Herbie run

Date:Wednesday, November 13th, 2024
Commit:b0f482cc on pavel-concrete-values
Hostname:nightly with Racket 8.10
Seed:2024318
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: 5.3min)

sample1.3min (25.3%)

Memory
320.7MiB live, 88 484.6MiB allocated
Samples
34.2s225 522×0valid
9.6s66 174×0invalid
6.6s22 701×1valid
4.1s12 161×1invalid
3.4s9 750×2valid
2.8s6 213×3valid
389.0ms1 819×1exit
212.0ms556×2invalid
25.0ms221×0exit
2.0ms4valid
Precisions
Click to see histograms. Total time spent on operations: 45.6s
ival-mult: 11.7s (25.6% of total)
ival-div: 7.2s (15.9% of total)
ival-sub: 3.4s (7.4% of total)
ival-add: 2.9s (6.4% of total)
ival-pow2: 2.8s (6.2% of total)
ival-pow: 2.4s (5.2% of total)
ival-sqrt: 2.3s (5.1% of total)
ival-exp: 2.2s (4.7% of total)
adjust: 2.2s (4.7% of total)
ival-sin: 2.0s (4.4% of total)
ival-cos: 918.0ms (2% of total)
ival-neg: 896.0ms (2% of total)
ival-tan: 891.0ms (2% of total)
ival-acos: 551.0ms (1.2% of total)
ival-pi: 507.0ms (1.1% of total)
const: 470.0ms (1% of total)
ival-hypot: 437.0ms (1% of total)
ival-log: 425.0ms (0.9% of total)
exact: 341.0ms (0.7% of total)
ival-true: 274.0ms (0.6% of total)
ival-asin: 207.0ms (0.5% of total)
ival-tanu: 172.0ms (0.4% of total)
ival-assert: 145.0ms (0.3% of total)
ival-fabs: 120.0ms (0.3% of total)
ival-atan: 93.0ms (0.2% of total)
ival-<: 86.0ms (0.2% of total)
ival-and: 11.0ms (0% of total)
Bogosity

simplify47.7s (14.9%)

Memory
1 202.7MiB live, 45 092.1MiB allocated
Algorithm
286×egg-herbie
Stop Event
381×iter limit
258×node limit
28×saturated
Counts
14 058 → 13 972

soundness42.2s (13.2%)

Memory
-152.2MiB live, 28 875.8MiB allocated
Stop Event
284×iter limit
189×node limit
31×fuel
done
Compiler

Compiled 69 782 to 30 023 computations (57% saved)

rewrite29.1s (9.1%)

Memory
-87.5MiB live, 30 349.9MiB allocated
Stop Event
258×iter limit
127×node limit
Counts
2 403 → 92 002

localize24.8s (7.7%)

Memory
-523.7MiB live, 28 850.1MiB allocated
Samples
10.0s23 820×0valid
3.2s3 521×1valid
2.4s2 072×2valid
1.4s738×3valid
901.0ms1 686×0invalid
510.0ms138×5exit
139.0ms326×0exit
112.0ms14×4exit
74.0ms74×2invalid
70.0ms98×1invalid
18.0ms4valid
17.0ms3exit
5.0ms1exit
Compiler

Compiled 43 990 to 5 339 computations (87.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.2s
ival-mult: 4.2s (29.3% of total)
ival-div: 2.7s (18.9% of total)
ival-add: 1.4s (9.7% of total)
adjust: 1.0s (7.1% of total)
ival-cos: 711.0ms (5% of total)
ival-sqrt: 706.0ms (5% of total)
ival-sub: 672.0ms (4.7% of total)
ival-pow: 509.0ms (3.6% of total)
ival-pow2: 507.0ms (3.6% of total)
ival-sin: 318.0ms (2.2% of total)
ival-neg: 229.0ms (1.6% of total)
ival-exp: 198.0ms (1.4% of total)
ival-log: 164.0ms (1.2% of total)
const: 158.0ms (1.1% of total)
ival-asin: 140.0ms (1% of total)
ival-acos: 140.0ms (1% of total)
ival-tan: 113.0ms (0.8% of total)
ival-hypot: 91.0ms (0.6% of total)
exact: 68.0ms (0.5% of total)
ival-pi: 52.0ms (0.4% of total)
ival-true: 30.0ms (0.2% of total)
ival-sinh: 28.0ms (0.2% of total)
ival-atan: 27.0ms (0.2% of total)
ival-tanu: 26.0ms (0.2% of total)
ival-tanh: 26.0ms (0.2% of total)
ival-cbrt: 18.0ms (0.1% of total)
ival-assert: 14.0ms (0.1% of total)
ival-fabs: 13.0ms (0.1% of total)
ival-cosh: 11.0ms (0.1% of total)
ival-expm1: 2.0ms (0% of total)

regimes21.3s (6.7%)

Memory
-208.9MiB live, 27 609.3MiB allocated
Counts
12 480 → 839
Calls

156 calls:

1.2s
l
1.0s
t
1.0s
k
446.0ms
F
445.0ms
x
Compiler

Compiled 13 371 to 13 771 computations (-3% saved)

eval20.7s (6.5%)

Memory
194.6MiB live, 27 220.6MiB allocated
Compiler

Compiled 4 495 767 to 436 878 computations (90.3% saved)

series11.0s (3.4%)

Memory
-194.5MiB live, 12 298.6MiB allocated
Counts
2 403 → 14 058
Calls

1197 calls:

TimeVariablePointExpression
267.0ms
f
@-inf
((/ (- (* 0 (* -1/4 (PI))) (* (* 1/4 (PI)) (log (tanh (* (* 1/4 f) (PI)))))) (* (* 1/4 (PI)) (* -1/4 (PI)))) (* 0 (* -1/4 (PI))) (- (* 0 (* -1/4 (PI))) (* (* 1/4 (PI)) (log (tanh (* (* 1/4 f) (PI)))))) (* (* 1/4 (PI)) (* -1/4 (PI))) (* (/ 4 (PI)) (log (tanh (* f (* 1/4 (PI)))))) (/ 4 (PI)) (PI) (log (tanh (* f (* 1/4 (PI))))) (/ (sqrt (PI)) (/ (* (log (tanh (* f (* 1/4 (PI))))) 4) (sqrt (PI)))) (/ 1 (/ (sqrt (PI)) (/ (* (log (tanh (* f (* 1/4 (PI))))) 4) (sqrt (PI))))) (sqrt (PI)) (* (sqrt (PI)) (sqrt (PI))) (/ (log (tanh (* f (* 1/4 (PI))))) (* 1/4 (* (sqrt (PI)) (sqrt (PI))))) (log (tanh (* f (* 1/4 (PI))))) (tanh (* f (* 1/4 (PI)))) (/ (- (log (/ (* (sinh (* (/ f 4) (PI))) 2) (cosh (* (/ f 4) (PI))))) (log 2)) (* 1/4 (PI))) (- (log (/ (* (sinh (* (/ f 4) (PI))) 2) (cosh (* (/ f 4) (PI))))) (log 2)) (log (/ (* (sinh (* (/ f 4) (PI))) 2) (cosh (* (/ f 4) (PI))))) (/ (* (sinh (* (/ f 4) (PI))) 2) (cosh (* (/ f 4) (PI)))) (log (tanh (* (* 1/4 f) (PI)))) (* (* 1/4 (PI)) (log (tanh (* (* 1/4 f) (PI))))) (tanh (* f (* 1/4 (PI)))) (* (/ f 4) (PI)))
235.0ms
l
@0
((+ (* (/ (tan (* l (PI))) F) (/ -1 F)) (* l (PI))) (/ (tan (* l (PI))) F) (tan (* l (PI))) (* l (PI)) (- (* (PI) l) (/ (/ (tan (* l (PI))) F) F)) (* (- (PI) (/ (PI) (* F F))) l) (- (PI) (/ (PI) (* F F))) (PI) (+ (* (PI) l) (/ (tan (* l (PI))) (* (neg F) F))) (/ (tan (* l (PI))) (* (neg F) F)) (* (/ (neg (PI)) F) (/ l F)) (cbrt (pow (PI) 3)) (- (* (PI) l) (* (/ 1 (* F F)) (tan (* (PI) l)))) (* (cbrt (pow (PI) 3)) l) (pow (PI) 3) (+ (* (pow (PI) 1/4) (* (pow (PI) 1/4) (* (sqrt (PI)) l))) (/ (tan (* l (PI))) (* (neg F) F))) (* (pow (PI) 1/4) (* (sqrt (PI)) l)) (pow (PI) 1/4) (/ (PI) (* F F)) (/ (neg (PI)) F) (/ (tan (* l (PI))) (* (neg F) F)) (sqrt (PI)))
207.0ms
n
@0
((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* -2 (PI)) (/ -1 n)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1) (* (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1)) (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (pow 2 (+ (* 1/2 k) 1/2)) (PI) (sqrt (* n (* (PI) 2))) (pow (* n (* (PI) 2)) (* k -1/2)) (* n (* (PI) 2)) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (pow (* n (PI)) (+ (* 1/2 k) 1/2)))
175.0ms
f
@0
((/ 1 (/ (/ 4 (PI)) f)) (/ (log (tanh (/ 1 (/ (/ 4 (PI)) f)))) (* 1/4 (PI))) (log (tanh (/ 1 (/ (/ 4 (PI)) f)))) (tanh (/ 1 (/ (/ 4 (PI)) f))) (/ (log (tanh (* f (* 1/4 (PI))))) (* 1/4 (PI))) (log (tanh (* f (* 1/4 (PI))))) (tanh (* f (* 1/4 (PI)))) (* (* (PI) f) 1/4) (/ (log (tanh (* f (* 1/4 (PI))))) (* 1/4 (PI))) (log (tanh (* f (* 1/4 (PI))))) (+ (log (* 1/4 (PI))) (log f)) (log (* 1/4 (PI))) (* (/ (- (* 0 (sqrt (PI))) (* (sqrt (PI)) (log (tanh (* (/ f 4) (PI)))))) (PI)) (/ 4 (sqrt (PI)))) (* 0 (sqrt (PI))) (neg (* (/ (- (* 0 (sqrt (PI))) (* (sqrt (PI)) (log (tanh (* (/ f 4) (PI)))))) (PI)) (/ 4 (sqrt (PI))))) (- (* 0 (sqrt (PI))) (* (sqrt (PI)) (log (tanh (* (/ f 4) (PI)))))) (* (* (PI) 1/4) (* 2 f)) (/ (neg (log (/ (+ (pow (pow (exp (PI)) 1/2) f) 1) (- (exp (* (* (PI) 1/4) (* 2 f))) 1)))) (* 1/4 (PI))) (pow (exp (PI)) 1/2) (neg (log (/ (+ (pow (pow (exp (PI)) 1/2) f) 1) (- (exp (* (* (PI) 1/4) (* 2 f))) 1)))) (/ (/ 4 (PI)) f) (PI) (sqrt (PI)) (log (tanh (* (/ f 4) (PI)))) (/ (- (* 0 (sqrt (PI))) (* (sqrt (PI)) (log (tanh (* (/ f 4) (PI)))))) (PI)) (* (sqrt (PI)) (log (tanh (* (/ f 4) (PI))))) (/ (+ (pow (pow (exp (PI)) 1/2) f) 1) (- (exp (* (* (PI) 1/4) (* 2 f))) 1)) (exp (PI)) (log (/ (+ (pow (pow (exp (PI)) 1/2) f) 1) (- (exp (* (* (PI) 1/4) (* 2 f))) 1))))
146.0ms
a2
@-inf
((/ 1 (/ (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (cos th))) (/ (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (/ (* a2 a2) (sqrt 2)) (* a2 a2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (/ 1 (/ (/ (sqrt 2) (cos th)) (+ (* a1 a1) (* a2 a2)))) (/ (/ (sqrt 2) (cos th)) (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2) (cos th)) (* (sqrt 2) (neg (sqrt 2))) (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/ 1 (/ (neg a1) (* (sqrt 2) (neg (sqrt 2))))) (/ (neg a1) (* (sqrt 2) (neg (sqrt 2)))) (cos th) (/ a2 (sqrt 2)) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/ 1 (/ (neg a1) (* (sqrt 2) (neg (sqrt 2)))))))

preprocess10.4s (3.3%)

Memory
-35.8MiB live, 9 887.2MiB allocated
Algorithm
32×egg-herbie
Stop Event
64×iter limit
41×node limit
23×saturated
Compiler

Compiled 88 779 to 19 875 computations (77.6% saved)

explain9.2s (2.9%)

Memory
-106.5MiB live, 11 896.9MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation4532
sqrt.f64#foflow-rescue4390
cos.f64#fsensitivity4080
acos.f64(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))sensitivity2530
*.f64#fn*o2470
+.f64#fnan-rescue2170
sqrt.f64#fuflow-rescue1670
asin.f64(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))sensitivity1291
tan.f64(tan.f64 (*.f64 (PI.f64) l))sensitivity1270
pow.f64#foflow-rescue1230
*.f64#fu*o1230
-.f64#fnan-rescue1120
pow.f64(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))sensitivity9527
/.f64#fo/o790
*.f64#fn*u760
/.f64#fo/n640
*.f64#fo*u610
cos.f64(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))oflow-rescue570
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))overflow57
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)overflow57
(*.f64 K (+.f64 m n))overflow57
pow.f64#fuflow-rescue540
+.f64#fcancellation540
/.f64#fu/u490
/.f64#fn/o440
/.f64#fn/u280
/.f64#fu/n200
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))))))sensitivity110
exp.f64#fsensitivity33
tan.f64(tan.f64 (*.f64 (PI.f64) l))oflow-rescue10
(*.f64 (PI.f64) l)overflow1
Confusion
Predicted +Predicted -
+193746
-11225087
Precision
0.633213468453743
Recall
0.9768028240040343
Confusion?
Predicted +Predicted MaybePredicted -
+1937244
-1122295058
Precision?
0.6275080906148868
Recall?
0.9778113968734241
Freqs
test
numberfreq
05133
12675
2336
345
43
Total Confusion?
Predicted +Predicted MaybePredicted -
+2600
-006
Precision?
1.0
Recall?
1.0
Samples
2.2s13 354×0valid
590.0ms1 880×1valid
267.0ms778×2valid
184.0ms354×3valid
11.0ms18×5exit
Compiler

Compiled 7 569 to 1 655 computations (78.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.1s
ival-mult: 430.0ms (20.2% of total)
ival-div: 264.0ms (12.4% of total)
ival-sub: 162.0ms (7.6% of total)
adjust: 150.0ms (7% of total)
ival-sqrt: 140.0ms (6.6% of total)
ival-pow2: 129.0ms (6% of total)
ival-sin: 127.0ms (6% of total)
ival-add: 122.0ms (5.7% of total)
ival-exp: 103.0ms (4.8% of total)
ival-pow: 97.0ms (4.5% of total)
ival-cos: 94.0ms (4.4% of total)
ival-neg: 67.0ms (3.1% of total)
ival-tan: 57.0ms (2.7% of total)
ival-acos: 42.0ms (2% of total)
ival-hypot: 22.0ms (1% of total)
ival-pi: 19.0ms (0.9% of total)
ival-log: 19.0ms (0.9% of total)
exact: 19.0ms (0.9% of total)
ival-true: 16.0ms (0.7% of total)
const: 12.0ms (0.6% of total)
ival-tanu: 11.0ms (0.5% of total)
ival-fabs: 10.0ms (0.5% of total)
ival-asin: 8.0ms (0.4% of total)
ival-assert: 7.0ms (0.3% of total)
ival-atan: 5.0ms (0.2% of total)

analyze9.1s (2.8%)

Memory
91.1MiB live, 10 794.6MiB 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)

prune8.2s (2.6%)

Memory
8.0MiB live, 12 007.0MiB allocated
Counts
105 170 → 3 292
Compiler

Compiled 282 219 to 146 767 computations (48% saved)

bsearch5.4s (1.7%)

Memory
-178.8MiB live, 6 094.4MiB allocated
Algorithm
244×binary-search
208×left-value
Stop Event
229×narrow-enough
15×predicate-same
Samples
2.7s16 737×0valid
402.0ms2 516×0invalid
100.0ms352×1valid
61.0ms146×2valid
26.0ms61×3valid
23.0ms41×1invalid
1.0ms5exit
Compiler

Compiled 164 923 to 114 996 computations (30.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.5s
ival-mult: 639.0ms (25.1% of total)
ival-div: 414.0ms (16.3% of total)
ival-add: 222.0ms (8.7% of total)
ival-sub: 181.0ms (7.1% of total)
ival-tan: 178.0ms (7% of total)
ival-pow: 172.0ms (6.8% of total)
ival-sin: 167.0ms (6.6% of total)
ival-pow2: 156.0ms (6.1% of total)
ival-neg: 133.0ms (5.2% of total)
const: 78.0ms (3.1% of total)
ival-exp: 69.0ms (2.7% of total)
ival-sqrt: 31.0ms (1.2% of total)
adjust: 25.0ms (1% of total)
exact: 21.0ms (0.8% of total)
ival-cos: 17.0ms (0.7% of total)
ival-true: 16.0ms (0.6% of total)
ival-assert: 8.0ms (0.3% of total)
ival-asin: 8.0ms (0.3% of total)
ival-atan: 5.0ms (0.2% of total)
ival-fabs: 5.0ms (0.2% 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...