Herbie run

Date:Thursday, August 22nd, 2024
Commit:efa1c98c on faster-localize
Hostname:nightly with Racket 8.11.1
Seed:2024235
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: 6.4min)

sample1.3min (21%)

Memory
971.3MiB live, 98 378.5MiB allocated
Samples
30.3s221 754×0valid
10.9s26 502×1valid
8.6s65 654×0invalid
3.3s9 789×2valid
3.3s12 368×1invalid
2.8s6 144×3valid
606.0ms1 891×1exit
145.0ms507×2invalid
45.0ms239×0exit
1.0ms5exit
1.0ms4valid
0.0ms3exit
0.0ms4exit
Precisions
Click to see histograms. Total time spent on operations: 46.1s
ival-mult: 10.9s (23.7% of total)
ival-div: 7.1s (15.3% of total)
ival-tan: 3.8s (8.2% of total)
ival-sub: 3.2s (7% of total)
ival-add: 2.7s (5.9% of total)
ival-sqrt: 2.5s (5.5% of total)
ival-pow2: 2.4s (5.1% of total)
adjust: 2.2s (4.8% of total)
ival-pow: 2.1s (4.6% of total)
ival-exp: 2.0s (4.4% of total)
ival-sin: 1.8s (3.9% of total)
ival-cos: 1.0s (2.2% of total)
ival-acos: 676.0ms (1.5% of total)
const: 593.0ms (1.3% of total)
ival-neg: 556.0ms (1.2% of total)
ival-pi: 516.0ms (1.1% of total)
ival-log: 445.0ms (1% of total)
ival-hypot: 399.0ms (0.9% of total)
exact: 317.0ms (0.7% of total)
ival-true: 248.0ms (0.5% of total)
ival-asin: 196.0ms (0.4% of total)
ival-assert: 134.0ms (0.3% of total)
ival-fabs: 88.0ms (0.2% of total)
ival-atan: 76.0ms (0.2% of total)
ival-<: 38.0ms (0.1% of total)
ival-and: 11.0ms (0% of total)
Bogosity

simplify53.0s (13.8%)

Memory
487.5MiB live, 56 753.6MiB allocated
Algorithm
288×egg-herbie
Rules
2 436 780×lower-fma.f32
2 436 036×lower-fma.f64
1 285 456×lower-*.f32
1 282 914×lower-*.f64
664 186×lower-+.f32
Stop Event
384×iter limit
227×node limit
61×saturated
Counts
71 076 → 70 548

prune41.4s (10.8%)

Memory
-1 216.0MiB live, 60 790.5MiB allocated
Counts
196 131 → 3 485
Compiler

Compiled 184 438 to 90 682 computations (50.8% saved)

soundness40.8s (10.6%)

Memory
27.8MiB live, 32 596.0MiB allocated
Rules
1 484 832×lower-fma.f32
1 484 404×lower-fma.f64
998 790×lower-*.f32
996 904×lower-*.f64
482 402×lower-/.f32
Stop Event
274×iter limit
179×node limit
31×fuel
done
Compiler

Compiled 49 165 to 21 965 computations (55.3% saved)

eval35.4s (9.2%)

Memory
768.9MiB live, 50 242.1MiB allocated
Compiler

Compiled 7 060 786 to 456 197 computations (93.5% saved)

rewrite32.2s (8.4%)

Memory
-213.7MiB live, 38 803.1MiB allocated
Rules
589 376×lower-fma.f32
588 634×lower-fma.f64
581 546×lower-*.f32
579 030×lower-*.f64
453 246×lower-/.f32
Stop Event
263×iter limit
128×node limit
Counts
2 511 → 99 165

localize29.9s (7.8%)

Memory
-200.4MiB live, 37 786.5MiB allocated
Samples
9.0s22 646×0valid
4.3s4 376×1valid
4.1s378×3exit
3.6s2 392×2valid
1.6s767×3valid
632.0ms1 452×0invalid
304.0ms499×0exit
63.0ms4exit
53.0ms140×1exit
48.0ms63×1invalid
48.0ms35×2invalid
15.0ms12×5exit
Compiler

Compiled 49 819 to 5 590 computations (88.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.9s
ival-mult: 4.3s (23% of total)
ival-tan: 4.0s (21.3% of total)
ival-div: 2.5s (13.2% of total)
ival-add: 1.4s (7.3% of total)
ival-cos: 1.2s (6.3% of total)
adjust: 1.2s (6.1% of total)
ival-sqrt: 780.0ms (4.1% of total)
ival-sub: 699.0ms (3.7% of total)
ival-acos: 495.0ms (2.6% of total)
ival-pow: 382.0ms (2% of total)
ival-pow2: 313.0ms (1.7% of total)
ival-sin: 269.0ms (1.4% of total)
const: 268.0ms (1.4% of total)
ival-neg: 208.0ms (1.1% of total)
ival-exp: 199.0ms (1.1% of total)
ival-pi: 162.0ms (0.9% of total)
ival-asin: 121.0ms (0.6% of total)
ival-log: 99.0ms (0.5% of total)
ival-hypot: 96.0ms (0.5% of total)
ival-atan: 66.0ms (0.3% of total)
exact: 62.0ms (0.3% of total)
ival-true: 27.0ms (0.1% of total)
ival-cbrt: 22.0ms (0.1% of total)
ival-tanh: 20.0ms (0.1% of total)
ival-assert: 14.0ms (0.1% of total)
ival-fabs: 11.0ms (0.1% of total)
ival-sinh: 5.0ms (0% of total)

regimes23.3s (6.1%)

Memory
45.1MiB live, 32 642.5MiB allocated
Counts
13 419 → 833
Calls

156 calls:

1.2s
l
1.2s
t
791.0ms
k
558.0ms
(*.f64 l l)
538.0ms
x
Compiler

Compiled 18 762 to 13 035 computations (30.5% saved)

series14.6s (3.8%)

Memory
217.1MiB live, 19 906.9MiB allocated
Counts
2 511 → 71 076
Calls

1200 calls:

TimeVariablePointExpression
114.0ms
x
@0
((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
84.0ms
t
@0
((pow t 3) (pow (/ k t) 2) (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (+ (+ 1 (pow (/ k t) 2)) 1) (/ (pow t 3) (* l l)) (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)) (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (* (/ (pow t 3) (* l l)) (sin k)))
81.0ms
l
@0
((+ (* (* (/ l Om) 4) (* (/ l Om) (- 1/2 (- (* 1/2 (cos (+ ky ky))) (- 1/2 (* 1/2 (cos (+ kx kx)))))))) 1) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (- 1/2 (- (* 1/2 (cos (+ ky ky))) (- 1/2 (* 1/2 (cos (+ kx kx)))))))) 1))))) (- 1 (* (+ (cos (* kx 2)) (cos (* ky 2))) 1/2)) (* kx 2) (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) (+ (* (sqrt (/ 1 (+ (* (* 4 (* l l)) (/ (pow (sin ky) 2) (* Om Om))) 1))) 1/2) 1/2) (+ (* (/ Om (* (sin ky) l)) 1/4) 1/2) (/ 1 2) (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) (- 1 (* (+ (cos (* ky 2)) 1) 1/2)) (* (+ (cos (* ky 2)) 1) 1/2) (* ky 2) (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (- 1/2 (- (* 1/2 (cos (+ ky ky))) (- 1/2 (* 1/2 (cos (+ kx kx)))))))) 1)))))) (+ (* (* (* l l) (/ (- 1/2 (* (cos (* ky 2)) 1/2)) (* Om Om))) 4) 1) (- 1/2 (* (cos (* ky 2)) 1/2)) (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (- 1/2 (- (* 1/2 (cos (+ ky ky))) (- 1/2 (* 1/2 (cos (+ kx kx)))))))) 1)))))) (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (- 1/2 (- (* 1/2 (cos (+ ky ky))) (- 1/2 (* 1/2 (cos (+ kx kx)))))))) 1)) (* (/ l Om) (- 1/2 (- (* 1/2 (cos (+ ky ky))) (- 1/2 (* 1/2 (cos (+ kx kx))))))) (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (- 1/2 (- (* 1/2 (cos (+ ky ky))) (- 1/2 (* 1/2 (cos (+ kx kx)))))))) 1))) (/ Om (* (sin ky) l)) (/ Om (* ky l)) (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (+ (* (* ky ky) (* l (/ l (* Om Om)))) (* (pow (sin kx) 2) (* l (/ l (* Om Om))))) (/ (* (* kx l) (* kx l)) (* Om Om)) (* (pow (sin kx) 2) (* l (/ l (* Om Om)))) (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (- 1/2 (- (* 1/2 (cos (+ ky ky))) (- 1/2 (* 1/2 (cos (+ kx kx)))))))) 1))))) (- 1 (* 1/2 (+ (cos (* kx 2)) (cos (* ky 2))))) (+ (* (neg (* l l)) (/ (- 1 (* 1/2 (+ (cos (* kx 2)) (cos (* ky 2))))) (* Om Om))) 1) (* (* l l) (/ (- 1/2 (* (cos (* ky 2)) 1/2)) (* Om Om))) (sqrt (/ 1 (+ (* (* (* l l) (/ (- 1/2 (* (cos (* ky 2)) 1/2)) (* Om Om))) 4) 1))) (/ (- 1/2 (* (cos (* ky 2)) 1/2)) (* Om Om)))
77.0ms
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)) (/ 2 (* (* 1/2 (PI)) f)) (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))))))) (* (/ (neg (log (tanh (* f (* 1/4 (PI)))))) (sqrt (PI))) (/ 4 (sqrt (PI)))) (neg (* (/ (neg (log (tanh (* f (* 1/4 (PI)))))) (sqrt (PI))) (/ 4 (sqrt (PI))))) (/ (neg (log (tanh (* f (* 1/4 (PI)))))) (sqrt (PI))) (neg (log (tanh (* f (* 1/4 (PI)))))) (/ (* (neg (log (tanh (* f (* 1/4 (PI)))))) (/ 4 (pow (PI) 2/3))) (cbrt (PI))) (neg (/ (* (neg (log (tanh (* f (* 1/4 (PI)))))) (/ 4 (pow (PI) 2/3))) (cbrt (PI)))) (* (neg (log (tanh (* f (* 1/4 (PI)))))) (/ 4 (pow (PI) 2/3))) (/ (neg (pow (* (log (tanh (* f (* 1/4 (PI))))) (/ -4 (PI))) 3)) (+ (pow (* (log (tanh (* f (* 1/4 (PI))))) (/ -4 (PI))) 2) 0)) (+ (pow (* (log (tanh (* f (* 1/4 (PI))))) (/ -4 (PI))) 2) 0) (neg (pow (* (log (tanh (* f (* 1/4 (PI))))) (/ -4 (PI))) 3)) (pow (* (log (tanh (* f (* 1/4 (PI))))) (/ -4 (PI))) 3) (PI) (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))) (* (* 1/2 (PI)) f) (sqrt (PI)) (cbrt (PI)) (/ 4 (pow (PI) 2/3)) (pow (* (log (tanh (* f (* 1/4 (PI))))) (/ -4 (PI))) 2))
72.0ms
a
@0
((+ (+ 1 (* 10 k)) (* k k)) (+ 1 (* 10 k)) (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))) (* a (pow k m)) (* 10 k))

preprocess10.2s (2.6%)

Memory
382.1MiB live, 11 354.0MiB allocated
Algorithm
32×egg-herbie
Rules
229 844×lower-fma.f64
229 844×lower-fma.f32
79 498×lower-*.f32
79 270×lower-*.f64
36 848×lower-/.f32
Stop Event
64×iter limit
41×node limit
23×saturated
Compiler

Compiled 55 217 to 16 583 computations (70% saved)

explain9.8s (2.5%)

Memory
-560.8MiB live, 13 266.2MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64#foflow-rescue4750
-.f64#fcancellation4401
cos.f64#fsensitivity4122
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#fnan-rescue2430
*.f64#fn*o2290
sqrt.f64#fuflow-rescue1590
pow.f64#foflow-rescue1350
tan.f64(tan.f64 (*.f64 (PI.f64) l))sensitivity1291
-.f64#fnan-rescue1220
*.f64#fu*o1200
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)))))))sensitivity1082
pow.f64(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))sensitivity9423
*.f64#fn*u680
/.f64#fo/n660
/.f64#fo/o650
+.f64#fcancellation640
*.f64#fo*u570
pow.f64#fuflow-rescue560
/.f64#fu/u500
cos.f64(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))oflow-rescue480
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))overflow48
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)overflow48
(*.f64 K (+.f64 m n))overflow48
/.f64#fn/o340
/.f64#fn/u340
/.f64#fu/n150
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))))))sensitivity80
exp.f64#fsensitivity52
Confusion
Predicted +Predicted -
+193730
-11125113
Precision
0.6352902591013447
Recall
0.9847483477376716
Confusion?
Predicted +Predicted MaybePredicted -
+1937129
-1112295084
Precision?
0.6294251380318285
Recall?
0.9852567361464158
Freqs
test
numberfreq
05143
12680
2308
352
48
51
Total Confusion?
Predicted +Predicted MaybePredicted -
+2500
-007
Precision?
1.0
Recall?
1.0
Samples
2.2s13 194×0valid
940.0ms2 022×1valid
447.0ms800×2valid
217.0ms362×3valid
3.0ms5exit
Compiler

Compiled 7 669 to 1 655 computations (78.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-mult: 515.0ms (19.9% of total)
ival-tan: 380.0ms (14.7% of total)
ival-add: 356.0ms (13.8% of total)
ival-div: 293.0ms (11.3% of total)
ival-sub: 135.0ms (5.2% of total)
adjust: 127.0ms (4.9% of total)
ival-pow2: 118.0ms (4.6% of total)
ival-sin: 110.0ms (4.3% of total)
ival-exp: 94.0ms (3.6% of total)
ival-sqrt: 92.0ms (3.6% of total)
ival-pow: 73.0ms (2.8% of total)
ival-pi: 67.0ms (2.6% of total)
ival-cos: 65.0ms (2.5% of total)
ival-neg: 30.0ms (1.2% of total)
ival-acos: 26.0ms (1% of total)
ival-hypot: 22.0ms (0.9% of total)
ival-log: 20.0ms (0.8% of total)
exact: 18.0ms (0.7% of total)
ival-true: 15.0ms (0.6% of total)
const: 8.0ms (0.3% of total)
ival-asin: 7.0ms (0.3% of total)
ival-assert: 7.0ms (0.3% of total)
ival-atan: 5.0ms (0.2% of total)
ival-fabs: 4.0ms (0.2% of total)

analyze8.6s (2.2%)

Memory
-1.9MiB live, 11 953.7MiB 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)

bsearch4.5s (1.2%)

Memory
15.5MiB live, 5 458.8MiB allocated
Algorithm
280×left-value
180×binary-search
Stop Event
165×narrow-enough
15×predicate-same
Samples
2.2s14 108×0valid
244.0ms1 881×0invalid
117.0ms508×1valid
71.0ms241×2valid
51.0ms87×3valid
9.0ms51×1invalid
2.0ms2invalid
Compiler

Compiled 57 476 to 37 616 computations (34.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.1s
ival-div: 496.0ms (24.1% of total)
ival-mult: 426.0ms (20.7% of total)
ival-pow: 215.0ms (10.4% of total)
ival-add: 188.0ms (9.1% of total)
ival-sin: 169.0ms (8.2% of total)
ival-tan: 143.0ms (6.9% of total)
ival-pow2: 92.0ms (4.5% of total)
ival-sub: 86.0ms (4.2% of total)
ival-neg: 66.0ms (3.2% of total)
adjust: 38.0ms (1.8% of total)
ival-exp: 34.0ms (1.6% of total)
ival-sqrt: 26.0ms (1.3% of total)
ival-cos: 26.0ms (1.3% of total)
exact: 16.0ms (0.8% of total)
ival-true: 12.0ms (0.6% of total)
const: 9.0ms (0.4% of total)
ival-assert: 6.0ms (0.3% of total)
ival-atan: 5.0ms (0.2% of total)
ival-fabs: 4.0ms (0.2% of total)
ival-asin: 3.0ms (0.1% of total)

start1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated

end0.0ms (0%)

Memory
0.5MiB live, 0.4MiB allocated

Profiling

Loading profile data...