Herbie run

Date:Friday, November 22nd, 2024
Commit:97e637cb on bhargav-double-double
Hostname:nightly with Racket 8.10
Seed:2024327
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: 4.3min)

sample1.9min (44.6%)

Memory
640.8MiB live, 106 629.5MiB allocated
Samples
29.4s41 168×2valid
24.3s145 546×0invalid
19.0s92 399×1valid
9.9s5 007×5exit
8.6s94 656×0valid
1.8s2 943×3valid
465.0ms2 372×1exit
422.0ms4 207×0exit
32.0ms4exit
5.0ms2exit
2.0ms4valid
0.0ms3exit
Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-tan: 12.8s (16.4% of total)
ival-pow: 10.2s (13% of total)
adjust: 6.1s (7.8% of total)
ival-mult: 6.0s (7.6% of total)
const: 5.0s (6.4% of total)
ival-div: 4.0s (5.1% of total)
ival-cos: 4.0s (5.1% of total)
ival-sub: 3.9s (5% of total)
ival-sin: 3.8s (4.9% of total)
ival-add: 3.3s (4.3% of total)
ival-log: 3.2s (4.1% of total)
ival-fabs: 2.6s (3.3% of total)
ival-exp: 2.2s (2.8% of total)
ival-<=: 2.1s (2.7% of total)
ival-expm1: 2.0s (2.5% of total)
ival-<: 1.3s (1.7% of total)
ival-log1p: 1.3s (1.6% of total)
ival-sqrt: 1.2s (1.6% of total)
ival-and: 640.0ms (0.8% of total)
ival-atan: 613.0ms (0.8% of total)
ival-fmin: 468.0ms (0.6% of total)
exact: 369.0ms (0.5% of total)
ival-cbrt: 320.0ms (0.4% of total)
ival->: 305.0ms (0.4% of total)
ival-neg: 280.0ms (0.4% of total)
ival-assert: 158.0ms (0.2% of total)
ival-true: 78.0ms (0.1% of total)
Bogosity

simplify35.7s (13.8%)

Memory
45.6MiB live, 27 478.3MiB allocated
Algorithm
246×egg-herbie
Stop Event
327×iter limit
166×node limit
80×saturated
Counts
8 630 → 8 538

soundness26.2s (10.1%)

Memory
87.7MiB live, 13 137.1MiB allocated
Stop Event
186×iter limit
120×node limit
22×fuel
done
saturated
Compiler

Compiled 13 382 to 5 942 computations (55.6% saved)

rewrite22.0s (8.5%)

Memory
-54.6MiB live, 20 415.4MiB allocated
Stop Event
223×iter limit
109×node limit
Counts
1 587 → 64 802

localize21.1s (8.1%)

Memory
270.3MiB live, 19 852.8MiB allocated
Samples
6.3s10 836×1valid
6.3s5 146×2valid
3.7s10 724×0valid
630.0ms348×3valid
253.0ms750×0invalid
32.0ms15×5exit
29.0ms82×0exit
3.0ms4valid
Compiler

Compiled 47 406 to 6 781 computations (85.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.6s
ival-mult: 2.4s (17.7% of total)
ival-tan: 1.7s (12.5% of total)
adjust: 1.5s (11.2% of total)
ival-div: 1.5s (11% of total)
ival-add: 1.3s (9.7% of total)
ival-sub: 716.0ms (5.3% of total)
ival-pow: 666.0ms (4.9% of total)
ival-cos: 561.0ms (4.1% of total)
const: 559.0ms (4.1% of total)
ival-sin: 538.0ms (3.9% of total)
ival-log: 471.0ms (3.5% of total)
ival-exp: 454.0ms (3.3% of total)
ival-sqrt: 321.0ms (2.4% of total)
ival-neg: 178.0ms (1.3% of total)
ival-log1p: 176.0ms (1.3% of total)
ival-pow2: 129.0ms (0.9% of total)
ival-cbrt: 97.0ms (0.7% of total)
ival-cosh: 92.0ms (0.7% of total)
ival-expm1: 74.0ms (0.5% of total)
exact: 52.0ms (0.4% of total)
ival-true: 25.0ms (0.2% of total)
ival-atan: 20.0ms (0.1% of total)
ival-atan2: 17.0ms (0.1% of total)
ival-assert: 12.0ms (0.1% of total)
ival-hypot: 12.0ms (0.1% of total)
ival-fabs: 1.0ms (0% of total)

eval12.0s (4.6%)

Memory
-239.3MiB live, 14 882.3MiB allocated
Compiler

Compiled 2 700 776 to 278 186 computations (89.7% saved)

explain7.9s (3.1%)

Memory
-41.1MiB live, 8 053.2MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation532724
log.f64#fsensitivity7661
+.f64#fcancellation6891
sqrt.f64#foflow-rescue3740
/.f64#fu/n3650
/.f64#fu/u1630
pow.f64(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))sensitivity370
sqrt.f64#fuflow-rescue320
/.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/u250
(*.f64 b eps)underflow154
(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow139
(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow154
(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow235
(*.f64 a eps)underflow139
-.f64#fnan-rescue180
cos.f64(cos.f64 (+.f64 x eps))sensitivity30
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o30
(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow3
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow3
(exp.f64 x)overflow3
(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow3
tan.f64(tan.f64 (+.f64 x eps))sensitivity30
sin.f64(sin.f64 (+.f64 x eps))sensitivity21
exp.f64(exp.f64 (neg.f64 x))sensitivity10
Confusion
Predicted +Predicted -
+515849
-8441117
Precision
0.8593802065978007
Recall
0.9905895909352794
Confusion?
Predicted +Predicted MaybePredicted -
+5158841
-844171100
Precision?
0.8571428571428571
Recall?
0.9921259842519685
Freqs
test
numberfreq
01166
14828
2760
3196
4218
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.6s2 536×2valid
1.3s5 916×1valid
520.0ms5 732×0valid
92.0ms150×3valid
2.0ms4valid
Compiler

Compiled 3 914 to 1 430 computations (63.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0s
ival-tan: 904.0ms (30.3% of total)
ival-div: 277.0ms (9.3% of total)
adjust: 274.0ms (9.2% of total)
ival-cos: 219.0ms (7.3% of total)
ival-sin: 212.0ms (7.1% of total)
ival-log: 192.0ms (6.4% of total)
ival-sub: 147.0ms (4.9% of total)
ival-add: 139.0ms (4.7% of total)
ival-mult: 137.0ms (4.6% of total)
ival-exp: 134.0ms (4.5% of total)
ival-pow: 126.0ms (4.2% of total)
ival-log1p: 63.0ms (2.1% of total)
ival-sqrt: 57.0ms (1.9% of total)
ival-cbrt: 25.0ms (0.8% of total)
ival-expm1: 24.0ms (0.8% of total)
ival-atan: 19.0ms (0.6% of total)
ival-true: 14.0ms (0.5% of total)
ival-neg: 12.0ms (0.4% of total)
exact: 9.0ms (0.3% of total)
ival-assert: 6.0ms (0.2% of total)

regimes4.0s (1.5%)

Memory
-58.7MiB live, 4 525.8MiB allocated
Counts
4 064 → 295
Calls

43 calls:

1.0s
x
417.0ms
eps
207.0ms
b
187.0ms
(/.f64 #s(literal 1 binary64) n)
172.0ms
(/.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))))
Compiler

Compiled 1 966 to 1 856 computations (5.6% saved)

preprocess4.0s (1.5%)

Memory
239.3MiB live, 3 293.0MiB allocated
Algorithm
28×egg-herbie
Stop Event
56×iter limit
50×saturated
node limit
Compiler

Compiled 17 718 to 4 979 computations (71.9% saved)

series3.8s (1.5%)

Memory
-197.2MiB live, 3 599.5MiB allocated
Counts
1 587 → 8 630
Calls

507 calls:

TimeVariablePointExpression
291.0ms
eps
@0
((log (/ (- 1 eps) (+ 1 eps))) (* (+ (* (+ (* (+ (* -2/7 (* eps eps)) -2/5) (* eps eps)) -2/3) (* eps eps)) -2) eps) (* (- (- -2/7 (/ 2/5 (* eps eps))) (/ (+ (/ (/ 2 eps) eps) 2/3) (pow eps 4))) (pow eps 7)) (- (- -2/7 (/ 2/5 (* eps eps))) (/ (+ (/ (/ 2 eps) eps) 2/3) (pow eps 4))) (+ (* (* -2/3 (* eps eps)) eps) (* -2 eps)) (log (/ (- 1 eps) (+ 1 eps))) (* -2/3 (* eps eps)) (* eps eps) (+ (* (* (* (+ (* (+ (* (* eps eps) -2/7) -2/5) (* eps eps)) -2/3) eps) eps) eps) (* -2 eps)) (log (/ (- 1 eps) (+ 1 eps))) (* (* (+ (* (+ (* (* eps eps) -2/7) -2/5) (* eps eps)) -2/3) eps) eps) (* (+ (* (+ (* (* eps eps) -2/7) -2/5) (* eps eps)) -2/3) eps) (+ (* (+ (* (+ (* (* -2/7 eps) eps) -2/5) (pow eps 4)) -2) eps) (* (pow eps 3) -2/3)) (log (/ (- 1 eps) (+ 1 eps))) (+ (* (+ (* (* -2/7 eps) eps) -2/5) (pow eps 4)) -2) (+ (* (* -2/7 eps) eps) -2/5) (/ 2/5 (* eps eps)) (/ (/ 2 eps) eps) (/ (+ (/ (/ 2 eps) eps) 2/3) (pow eps 4)) (* -2 eps) (+ (* (+ (* (* eps eps) -2/7) -2/5) (* eps eps)) -2/3) (* -2/7 eps) (* (pow eps 3) -2/3))
135.0ms
a
@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))))
93.0ms
N
@-inf
((- (log (+ N 1)) (log N)) (/ (- (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) -1) N) (- (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) -1) (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) (- (log (+ N 1)) (log N)) (/ 1 N) (/ (/ N (+ 1 N)) 1) (neg (log (/ (/ N (+ 1 N)) 1))) (log (/ (/ N (+ 1 N)) 1)) (/ N (+ 1 N)) (pow (pow (- (pow (log (+ 1 N)) 3) (pow (log N) 3)) -1) -1) (* (pow (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) -1) (pow (pow (- (pow (log (+ 1 N)) 3) (pow (log N) 3)) -1) -1)) (pow (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) -1) (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) (/ (- (* (pow (log (+ 1 N)) 3) (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2))) (* (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) (pow (log N) 3))) (pow (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) 2)) (- (* (pow (log (+ 1 N)) 3) (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2))) (* (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2)) (pow (log N) 3))) (* (pow (log (+ 1 N)) 3) (+ (* (+ (log N) (log (+ 1 N))) (log N)) (pow (log (+ 1 N)) 2))) (pow (log (+ 1 N)) 3) (/ (- (/ 1/4 N) 1/3) N) (- (/ 1/4 N) 1/3) (+ 1 N) (- (pow (log (+ 1 N)) 3) (pow (log N) 3)) (pow (log N) 3) (pow (log (+ 1 N)) 2))
92.0ms
x
@inf
((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (neg (sin x)) (+ (* (neg (tan eps)) (tan x)) 1)) (* (+ (tan eps) (tan x)) (cos x))) (neg (sin x)) (sin x) (+ (* (neg (tan eps)) (tan x)) 1) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (cos (+ eps x)) (cos x) (pow (cos x) 2) (* (+ (tan eps) (tan x)) (cos x)) (/ (+ (* (neg (sin x)) (+ (* (neg (tan eps)) (tan x)) 1)) (* (+ (tan eps) (tan x)) (cos x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (+ (tan eps) (tan x)))
56.0ms
n
@-inf
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (pow x (- (/ 1 n) 1)) n) (pow x (- (/ 1 n) 1)) (- (/ 1 n) 1) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow x (pow n -1)) (* n x) (/ (pow x (pow n -1)) (* n x)) (+ (* (/ (- (/ 1/3 x) 1/2) n) n) x) (/ (/ (+ (* (/ (- (/ 1/3 x) 1/2) n) n) x) (* n x)) x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (+ (/ (/ (- (* 1 n) (* (/ x (/ 1/3 n)) 1/2)) (* (/ x (/ 1/3 n)) n)) x) (/ 1 n)) (/ (- (* 1 n) (* (/ x (/ 1/3 n)) 1/2)) (* (/ x (/ 1/3 n)) n)) (/ x (/ 1/3 n)) (/ (/ (- (* 1 n) (* (/ x (/ 1/3 n)) 1/2)) (* (/ x (/ 1/3 n)) n)) x) (* (neg (- (log (+ 1 x)) (log x))) (/ -1 n)) (neg (- (log (+ 1 x)) (log x))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (- (log (+ 1 x)) (log x)) (/ (+ (* (/ (- (/ 1/3 x) 1/2) n) n) x) (* n x)) (/ (- (log (+ 1 x)) (log x)) n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ 1/3 n) (log x))

prune3.7s (1.4%)

Memory
-3.7MiB live, 5 834.5MiB allocated
Counts
71 071 → 1 970
Compiler

Compiled 114 267 to 57 415 computations (49.8% saved)

analyze1.8s (0.7%)

Memory
-72.6MiB live, 1 734.1MiB 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)

bsearch1.3s (0.5%)

Memory
9.3MiB live, 1 471.0MiB allocated
Algorithm
72×binary-search
24×left-value
Stop Event
64×narrow-enough
predicate-same
Samples
288.0ms3 497×0valid
255.0ms566×2valid
149.0ms758×1valid
53.0ms711×0invalid
17.0ms139×0exit
3.0ms11×3valid
Compiler

Compiled 24 885 to 19 039 computations (23.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 541.0ms
ival-pow: 168.0ms (31% of total)
ival-mult: 85.0ms (15.7% of total)
ival-div: 56.0ms (10.3% of total)
ival-sub: 55.0ms (10.2% of total)
adjust: 46.0ms (8.5% of total)
ival-add: 34.0ms (6.3% of total)
ival-sqrt: 32.0ms (5.9% of total)
ival-cos: 21.0ms (3.9% of total)
ival-neg: 21.0ms (3.9% of total)
ival-sin: 7.0ms (1.3% of total)
ival-true: 5.0ms (0.9% of total)
ival-assert: 3.0ms (0.6% of total)
ival-log: 3.0ms (0.6% of total)
exact: 3.0ms (0.6% of total)
ival-cbrt: 2.0ms (0.4% of total)
ival-expm1: 2.0ms (0.4% of total)
ival-log1p: 1.0ms (0.2% of total)

start1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated

end0.0ms (0%)

Memory
0.4MiB live, 0.3MiB allocated

Profiling

Loading profile data...