Herbie run

Date:Friday, September 27th, 2024
Commit:064660f8 on bhargav-log-space
Hostname:nightly with Racket 8.10
Seed:2024271
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: 3.7min)

sample1.3min (35%)

Memory
630.8MiB live, 92 701.3MiB allocated
Samples
31.7s225 497×0valid
9.0s65 943×0invalid
6.8s22 827×1valid
3.8s12 334×1invalid
3.0s9 640×2valid
2.2s6 224×3valid
378.0ms1 924×1exit
131.0ms504×2invalid
36.0ms226×0exit
1.0ms4valid
1.0ms5exit
Precisions
Click to see histograms. Total time spent on operations: 43.3s
ival-mult: 10.7s (24.7% of total)
ival-div: 6.7s (15.4% of total)
ival-sub: 3.6s (8.4% of total)
ival-pow2: 2.7s (6.2% of total)
ival-add: 2.7s (6.2% of total)
ival-sqrt: 2.6s (5.9% of total)
ival-exp: 2.1s (5% of total)
adjust: 2.1s (4.8% of total)
ival-pow: 2.1s (4.7% of total)
ival-sin: 2.0s (4.5% of total)
ival-tan: 1.0s (2.4% of total)
ival-cos: 780.0ms (1.8% of total)
ival-neg: 685.0ms (1.6% of total)
ival-acos: 624.0ms (1.4% of total)
ival-pi: 459.0ms (1.1% of total)
ival-hypot: 397.0ms (0.9% of total)
const: 394.0ms (0.9% of total)
ival-log: 385.0ms (0.9% of total)
exact: 346.0ms (0.8% of total)
ival-true: 265.0ms (0.6% of total)
ival-asin: 192.0ms (0.4% of total)
ival-tanu: 171.0ms (0.4% of total)
ival-assert: 144.0ms (0.3% of total)
ival-fabs: 105.0ms (0.2% of total)
ival-atan: 83.0ms (0.2% of total)
ival-<: 66.0ms (0.2% of total)
ival-and: 11.0ms (0% of total)
Bogosity

simplify29.9s (13.6%)

Memory
291.6MiB live, 29 367.1MiB allocated
Algorithm
162×egg-herbie
Stop Event
216×iter limit
123×node limit
39×saturated
Counts
30 792 → 30 578

soundness21.9s (9.9%)

Memory
193.4MiB live, 14 981.7MiB allocated
Stop Event
140×iter limit
96×node limit
16×fuel
done
Compiler

Compiled 15 023 to 8 965 computations (40.3% saved)

eval17.8s (8.1%)

Memory
274.8MiB live, 24 344.2MiB allocated
Compiler

Compiled 2 521 438 to 229 098 computations (90.9% saved)

rewrite15.9s (7.2%)

Memory
173.9MiB live, 16 876.5MiB allocated
Stop Event
145×iter limit
72×node limit
Counts
1 304 → 47 770

localize11.8s (5.4%)

Memory
2.4MiB live, 14 878.7MiB allocated
Samples
5.3s14 310×0valid
1.6s1 785×1valid
571.0ms1 569×0invalid
544.0ms132×5exit
345.0ms409×2valid
101.0ms87×3valid
73.0ms140×0exit
Compiler

Compiled 39 877 to 5 043 computations (87.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.1s
ival-mult: 1.7s (28.4% of total)
ival-div: 889.0ms (14.7% of total)
ival-add: 875.0ms (14.4% of total)
ival-cos: 426.0ms (7% of total)
adjust: 256.0ms (4.2% of total)
ival-sqrt: 254.0ms (4.2% of total)
ival-pow: 246.0ms (4.1% of total)
ival-sub: 245.0ms (4% of total)
const: 241.0ms (4% of total)
ival-exp: 234.0ms (3.9% of total)
ival-log: 128.0ms (2.1% of total)
ival-tan: 111.0ms (1.8% of total)
ival-neg: 96.0ms (1.6% of total)
ival-sin: 88.0ms (1.5% of total)
ival-pow2: 52.0ms (0.9% of total)
exact: 39.0ms (0.6% of total)
ival-true: 38.0ms (0.6% of total)
ival-tanu: 29.0ms (0.5% of total)
ival-pi: 28.0ms (0.5% of total)
ival-tanh: 15.0ms (0.2% of total)
ival-sinh: 15.0ms (0.2% of total)
ival-assert: 14.0ms (0.2% of total)
ival-cosh: 9.0ms (0.1% of total)
ival-e: 5.0ms (0.1% of total)
ival-cbrt: 2.0ms (0% of total)

regimes9.6s (4.3%)

Memory
148.3MiB live, 11 963.5MiB allocated
Counts
5 837 → 390
Calls

83 calls:

472.0ms
F
415.0ms
x
391.0ms
k
300.0ms
n
290.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 5 542 to 5 928 computations (-7% saved)

analyze9.2s (4.2%)

Memory
-106.0MiB live, 11 931.3MiB allocated
Algorithm
32×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%98.2%1.8%0%0%0%0
22.2%21.8%76.4%1.8%0%0%0%1
22.6%21.8%74.8%1.8%0%1.6%0%2
28.6%26.5%66.3%1.8%0%5.5%0%3
32.6%29.6%61.2%1.8%0%7.4%0%4
35.8%32.3%58%1.8%0%8%0%5
40.1%36.1%54%1.8%0%8.1%0%6
45.5%40.6%48.7%1.8%0%8.9%0%7
47.9%42.1%45.8%1.8%0%10.3%0%8
51%44.7%42.9%1.8%0%10.6%0%9
52.2%45.5%41.7%1.8%0%11%0%10
53.9%46.8%39.9%1.8%0%11.5%0%11
55.7%47.9%38.2%1.8%0%12.2%0%12
Compiler

Compiled 798 to 574 computations (28.1% saved)

series8.0s (3.6%)

Memory
-403.9MiB live, 8 753.8MiB allocated
Counts
1 304 → 30 792
Calls

576 calls:

TimeVariablePointExpression
279.0ms
NdChar
@0
((neg (- (- (- Ec Vef) EDonor) mu)) (+ (+ (+ Ev Vef) EAccept) (neg mu)) (+ (/ NdChar (+ 1 (exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1 (exp (/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT))))) (/ NdChar (+ 1 (exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)))) (exp (/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)) (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT) (/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT) (exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)))
146.0ms
f
@0
((* (* (/ 4 (sqrt (PI))) (log (tanh (* (* (PI) 1/4) f)))) (pow (PI) -1/2)) (* (/ 4 (sqrt (PI))) (log (tanh (* (* (PI) 1/4) f)))) (/ 4 (sqrt (PI))) (sqrt (PI)) (/ (log (tanh (* f (* 1/4 (PI))))) (* 1/4 (PI))) (log (tanh (* f (* 1/4 (PI))))) (tanh (* f (* 1/4 (PI)))) (* (PI) f) (* (* 1/4 (sqrt (PI))) (sqrt (PI))) (/ (/ 4 (PI)) f) (/ 1 (* (* 1/4 (sqrt (PI))) (sqrt (PI)))) (neg (* (/ 1 (* (* 1/4 (sqrt (PI))) (sqrt (PI)))) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (- (log (/ 4 (PI))) (log f)) (/ -4 (PI))) (- (log (/ 4 (PI))) (log f)) (log (/ 4 (PI))) (neg (* (* (pow (PI) -1/2) (/ 4 (sqrt (PI)))) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (* (pow (PI) -1/2) (/ 4 (sqrt (PI)))) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))) (* (pow (PI) -1/2) (/ 4 (sqrt (PI)))) (log (tanh (* (* (PI) 1/4) f))) (* (* (PI) 1/4) f) (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))
136.0ms
F
@0
((+ (* (neg F) (* (/ -1 (sin B)) (pow (+ (* x 2) (+ (* F F) 2)) -1/2))) (/ (neg x) (tan B))) (* (/ -1 (sin B)) (pow (+ (* x 2) (+ (* F F) 2)) -1/2)) (neg F) (/ -1 (sin B)) (+ (neg (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (neg (/ 1 2))))) (/ (+ (* (sqrt (/ 1 (+ (* F F) (+ (* 2 x) 2)))) F) (neg x)) B) (+ (* (sqrt (/ 1 (+ (* F F) (+ (* 2 x) 2)))) F) (neg x)) (sqrt (/ 1 (+ (* F F) (+ (* 2 x) 2)))) (+ (neg (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (neg (/ 1 2))))) (* (neg x) (/ (cos B) (sin B))) (neg x) (/ (cos B) (sin B)) (+ (* (neg x) (/ (cos B) (sin B))) (/ -1 (sin B))) (+ (neg (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (neg (/ 1 2))))) (* (+ (* (+ x 1) (/ 2 (* F F))) 1) (* F F)) (/ 1 2) (* x (/ 1 (tan B))) (+ (neg (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (neg (/ 1 2))))) (pow (+ (* x 2) (+ (* F F) 2)) -1/2) (/ (neg x) (tan B)) (/ 1 (+ (* F F) (+ (* 2 x) 2))) (cos B) (pow (+ (+ (* F F) 2) (* 2 x)) (neg (/ 1 2))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (neg (/ 1 2)))) (/ 2 (* F F)))
121.0ms
f
@inf
((/ (log (tanh (* f (* 1/4 (PI))))) (* 1/4 (PI))) (log (tanh (* f (* 1/4 (PI))))) (tanh (* f (* 1/4 (PI)))) (* f (* 1/4 (PI))) (/ 1 (/ (PI) 4)) (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))) (/ (PI) 4) (/ 1 (/ (* 1/4 (PI)) (log (tanh (* f (* 1/4 (PI))))))) (/ (* 1/4 (PI)) (log (tanh (* f (* 1/4 (PI)))))) (* 1/4 (PI)) (PI) (/ (* (neg (log (tanh (* f (* 1/4 (PI)))))) (/ 4 (sqrt (PI)))) (sqrt (PI))) (neg (/ (* (neg (log (tanh (* f (* 1/4 (PI)))))) (/ 4 (sqrt (PI)))) (sqrt (PI)))) (* (neg (log (tanh (* f (* 1/4 (PI)))))) (/ 4 (sqrt (PI)))) (neg (log (tanh (* f (* 1/4 (PI)))))) (- (/ (log (* (cosh (* f (* 1/4 (PI)))) 2)) (* -1/4 (PI))) (/ (log (* (sinh (* f (* 1/4 (PI)))) 2)) (* -1/4 (PI)))) (/ (log (* (cosh (* f (* 1/4 (PI)))) 2)) (* -1/4 (PI))) (log (* (cosh (* f (* 1/4 (PI)))) 2)) (* (cosh (* f (* 1/4 (PI)))) 2) (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))) (/ (/ 4 (PI)) f) (sqrt (PI)) (/ (log (* (sinh (* f (* 1/4 (PI)))) 2)) (* -1/4 (PI))))
111.0ms
f
@inf
((log (/ 1 (tanh (* f (* 1/4 (PI)))))) (/ (PI) 4) (/ 1 (/ (PI) 4)) (neg (* (/ 1 (/ (PI) 4)) (log (/ 1 (tanh (* f (* 1/4 (PI)))))))) (/ f 4) (* (/ 4 (PI)) (log (tanh (* f (* 1/4 (PI)))))) (/ 4 (PI)) (PI) (/ (/ (* (log (tanh (* f (* 1/4 (PI))))) 4) (sqrt (PI))) (sqrt (PI))) (/ (* (log (tanh (* f (* 1/4 (PI))))) 4) (sqrt (PI))) (* (log (tanh (* f (* 1/4 (PI))))) 4) (+ (* -2 (* (PI) 1/48)) (* 1/8 (PI))) (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (- (/ (log 4) (* -1/4 (PI))) (/ (log (* f (PI))) (* -1/4 (PI)))) (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (/ (log 4) (* -1/4 (PI))) (log 4) (* (/ 1 (/ (PI) 4)) (log (/ 1 (tanh (* f (* 1/4 (PI))))))) (/ 1 (tanh (* f (* 1/4 (PI))))) (* f (* 1/4 (PI))) (tanh (* f (* 1/4 (PI)))) (log (tanh (* f (* 1/4 (PI))))) (* (/ f 4) (PI)) (sqrt (PI)) (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))) (* (PI) 1/48) (* (+ (* -2 (* (PI) 1/48)) (* 1/8 (PI))) f) (/ (log (* f (PI))) (* -1/4 (PI))) (* f (PI)))

preprocess6.0s (2.7%)

Memory
110.2MiB live, 5 672.0MiB allocated
Algorithm
18×egg-herbie
Stop Event
36×iter limit
20×node limit
16×saturated
Compiler

Compiled 17 956 to 7 062 computations (60.7% saved)

prune5.6s (2.6%)

Memory
-364.5MiB live, 10 317.1MiB allocated
Counts
92 460 → 1 597
Compiler

Compiled 58 077 to 38 344 computations (34% saved)

explain5.2s (2.3%)

Memory
-206.6MiB live, 6 146.3MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation5411
+.f64#fnan-rescue4780
sqrt.f64#foflow-rescue1650
tan.f64(tan.f64 (*.f64 (PI.f64) l))sensitivity1330
cos.f64(cos.f64 (/.f64 K #s(literal 2 binary64)))sensitivity1240
pow.f64(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))sensitivity9217
sqrt.f64#fuflow-rescue510
-.f64(-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))oflow-left470
+.f64(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (*.f64 F F) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) x)) (neg.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))))))oflow-left210
*.f64(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 F F)) (tan.f64 (*.f64 (PI.f64) l)))n*o150
/.f64(/.f64 A (*.f64 V l))n/u120
(*.f64 V l)underflow31
/.f64(/.f64 A (*.f64 V l))n/o90
(*.f64 V l)overflow28
log.f64(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))sensitivity50
/.f64(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))o/o40
(exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))overflow4
(+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))overflow4
(exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))overflow4
(-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))overflow4
exp.f64#fsensitivity30
Confusion
Predicted +Predicted -
+757155
-7942902
Precision
0.4880722114764668
Recall
0.8300438596491229
Confusion?
Predicted +Predicted MaybePredicted -
+7571154
-794182884
Precision?
0.48280254777070064
Recall?
0.831140350877193
Freqs
test
numberfreq
03057
11424
2105
322
Total Confusion?
Predicted +Predicted MaybePredicted -
+1200
-204
Precision?
0.8571428571428571
Recall?
1.0
Samples
1.1s8 136×0valid
356.0ms904×1valid
73.0ms176×2valid
29.0ms41×3valid
Compiler

Compiled 9 674 to 2 911 computations (69.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.1s
ival-mult: 325.0ms (29.6% of total)
ival-exp: 125.0ms (11.4% of total)
ival-div: 120.0ms (10.9% of total)
ival-add: 100.0ms (9.1% of total)
ival-sqrt: 83.0ms (7.6% of total)
ival-sub: 65.0ms (5.9% of total)
adjust: 64.0ms (5.8% of total)
ival-pow: 37.0ms (3.4% of total)
ival-cos: 28.0ms (2.5% of total)
ival-sin: 24.0ms (2.2% of total)
ival-neg: 22.0ms (2% of total)
ival-tan: 22.0ms (2% of total)
ival-pow2: 21.0ms (1.9% of total)
ival-pi: 14.0ms (1.3% of total)
ival-log: 13.0ms (1.2% of total)
ival-tanu: 11.0ms (1% of total)
exact: 11.0ms (1% of total)
ival-true: 9.0ms (0.8% of total)
ival-assert: 4.0ms (0.4% of total)

bsearch2.3s (1%)

Memory
-71.9MiB live, 2 694.6MiB allocated
Algorithm
117×binary-search
80×left-value
Stop Event
113×narrow-enough
predicate-same
Samples
1.3s8 912×0valid
92.0ms734×0invalid
29.0ms160×1valid
8.0ms38×1invalid
1.0ms5exit
Compiler

Compiled 24 625 to 26 344 computations (-7% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.1s
ival-mult: 219.0ms (20.6% of total)
ival-div: 207.0ms (19.5% of total)
ival-add: 165.0ms (15.5% of total)
ival-tan: 100.0ms (9.4% of total)
ival-pow: 98.0ms (9.2% of total)
ival-sin: 73.0ms (6.9% of total)
ival-sub: 51.0ms (4.8% of total)
ival-neg: 51.0ms (4.8% of total)
ival-exp: 34.0ms (3.2% of total)
ival-sqrt: 25.0ms (2.4% of total)
ival-pow2: 13.0ms (1.2% of total)
exact: 9.0ms (0.8% of total)
ival-true: 8.0ms (0.8% of total)
adjust: 7.0ms (0.7% of total)
ival-assert: 4.0ms (0.4% of total)
ival-pi: 0.0ms (0% of total)

start1.0ms (0%)

Memory
2.3MiB live, 2.3MiB allocated

end0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated

Profiling

Loading profile data...