes4.0s (1.5%)

Memory
-1.5MiB live, 4 691.5MiB allocated
Counts
4 486 → 338
Calls

43 calls:

1.2s
x
383.0ms
eps
155.0ms
n
153.0ms
(-.f64 (cbrt.f64 (+.f64 x #s(literal 1 binary64))) (cbrt.f64 x))
139.0ms
b
Compiler

Compiled 2 297 to 2 125 computations (7.5% saved)

preprocess3.9s (1.5%)

Memory
-136.2MiB live, 3 866.4MiB allocated
Algorithm
28×egg-herbie
Stop Event
56×iter limit
50×saturated
node limit
Compiler

Compiled 18 400 to 5 291 computations (71.2% saved)

bsearch1.7s (0.6%)

Memory
-67.6MiB live, 1 210.3MiB allocated
Algorithm
75×binary-search
32×left-value
Stop Event
65×narrow-enough
10×predicate-same
Samples
432.0ms3 883×0valid
145.0ms846×1valid
122.0ms387×2valid
83.0ms831×0invalid
28.0ms90×0exit
1.0ms3valid
Compiler

Compiled 23 406 to 18 085 computations (22.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 611.0ms
ival-pow: 147.0ms (24% of total)
ival-mult: 118.0ms (19.3% of total)
ival-div: 80.0ms (13.1% of total)
ival-sqrt: 53.0ms (8.7% of total)
ival-sub: 43.0ms (7% of total)
adjust: 35.0ms (5.7% of total)
ival-neg: 35.0ms (5.7% of total)
ival-cos: 34.0ms (5.6% of total)
ival-add: 34.0ms (5.6% of total)
ival-cbrt: 10.0ms (1.6% of total)
ival-expm1: 5.0ms (0.8% of total)
ival-true: 5.0ms (0.8% of total)
ival-sin: 4.0ms (0.7% of total)
exact: 4.0ms (0.7% of total)
ival-exp: 2.0ms (0.3% of total)
ival-assert: 2.0ms (0.3% of total)
ival-log1p: 1.0ms (0.2% of total)
ival-log: 0.0ms (0% of total)

analyze1.7s (0.6%)

Memory
92.6MiB live, 1 900.9MiB 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)

start1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated

end0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated

Profiling

Loading profile data...