Herbie run

Date:Thursday, October 3rd, 2024
Commit:6e4f2b10 on rival-256-starting-prec
Hostname:nightly with Racket 8.10
Seed:2024277
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: 14.1min)

soundness3.1min (22.4%)

Memory
-99.4MiB live, 33 523.8MiB allocated
Stop Event
324×iter limit
210×node limit
36×fuel
21×done
saturated
unsound
Compiler

Compiled 39 314 to 17 824 computations (54.7% saved)

end2.1min (15.1%)

Memory
-4.2MiB live, 5 146.5MiB allocated

sample1.7min (11.9%)

Memory
264.8MiB live, 108 319.5MiB allocated
Samples
1.1min445 652×0valid
9.5s22 895×1valid
2.5s4 455×0invalid
838.0ms8 058×0exit
489.0ms1 637×2valid
148.0ms421×3valid
Precisions
Click to see histograms. Total time spent on operations: 55.6s
ival-mult: 16.4s (29.6% of total)
ival-add: 6.0s (10.8% of total)
const: 4.8s (8.7% of total)
ival-div: 4.2s (7.6% of total)
ival-exp: 3.8s (6.8% of total)
ival-hypot: 2.9s (5.3% of total)
ival-log: 2.4s (4.4% of total)
ival-sub: 2.0s (3.6% of total)
ival-sin: 1.7s (3% of total)
adjust: 1.2s (2.2% of total)
ival-asin: 1.2s (2.2% of total)
ival-cos: 1.2s (2.1% of total)
ival-asinh: 1.1s (2.1% of total)
ival-atan2: 958.0ms (1.7% of total)
ival-sqrt: 897.0ms (1.6% of total)
ival->: 535.0ms (1% of total)
ival-pow: 530.0ms (1% of total)
ival-neg: 471.0ms (0.8% of total)
ival-acosh: 414.0ms (0.7% of total)
ival-atanh: 385.0ms (0.7% of total)
exact: 385.0ms (0.7% of total)
ival-pi: 351.0ms (0.6% of total)
ival-<=: 303.0ms (0.5% of total)
ival-sinu: 291.0ms (0.5% of total)
ival-true: 283.0ms (0.5% of total)
ival-cosu: 230.0ms (0.4% of total)
ival-fabs: 204.0ms (0.4% of total)
ival-assert: 197.0ms (0.4% of total)
ival->=: 98.0ms (0.2% of total)
ival-and: 82.0ms (0.1% of total)
Bogosity

prune1.5min (11%)

Memory
-530.0MiB live, 25 764.9MiB allocated
Counts
224 153 → 3 207
Compiler

Compiled 189 779 to 89 845 computations (52.7% saved)

simplify1.4min (10%)

Memory
533.2MiB live, 71 788.0MiB allocated
Algorithm
453×egg-herbie
Stop Event
594×iter limit
274×node limit
179×saturated
Counts
59 580 → 58 815

regimes1.0min (7.5%)

Memory
44.0MiB live, 20 244.8MiB allocated
Counts
9 230 → 919
Calls

132 calls:

16.6s
(-.f64 #s(literal 1 binary64) x)
16.0s
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
15.0s
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
787.0ms
re
787.0ms
y.re
Compiler

Compiled 13 710 to 9 864 computations (28.1% saved)

eval50.6s (6%)

Memory
1 155.4MiB live, 73 229.2MiB allocated
Compiler

Compiled 10 484 985 to 614 708 computations (94.1% saved)

rewrite43.5s (5.2%)

Memory
-150.4MiB live, 47 329.8MiB allocated
Stop Event
416×iter limit
187×node limit
unsound
saturated
Counts
2 925 → 111 733

localize32.8s (3.9%)

Memory
-990.7MiB live, 38 173.4MiB allocated
Samples
15.6s42 498×0valid
5.3s4 007×1valid
1.9s3 259×0invalid
570.0ms468×1exit
164.0ms207×0exit
106.0ms193×2valid
68.0ms35×5exit
17.0ms21×3valid
Compiler

Compiled 147 061 to 11 880 computations (91.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.9s
ival-mult: 5.4s (30.2% of total)
ival-add: 2.2s (12.5% of total)
ival-div: 2.0s (11% of total)
ival-log: 1.2s (6.8% of total)
const: 1.2s (6.6% of total)
ival-pow: 825.0ms (4.6% of total)
ival-exp: 614.0ms (3.4% of total)
ival-sub: 594.0ms (3.3% of total)
adjust: 586.0ms (3.3% of total)
ival-neg: 526.0ms (2.9% of total)
ival-hypot: 523.0ms (2.9% of total)
ival-sqrt: 391.0ms (2.2% of total)
ival-cos: 369.0ms (2.1% of total)
ival-sin: 262.0ms (1.5% of total)
ival-asin: 221.0ms (1.2% of total)
ival-pow2: 178.0ms (1% of total)
ival-atan2: 150.0ms (0.8% of total)
ival-acos: 138.0ms (0.8% of total)
ival-log1p: 121.0ms (0.7% of total)
exact: 104.0ms (0.6% of total)
ival-fabs: 70.0ms (0.4% of total)
ival-copysign: 47.0ms (0.3% of total)
ival-true: 45.0ms (0.3% of total)
ival-pi: 35.0ms (0.2% of total)
ival-cosu: 23.0ms (0.1% of total)
ival-assert: 22.0ms (0.1% of total)
ival-sinu: 20.0ms (0.1% of total)
ival-cosh: 18.0ms (0.1% of total)

explain19.8s (2.3%)

Memory
-17.6MiB live, 20 002.4MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64#foflow-rescue11530
-.f64#fcancellation7492
/.f64#fo/o5940
/.f64#fo/n2040
sqrt.f32#foflow-rescue1940
sin.f64#fsensitivity1881
cos.f64(cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))sensitivity1820
+.f64#fcancellation1620
sqrt.f64#fuflow-rescue1380
log.f32(log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) #s(literal 1 binary32)))))sensitivity1301
-.f64#fnan-rescue1230
log.f64(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))sensitivity1101
/.f64#fn/o850
/.f64#fu/u770
*.f64#fn*u710
+.f64#fnan-rescue640
*.f64#fn*o340
/.f64#fu/n330
/.f64#fn/u180
*.f64(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)))))o*u40
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64))))overflow4
(pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))overflow4
(exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64))))underflow4
pow.f64(pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))sensitivity30
log.f32(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))oflow-rescue20
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))overflow2
(*.f32 x x)overflow125
(-.f32 (*.f32 x x) #s(literal 1 binary32))overflow125
exp.f64(exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))sensitivity20
cos.f64(cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))oflow-rescue10
(+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))overflow1
(*.f64 x.re x.re)overflow57
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))overflow100
(*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im)overflow1
(*.f64 x.im x.im)overflow56
sin.f64(sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))oflow-rescue10
(+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))overflow1
(*.f64 x.re x.re)overflow57
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))overflow100
(*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im)overflow1
(*.f64 x.im x.im)overflow56
Confusion
Predicted +Predicted -
+359062
-19510745
Precision
0.9484808454425363
Recall
0.9830230010952903
Confusion?
Predicted +Predicted MaybePredicted -
+3590359
-195210743
Precision?
0.9480211081794195
Recall?
0.9838444687842278
Freqs
test
numberfreq
010807
13250
2533
32
Total Confusion?
Predicted +Predicted MaybePredicted -
+3801
-0018
Precision?
1.0
Recall?
0.9743589743589743
Samples
4.0s26 766×0valid
1.3s2 284×1valid
46.0ms116×2valid
5.0ms14×3valid
2.0ms5exit
Compiler

Compiled 19 577 to 2 968 computations (84.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.3s
ival-mult: 885.0ms (27.2% of total)
ival-add: 367.0ms (11.3% of total)
ival-div: 315.0ms (9.7% of total)
ival-log: 270.0ms (8.3% of total)
const: 257.0ms (7.9% of total)
ival-hypot: 184.0ms (5.7% of total)
ival-exp: 179.0ms (5.5% of total)
adjust: 159.0ms (4.9% of total)
ival-sub: 128.0ms (3.9% of total)
ival-cos: 96.0ms (2.9% of total)
ival-sin: 79.0ms (2.4% of total)
ival-atan2: 60.0ms (1.8% of total)
ival-asin: 57.0ms (1.8% of total)
ival-sqrt: 46.0ms (1.4% of total)
ival-true: 27.0ms (0.8% of total)
ival-pow: 24.0ms (0.7% of total)
ival-pi: 22.0ms (0.7% of total)
exact: 22.0ms (0.7% of total)
ival-fabs: 18.0ms (0.6% of total)
ival-assert: 13.0ms (0.4% of total)
ival-copysign: 12.0ms (0.4% of total)
ival-neg: 11.0ms (0.3% of total)
ival-log1p: 10.0ms (0.3% of total)
ival-sinu: 9.0ms (0.3% of total)
ival-cosu: 7.0ms (0.2% of total)

series17.4s (2.1%)

Memory
217.8MiB live, 21 507.9MiB allocated
Counts
2 925 → 59 580
Calls

1203 calls:

TimeVariablePointExpression
405.0ms
y.re
@-inf
((* (/ (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (pow (exp y.im) (atan2 x.im x.re))) (cos (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re))))) (/ (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (pow (exp y.im) (atan2 x.im x.re))) (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (sqrt (+ (* x.im x.im) (* x.re x.re))) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (cos (* (atan2 x.im x.re) y.re))) (* x.re (+ (* (/ 1/2 x.re) (/ (* x.im x.im) x.re)) 1)) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (cos (* (atan2 x.im x.re) y.re))) (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)) (+ (* x.re x.re) (* x.im x.im)) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (* y.re (+ (* y.im (/ (log x.re) y.re)) (atan2 x.im x.re))) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)) (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re))) (cos (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re)))) (pow (exp y.im) (atan2 x.im x.re)) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (sqrt (+ (* x.re x.re) (* x.im x.im))) (cos (* (atan2 x.im x.re) y.re)) (/ (* x.im x.im) x.re) (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)) (sqrt (+ (* x.re x.re) (* x.im x.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) (* (atan2 x.im x.re) y.re) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) (* (+ (* y.im (/ (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (atan2 x.im x.re)) y.re))
260.0ms
x.re
@0
((+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)) (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) (* x.re y.re) (* x.im y.im))
227.0ms
x
@-inf
((copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (log (+ 1 (fabs x))) (fabs x) (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (log x) (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (+ (fabs x) (sqrt (+ (* x x) 1))) (+ (fabs x) x) (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (+ (fabs x) (sqrt (+ (* x x) 1))) (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (+ (fabs x) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1)) (- x (/ -1/2 x)))
179.0ms
d2
@0
((+ (* (- d4 d1) d1) (* (- d2 d3) d1)) (- d4 d1) (* (- d2 d3) d1) (- d2 d3) (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)) (* d4 d1) (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)) (* (- (+ d4 d2) d1) d1) (- (+ d4 d2) d1) (+ d4 d2) (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)) (* (- (- d2 d3) d1) d1) (- (- d2 d3) d1) (- d2 d1) (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)) (* (- (- d2 d3) d1) d1) (- (- d2 d3) d1) (- d2 d3) (neg d3))
178.0ms
re
@inf
((* (/ (/ (atan2 im re) (log base)) (log base)) (log base)) (/ (/ (atan2 im re) (log base)) (log base)) (/ (atan2 im re) (log base)) (atan2 im re) (/ 1 (* (/ 1 (atan2 im re)) (log base))) (* (/ 1 (atan2 im re)) (log base)) (/ 1 (atan2 im re)) (sqrt (pow (/ (log base) (atan2 im re)) -2)) (pow (/ (log base) (atan2 im re)) -2) (/ (log base) (atan2 im re)) (log base) (/ 1 (pow (sqrt (/ (atan2 im re) (log base))) -2)) (pow (sqrt (/ (atan2 im re) (log base))) -2) (sqrt (/ (atan2 im re) (log base))) (pow (pow (/ (log base) (atan2 im re)) -1/4) 4) (pow (/ (log base) (atan2 im re)) -1/4))

preprocess16.9s (2%)

Memory
645.2MiB live, 15 362.9MiB allocated
Algorithm
57×egg-herbie
Stop Event
114×iter limit
76×saturated
38×node limit
Compiler

Compiled 47 448 to 13 791 computations (70.9% saved)

bsearch4.7s (0.6%)

Memory
-55.3MiB live, 4 624.0MiB allocated
Algorithm
244×left-value
216×binary-search
Stop Event
205×narrow-enough
11×predicate-same
Samples
2.1s13 631×0valid
863.0ms1 642×1valid
13.0ms65×2valid
2.0ms3valid
Compiler

Compiled 43 882 to 39 989 computations (8.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.1s
ival-mult: 616.0ms (29.1% of total)
ival-hypot: 340.0ms (16.1% of total)
ival-log: 181.0ms (8.6% of total)
ival-add: 150.0ms (7.1% of total)
ival-sin: 149.0ms (7% of total)
ival-exp: 138.0ms (6.5% of total)
ival-sub: 135.0ms (6.4% of total)
ival-cos: 107.0ms (5.1% of total)
ival-atan2: 102.0ms (4.8% of total)
ival-div: 59.0ms (2.8% of total)
const: 56.0ms (2.6% of total)
adjust: 53.0ms (2.5% of total)
ival-true: 12.0ms (0.6% of total)
ival-sqrt: 8.0ms (0.4% of total)
ival-assert: 6.0ms (0.3% of total)
exact: 4.0ms (0.2% of total)

analyze2.0s (0.2%)

Memory
138.7MiB live, 2 664.0MiB allocated
Algorithm
58×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%86.3%13.7%0%0%0%0
57.6%49.7%36.6%13.7%0%0%0%1
67.2%56.8%27.8%13.7%0%1.7%0%2
72%59%23%13.7%0%4.3%0%3
79.4%63.6%16.5%13.7%0%6.2%0%4
85.9%68.7%11.3%13.7%0%6.3%0%5
89.7%71.4%8.2%13.7%0%6.6%0%6
92.6%73.8%5.9%13.7%0%6.6%0%7
94%74.8%4.7%13.7%0%6.8%0%8
94.7%75.3%4.2%13.7%0%6.8%0%9
96.1%76.4%3.1%13.7%0%6.8%0%10
96.6%76.8%2.7%13.7%0%6.8%0%11
96.9%77%2.5%13.7%0%6.9%0%12
Compiler

Compiled 1 498 to 816 computations (45.5% saved)

start2.0ms (0%)

Memory
6.0MiB live, 5.9MiB allocated

Profiling

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