Herbie run

Date:Thursday, May 16th, 2024
Commit:9db37a23 on report-cost-multi-alts
Hostname:nightly with Racket 8.11.1
Seed:2024137
Parameters:256 points for 4 iterations
Flags:
reduce: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: 8.6min)

sample2.2min (25.9%)

Results
54.8s433959×0valid
13.1s29351×1valid
34.9s7782×5exit
3.0s6882×2valid
371.0ms4121×0unsamplable
38.0ms510×0invalid
290.0ms400×3valid
Precisions
Click to see histograms. Total time spent on operations: 1.4min
ival-sin: 26.3s (31.6% of total)
ival-mult: 19.4s (23.3% of total)
ival-add: 8.7s (10.5% of total)
ival-div: 5.0s (6% of total)
backward-pass: 3.3s (4% of total)
ival-exp: 3.3s (3.9% of total)
ival-sub: 2.9s (3.5% of total)
ival-sqrt: 2.1s (2.5% of total)
ival-log: 2.1s (2.5% of total)
ival-cos: 1.5s (1.8% of total)
ival-pow: 1.4s (1.7% of total)
ival-asin: 1.1s (1.4% of total)
ival-atan2: 905.0ms (1.1% of total)
const: 879.0ms (1.1% of total)
ival-pi: 729.0ms (0.9% of total)
ival-<=: 689.0ms (0.8% of total)
ival->: 682.0ms (0.8% of total)
ival-fabs: 574.0ms (0.7% of total)
ival-neg: 389.0ms (0.5% of total)
ival-acosh: 372.0ms (0.4% of total)
ival-asinh: 320.0ms (0.4% of total)
ival-atanh: 288.0ms (0.3% of total)
ival->=: 176.0ms (0.2% of total)
ival-and: 84.0ms (0.1% of total)
Bogosity

simplify1.2min (14.3%)

Algorithm
242×egg-herbie
Rules
66147×fma-define
52627×fma-neg
52089×*-commutative
51630×distribute-lft-in
49848×associate-*r*
Stop Event
58×saturated
175×node limit
9×unsound
Counts
94184 → 89947

localize1.1min (12.7%)

Algorithm
189×egg-herbie
Rules
88940×fma-define
55862×associate-*r*
53677×fma-neg
42336×distribute-lft-in
35056×distribute-rgt-in
Stop Event
85×saturated
103×node limit
1×unsound
Results
13.9s37099×0valid
8.5s5282×1valid
2.6s4327×0invalid
2.6s1164×2valid
2.4s384×5exit
137.0ms114×0unsamplable
22.0ms14×3valid
Compiler

Compiled 50575 to 5365 computations (89.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.3s
ival-mult: 3.9s (22.8% of total)
ival-pow: 2.3s (13.4% of total)
ival-add: 1.7s (9.7% of total)
ival-div: 1.4s (8.2% of total)
backward-pass: 1.3s (7.3% of total)
ival-log: 901.0ms (5.2% of total)
ival-fma: 682.0ms (3.9% of total)
ival-sub: 631.0ms (3.6% of total)
ival-sin: 627.0ms (3.6% of total)
ival-exp: 508.0ms (2.9% of total)
ival-sqrt: 502.0ms (2.9% of total)
ival-hypot: 487.0ms (2.8% of total)
ival-cos: 475.0ms (2.7% of total)
ival-acos: 377.0ms (2.2% of total)
ival-asin: 293.0ms (1.7% of total)
ival-neg: 268.0ms (1.5% of total)
ival-log1p: 220.0ms (1.3% of total)
const: 182.0ms (1.1% of total)
ival-atan2: 155.0ms (0.9% of total)
ival-copysign: 124.0ms (0.7% of total)
ival-cbrt: 89.0ms (0.5% of total)
ival-fabs: 85.0ms (0.5% of total)
ival-pi: 46.0ms (0.3% of total)
ival-expm1: 36.0ms (0.2% of total)

soundness56.8s (11.1%)

Rules
63338×fma-define
58589×log1p-expm1-u
49170×fma-neg
45501×associate-*r*
43249×expm1-log1p-u
Stop Event
22×saturated
206×node limit
36×fuel
10×unsound
21×done
Compiler

Compiled 51218 to 14539 computations (71.6% saved)

rewrite49.0s (9.6%)

Algorithm
185×batch-egg-rewrite
Rules
120215×log1p-expm1-u
89340×expm1-log1p-u
40004×pow1
38398×add-exp-log
36241×add-log-exp
Stop Event
1×saturated
176×node limit
8×unsound
Counts
2110 → 58169

prune34.5s (6.7%)

Counts
137892 → 3276
Compiler

Compiled 174852 to 86833 computations (50.3% saved)

eval29.8s (5.8%)

Compiler

Compiled 4643244 to 560558 computations (87.9% saved)

series19.1s (3.7%)

Counts
2110 → 36015
Calls

9300 calls:

TimeVariablePointExpression
365.0ms
alpha
@-inf
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
312.0ms
im
@inf
(log (+ 1 (log im)))
298.0ms
x
@0
(* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ (* (/ 1 (+ (* 3275911/10000000 x) 1)) (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 x) 1)))) 1421413741/1000000000) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1)) (exp (neg (pow x 2))))
262.0ms
x
@-inf
(log (/ x (log x)))
207.0ms
u1
@inf
(pow (* -2 (log u1)) 1/4)

preprocess14.2s (2.8%)

Algorithm
57×egg-herbie
Rules
20546×fma-neg
20224×fma-define
10466×unsub-neg
9196×sub-neg
8861×distribute-lft-in
Stop Event
32×saturated
25×node limit
Compiler

Compiled 33720 to 12822 computations (62% saved)

regimes13.0s (2.5%)

Counts
9713 → 800
Calls

132 calls:

1.2s
x.im
1.1s
im
967.0ms
y.re
955.0ms
y.im
719.0ms
re
Compiler

Compiled 6949 to 4265 computations (38.6% saved)

explain11.7s (2.3%)

Results
4.7s25658×0valid
2.3s2930×1valid
448.0ms572×2valid
9.0ms18×3valid
4.0ms6×5exit
Compiler

Compiled 13779 to 2169 computations (84.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.6s
ival-mult: 1.3s (27.2% of total)
ival-add: 912.0ms (19.7% of total)
ival-sub: 532.0ms (11.5% of total)
ival-sqrt: 380.0ms (8.2% of total)
ival-log: 288.0ms (6.2% of total)
ival-div: 232.0ms (5% of total)
backward-pass: 207.0ms (4.5% of total)
ival-cos: 198.0ms (4.3% of total)
ival-atan2: 155.0ms (3.3% of total)
ival-exp: 139.0ms (3% of total)
ival-sin: 77.0ms (1.7% of total)
ival-asin: 61.0ms (1.3% of total)
const: 59.0ms (1.3% of total)
ival-pow: 49.0ms (1.1% of total)
ival-fabs: 27.0ms (0.6% of total)
ival-pi: 25.0ms (0.5% of total)
ival-neg: 15.0ms (0.3% of total)
ival-copysign: 15.0ms (0.3% of total)
ival-log1p: 8.0ms (0.2% of total)

bsearch10.0s (2%)

Algorithm
315×binary-search
53×left-value
Stop Event
12×predicate-same
303×narrow-enough
Results
5.3s33114×0valid
1.6s3001×1valid
68.0ms209×2valid
4.0ms12×3valid
Compiler

Compiled 71149 to 48351 computations (32% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.2s
ival-mult: 2.2s (41.9% of total)
ival-add: 525.0ms (10.2% of total)
ival-log: 389.0ms (7.5% of total)
ival-exp: 365.0ms (7.1% of total)
ival-sin: 344.0ms (6.7% of total)
ival-cos: 318.0ms (6.2% of total)
ival-sub: 307.0ms (5.9% of total)
ival-div: 279.0ms (5.4% of total)
ival-sqrt: 144.0ms (2.8% of total)
ival-atan2: 120.0ms (2.3% of total)
backward-pass: 85.0ms (1.6% of total)
const: 53.0ms (1% of total)
ival-neg: 26.0ms (0.5% of total)
ival-pow: 20.0ms (0.4% of total)
ival-copysign: 10.0ms (0.2% of total)
ival-fabs: 10.0ms (0.2% of total)
ival-pi: 4.0ms (0.1% of total)

analyze3.5s (0.7%)

Algorithm
58×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%86.3%13.7%0%0%0%0
53.4%46.1%40.2%13.7%0%0%0%1
62.8%53.1%31.4%13.7%0%1.7%0%2
71.2%58.4%23.6%13.7%0%4.3%0%3
77.4%62%18.1%13.7%0%6.2%0%4
83.5%66.8%13.2%13.7%0%6.3%0%5
85.8%68.3%11.3%13.7%0%6.6%0%6
88.3%70.3%9.4%13.7%0%6.6%0%7
89.9%71.5%8%13.7%0%6.8%0%8
91.1%72.5%7.1%13.7%0%6.8%0%9
92.6%73.6%5.9%13.7%0%6.8%0%10
94%74.7%4.8%13.7%0%6.8%0%11
94.5%75.1%4.4%13.7%0%6.9%0%12
Compiler

Compiled 1558 to 790 computations (49.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.3s
ival-mult: 680.0ms (30.1% of total)
ival-add: 432.0ms (19.1% of total)
ival-sqrt: 265.0ms (11.7% of total)
ival-log: 226.0ms (10% of total)
ival-sub: 214.0ms (9.5% of total)
ival-div: 122.0ms (5.4% of total)
ival-atan2: 77.0ms (3.4% of total)
ival-pow: 71.0ms (3.1% of total)
ival-exp: 56.0ms (2.5% of total)
const: 26.0ms (1.2% of total)
ival-sin: 23.0ms (1% of total)
ival-cos: 18.0ms (0.8% of total)
ival->: 12.0ms (0.5% of total)
ival-pi: 11.0ms (0.5% of total)
ival-<=: 10.0ms (0.4% of total)
backward-pass: 6.0ms (0.3% of total)
ival-neg: 6.0ms (0.3% of total)
ival-and: 2.0ms (0.1% of total)
ival-asin: 1.0ms (0% of total)
ival-atanh: 1.0ms (0% of total)
ival-asinh: 0.0ms (0% of total)
ival->=: 0.0ms (0% of total)
ival-fabs: 0.0ms (0% of total)
ival-acosh: 0.0ms (0% of total)

end0.0ms (0%)

Profiling

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