Herbie run

Date:Wednesday, October 2nd, 2024
Commit:e7d6e0c5 on bhargav-log-space
Hostname:nightly with Racket 8.10
Seed:2024276
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: 4.3min)

sample2.0min (45.9%)

Memory
428.6MiB live, 112 559.0MiB allocated
Samples
29.7s41 545×2valid
24.9s143 368×0invalid
21.2s92 032×1valid
9.3s4 838×5exit
8.4s94 538×0valid
2.1s3 051×3valid
491.0ms2 354×1exit
320.0ms4 125×0exit
13.0ms6×4exit
5.0ms2×3exit
3.0ms3×2exit
2.0ms2×4valid
Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-tan: 13.4s (16.8% of total)
ival-pow: 9.3s (11.6% of total)
adjust: 6.4s (8% of total)
ival-mult: 6.3s (7.9% of total)
const: 5.2s (6.5% of total)
ival-cos: 4.7s (5.9% of total)
ival-div: 4.3s (5.4% of total)
ival-sub: 4.2s (5.3% of total)
ival-add: 3.6s (4.5% of total)
ival-log: 3.6s (4.5% of total)
ival-sin: 3.6s (4.5% of total)
ival-exp: 2.4s (3% of total)
ival-<=: 2.1s (2.7% of total)
ival-fabs: 2.1s (2.6% of total)
ival-expm1: 1.9s (2.4% of total)
ival-sqrt: 1.3s (1.6% of total)
ival-<: 1.3s (1.6% of total)
ival-log1p: 1.2s (1.5% of total)
ival-and: 627.0ms (0.8% of total)
ival-fmin: 462.0ms (0.6% of total)
ival-atan: 412.0ms (0.5% of total)
ival-cbrt: 368.0ms (0.5% of total)
ival->: 351.0ms (0.4% of total)
exact: 349.0ms (0.4% of total)
ival-neg: 279.0ms (0.3% of total)
ival-assert: 150.0ms (0.2% of total)
ival-true: 72.0ms (0.1% of total)
Bogosity

simplify30.9s (12%)

Memory
326.9MiB live, 26 146.0MiB allocated
Algorithm
211×egg-herbie
Stop Event
279×iter limit
145×node limit
66×saturated
Counts
25 428 → 25 000

soundness25.6s (9.9%)

Memory
330.6MiB live, 14 312.6MiB allocated
Stop Event
172×iter limit
115×node limit
18×fuel
7×done
2×saturated
Compiler

Compiled 7 288 to 4 374 computations (40% saved)

localize19.2s (7.5%)

Memory
-25.1MiB live, 17 649.5MiB allocated
Samples
7.0s5 317×2valid
6.0s8 814×1valid
2.5s8 596×0valid
417.0ms331×3valid
217.0ms739×0invalid
20.0ms10×5exit
2.0ms1×4valid
Compiler

Compiled 35 164 to 5 106 computations (85.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.6s
ival-mult: 2.2s (17.2% of total)
adjust: 1.7s (13.7% of total)
ival-div: 1.6s (13.1% of total)
ival-add: 1.1s (8.9% of total)
ival-tan: 1.0s (8.3% of total)
const: 778.0ms (6.2% of total)
ival-cos: 570.0ms (4.5% of total)
ival-sub: 534.0ms (4.3% of total)
ival-pow: 501.0ms (4% of total)
ival-log: 440.0ms (3.5% of total)
ival-exp: 382.0ms (3% of total)
ival-sqrt: 347.0ms (2.8% of total)
ival-neg: 336.0ms (2.7% of total)
ival-sin: 333.0ms (2.7% of total)
ival-pow2: 163.0ms (1.3% of total)
ival-log1p: 152.0ms (1.2% of total)
ival-expm1: 111.0ms (0.9% of total)
ival-cbrt: 53.0ms (0.4% of total)
ival-cosh: 40.0ms (0.3% of total)
exact: 40.0ms (0.3% of total)
ival-sinh: 23.0ms (0.2% of total)
ival-true: 21.0ms (0.2% of total)
ival-hypot: 13.0ms (0.1% of total)
ival-assert: 12.0ms (0.1% of total)
ival-copysign: 11.0ms (0.1% of total)
ival-fabs: 9.0ms (0.1% of total)

eval18.2s (7.1%)

Memory
175.1MiB live, 21 034.4MiB allocated
Compiler

Compiled 2 505 726 to 260 308 computations (89.6% saved)

rewrite17.9s (7%)

Memory
111.4MiB live, 17 264.9MiB allocated
Stop Event
188×iter limit
93×node limit
Counts
1 419 → 57 901

explain7.3s (2.8%)

Memory
-12.4MiB live, 7 140.7MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation482523
log.f64#fsensitivity7592
+.f64#fcancellation6711
sqrt.f64#foflow-rescue4060
/.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/u270
↳(*.f64 b eps)underflow142
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow152
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow142
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow234
↳(*.f64 a eps)underflow152
sqrt.f64#fuflow-rescue240
/.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))))u/u230
↳(*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64)))underflow207
↳(*.f64 (+.f64 a b) eps)underflow112
↳(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))underflow112
↳(*.f64 b eps)underflow142
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow152
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow142
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow234
↳(*.f64 a eps)underflow152
cos.f64(cos.f64 (+.f64 x eps))sensitivity10
sin.f64(sin.f64 (+.f64 x eps))sensitivity10
-.f64(-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (*.f64 n (log.f64 n)))oflow-left10
tan.f64(tan.f64 (+.f64 x eps))sensitivity10
Confusion
Predicted +Predicted -
+470122
-821856
Precision
0.8513219847881203
Recall
0.9953419436798645
Confusion?
Predicted +Predicted MaybePredicted -
+4701913
-82116840
Precision?
0.8491076257436452
Recall?
0.9972475121744654
Freqs
test
numberfreq
0878
14601
2675
3196
450
Total Confusion?
Predicted +Predicted MaybePredicted -
+2500
-000
Precision?
1.0
Recall?
1.0
Samples
1.7s2 452×2valid
1.2s5 040×1valid
503.0ms5 116×0valid
118.0ms210×3valid
Compiler

Compiled 4 436 to 1 736 computations (60.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.7s
ival-tan: 603.0ms (22.2% of total)
ival-sub: 383.0ms (14.1% of total)
adjust: 342.0ms (12.6% of total)
ival-cos: 227.0ms (8.4% of total)
ival-log: 187.0ms (6.9% of total)
ival-div: 172.0ms (6.3% of total)
ival-add: 169.0ms (6.2% of total)
ival-sin: 146.0ms (5.4% of total)
ival-exp: 128.0ms (4.7% of total)
ival-mult: 121.0ms (4.5% of total)
ival-sqrt: 69.0ms (2.5% of total)
ival-log1p: 59.0ms (2.2% of total)
ival-expm1: 57.0ms (2.1% of total)
ival-cbrt: 16.0ms (0.6% of total)
ival-true: 12.0ms (0.4% 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)

prune5.6s (2.2%)

Memory
-617.7MiB live, 8 241.4MiB allocated
Counts
97 233 → 1 644
Compiler

Compiled 51 857 to 30 691 computations (40.8% saved)

series4.3s (1.7%)

Memory
-188.2MiB live, 3 778.0MiB allocated
Counts
1 419 → 25 428
Calls

441 calls:

TimeVariablePointExpression
286.0ms
x
@0
((/ -1 (- (exp (neg x)) 1)) (- (exp (neg x)) 1) (neg x) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (+ 1/2 (/ 1 x))) (+ 1/2 (/ 1 x)) (/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (* (+ (* (- (exp x) -1) (exp x)) 1) (exp x)) (- (exp (* 3 x)) 1)) (* (+ (* (- (exp x) -1) (exp x)) 1) (exp x)) (+ (* (- (exp x) -1) (exp x)) 1) (- (exp x) -1) (- (exp (* 3 x)) 1))
166.0ms
b
@0
((/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (/ (+ b a) b) a) (+ (/ 1 a) (/ 1 b)) (/ 1 a) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (+ a b) (* a b) (/ (+ a b) (* a b)) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (/ (+ b a) b) a) (/ (+ b a) b) (/ a b) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (/ (+ b a) b) a) (/ (+ (/ b a) 1) b) (+ (/ b a) 1) (/ 1 (/ (* a b) (+ a b))) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (* a b) (+ a b)))
55.0ms
x
@inf
((- (cbrt (+ x 1)) (cbrt x)) (cbrt (+ x 1)) (+ x 1) (cbrt x))
54.0ms
eps
@inf
((- (exp (* (+ a b) eps)) 1) (- (exp (* a eps)) 1) (- (exp (* b eps)) 1) (* eps (- (exp (* (+ a b) eps)) 1)) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))))
52.0ms
b
@-inf
((* (/ 1/2 a) (- (sqrt (+ (* (* c -4) a) (* b b))) b)) (/ 1/2 a) (- (sqrt (+ (* (* c -4) a) (* b b))) b) (sqrt (+ (* (* c -4) a) (* b b))) (/ (+ (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (+ (* (/ (/ c b) b) b) (/ (neg b) a)) (/ c b) (/ (- (/ (* c a) b) b) a) (/ (+ (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (+ (* (/ (/ c b) b) b) (/ (neg b) a)) (- (/ (* c a) b) b) (+ (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (/ (+ (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (neg b) (sqrt (- (* b b) (* 4 (* a c)))) (/ (- (* (* (sqrt (+ (* (* a c) -4) (* b b))) 1/2) a) (* a (* b 1/2))) (* a a)) (- (* (* (sqrt (+ (* (* a c) -4) (* b b))) 1/2) a) (* a (* b 1/2))) (* (* (sqrt (+ (* (* a c) -4) (* b b))) 1/2) a) (* (sqrt (+ (* (* a c) -4) (* b b))) 1/2) (+ (* (* c -4) a) (* b b)) (/ (* c a) b) (+ (* (* c -2) (/ a b)) b) (sqrt (+ (* (* a c) -4) (* b b))) (+ (* (* a c) -4) (* b b)))

preprocess3.8s (1.5%)

Memory
13.1MiB live, 3 966.9MiB allocated
Algorithm
25×egg-herbie
Stop Event
50×iter limit
46×saturated
4×node limit
Compiler

Compiled 7 936 to 3 615 computations (54.4% saved)

regimes3.7s (1.4%)

Memory
-101.6MiB live, 3 565.1MiB allocated
Counts
3 340 → 249
Calls

38 calls:

1.1s
x
275.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
243.0ms
eps
215.0ms
(+.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))
128.0ms
b
Compiler

Compiled 1 897 to 1 753 computations (7.6% saved)

analyze1.6s (0.6%)

Memory
70.6MiB live, 1 817.1MiB 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)

bsearch909.0ms (0.4%)

Memory
-19.3MiB live, 861.1MiB allocated
Algorithm
48×binary-search
14×left-value
Stop Event
46×narrow-enough
2×predicate-same
Samples
431.0ms3 139×0valid
67.0ms404×1valid
63.0ms700×0invalid
31.0ms164×2valid
1.0ms5×3valid
Compiler

Compiled 7 309 to 7 564 computations (-3.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 454.0ms
ival-sin: 140.0ms (30.8% of total)
ival-mult: 97.0ms (21.3% of total)
ival-add: 49.0ms (10.8% of total)
ival-div: 38.0ms (8.4% of total)
ival-sub: 33.0ms (7.3% of total)
ival-sqrt: 28.0ms (6.2% of total)
ival-neg: 23.0ms (5.1% of total)
ival-cos: 17.0ms (3.7% of total)
adjust: 13.0ms (2.9% of total)
ival-cbrt: 5.0ms (1.1% of total)
ival-expm1: 3.0ms (0.7% of total)
ival-true: 3.0ms (0.7% of total)
exact: 3.0ms (0.7% of total)
ival-exp: 2.0ms (0.4% of total)
ival-assert: 2.0ms (0.4% of total)

start1.0ms (0%)

Memory
1.9MiB live, 1.8MiB allocated

end0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated

Profiling

Loading profile data...