Herbie run

Date:Friday, April 19th, 2024
Commit:a62871db on main
Hostname:nightly with Racket 8.11.1
Seed:2024110
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: 2.2hr)

localize29.0min (22%)

Algorithm
7042×egg-herbie
Rules
2215303×fma-define
1626656×fma-neg
756865×distribute-lft-in
699486×unsub-neg
687767×distribute-rgt-in
Stop Event
5151×saturated
1891×node limit
Results
5.2min400872×0valid
3.7min41503×1valid
36.5s23925×0invalid
4.5min12233×5exit
1.5min12074×2valid
1.3s1595×0unsamplable
46.0s1490×3valid
5.6s242×1invalid
9.6s123×4valid
163.0ms16×2invalid
302.0ms7×5valid
Compiler

Compiled 440444 to 206926 computations (53% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.8min
ival-mult: 2.8min (20.6% of total)
ival-pow: 2.1min (15.5% of total)
ival-div: 1.3min (9.2% of total)
backward-pass: 1.3min (9.2% of total)
ival-sin: 1.2min (9% of total)
ival-add: 52.2s (6.3% of total)
ival-tan: 48.8s (5.9% of total)
ival-cos: 42.9s (5.2% of total)
ival-sub: 35.3s (4.3% of total)
ival-fma: 20.2s (2.4% of total)
ival-sqrt: 19.2s (2.3% of total)
const: 12.5s (1.5% of total)
ival-log: 11.3s (1.4% of total)
ival-atan: 8.8s (1.1% of total)
ival-exp: 7.9s (1% of total)
ival-log1p: 7.9s (1% of total)
ival-expm1: 7.0s (0.8% of total)
ival-hypot: 5.9s (0.7% of total)
ival-cbrt: 5.7s (0.7% of total)
ival-asin: 3.9s (0.5% of total)
ival-neg: 3.0s (0.4% of total)
ival-acos: 2.9s (0.3% of total)
ival-fmax: 2.0s (0.2% of total)
ival-atan2: 1.2s (0.1% of total)
ival-pi: 958.0ms (0.1% of total)
ival-fmod: 442.0ms (0.1% of total)
ival-sinh: 374.0ms (0% of total)
ival-if: 328.0ms (0% of total)
ival-fabs: 252.0ms (0% of total)
ival->=: 209.0ms (0% of total)
ival-log2: 202.0ms (0% of total)
ival->: 176.0ms (0% of total)
ival-floor: 168.0ms (0% of total)
ival-copysign: 81.0ms (0% of total)
ival-e: 33.0ms (0% of total)
ival-cosh: 32.0ms (0% of total)
ival-<: 26.0ms (0% of total)
ival-tanh: 15.0ms (0% of total)

sample24.8min (18.8%)

Results
9.2min3879683×0valid
3.6min463637×1valid
33.1s179879×0invalid
30.2s144516×0precondition
1.7min112423×2valid
2.2min62623×5exit
16.2s62035×0unsamplable
1.1min17254×3valid
8.8s14720×1invalid
20.5s1787×4valid
1.0s1382×2invalid
45.0ms45×1unsamplable
11.0ms8×5valid
Precisions
Click to see histograms. Total time spent on operations: 15.2min
ival-mult: 3.1min (20.4% of total)
ival-div: 1.6min (10.4% of total)
ival-sin: 1.5min (10.2% of total)
ival-pow: 1.4min (9.4% of total)
ival-add: 1.2min (7.9% of total)
ival-sub: 1.1min (7.1% of total)
backward-pass: 56.1s (6.1% of total)
ival-cos: 55.4s (6.1% of total)
ival-tan: 34.3s (3.8% of total)
ival-exp: 31.0s (3.4% of total)
ival-log: 29.0s (3.2% of total)
ival-<=: 24.8s (2.7% of total)
ival-sqrt: 23.2s (2.5% of total)
const: 13.2s (1.4% of total)
ival-neg: 8.8s (1% of total)
ival-fabs: 7.3s (0.8% of total)
ival-<: 5.9s (0.6% of total)
ival-pi: 3.5s (0.4% of total)
ival-and: 3.3s (0.4% of total)
ival-asin: 2.4s (0.3% of total)
ival-atan2: 2.3s (0.2% of total)
ival-atan: 2.1s (0.2% of total)
ival-acos: 1.8s (0.2% of total)
ival->: 1.6s (0.2% of total)
ival-fmod: 1.4s (0.2% of total)
ival-fmin: 1.1s (0.1% of total)
ival-floor: 850.0ms (0.1% of total)
ival-if: 720.0ms (0.1% of total)
ival-==: 710.0ms (0.1% of total)
ival-cbrt: 710.0ms (0.1% of total)
ival-sinh: 699.0ms (0.1% of total)
ival-hypot: 668.0ms (0.1% of total)
ival-tanh: 645.0ms (0.1% of total)
ival-fmax: 593.0ms (0.1% of total)
ival->=: 521.0ms (0.1% of total)
ival-cosh: 466.0ms (0.1% of total)
ival-acosh: 458.0ms (0.1% of total)
ival-asinh: 385.0ms (0% of total)
ival-atanh: 354.0ms (0% of total)
ival-fma: 265.0ms (0% of total)
ival-log2: 236.0ms (0% of total)
ival-or: 53.0ms (0% of total)
Bogosity

simplify14.6min (11%)

Algorithm
2429×egg-herbie
Rules
714286×fma-define
545286×*-commutative
537186×times-frac
524976×fma-neg
508267×distribute-lft-in
Stop Event
549×saturated
1852×node limit
28×unsound
Counts
1119774 → 969582

eval12.6min (9.5%)

Compiler

Compiled 51101144 to 24945303 computations (51.2% saved)

soundness11.0min (8.4%)

Rules
647954×fma-define
494183×log1p-expm1-u
474771×fma-neg
392714×associate-*r*
386938×times-frac
Stop Event
162×saturated
355×fuel
1935×node limit
28×unsound
184×done
Compiler

Compiled 445992 to 248392 computations (44.3% saved)

prune9.6min (7.3%)

Counts
1439799 → 38972
Compiler

Compiled 1787867 to 1182083 computations (33.9% saved)

rewrite8.2min (6.2%)

Algorithm
1890×batch-egg-rewrite
Rules
1224415×log1p-expm1-u
913940×expm1-log1p-u
417561×pow1
402316×add-exp-log
383988×add-log-exp
Stop Event
1×saturated
1873×node limit
16×unsound
Counts
21249 → 646109

regimes6.6min (5%)

Counts
110673 → 10570
Calls

1216 calls:

34.0s
x
33.4s
y
29.0s
z
21.8s
a
20.3s
t
Compiler

Compiled 96718 to 73496 computations (24% saved)

explain4.0min (3.1%)

Results
1.1min232028×0valid
53.1s34494×1valid
26.3s9476×2valid
26.9s1220×3valid
380.0ms174×5exit
8.1s110×4valid
3.0ms2×5valid
Compiler

Compiled 97157 to 47036 computations (51.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.5min
ival-mult: 33.9s (22.9% of total)
ival-sin: 18.3s (12.3% of total)
ival-div: 17.6s (11.9% of total)
ival-cos: 14.0s (9.5% of total)
ival-pow: 12.5s (8.4% of total)
backward-pass: 11.2s (7.6% of total)
ival-sub: 11.2s (7.6% of total)
ival-add: 10.8s (7.3% of total)
ival-log: 4.3s (2.9% of total)
ival-sqrt: 4.0s (2.7% of total)
ival-tan: 2.8s (1.9% of total)
const: 2.3s (1.6% of total)
ival-exp: 1.9s (1.3% of total)
ival-neg: 920.0ms (0.6% of total)
ival-pi: 577.0ms (0.4% of total)
ival-atan: 522.0ms (0.4% of total)
ival-atan2: 223.0ms (0.2% of total)
ival-if: 155.0ms (0.1% of total)
ival-asin: 113.0ms (0.1% of total)
ival-sinh: 104.0ms (0.1% of total)
ival-acos: 101.0ms (0.1% of total)
ival-hypot: 96.0ms (0.1% of total)
ival-fabs: 73.0ms (0% of total)
ival-cbrt: 67.0ms (0% of total)
ival-floor: 48.0ms (0% of total)
ival-fmod: 43.0ms (0% of total)
ival->=: 34.0ms (0% of total)
ival-fmax: 21.0ms (0% of total)
ival-log1p: 19.0ms (0% of total)
ival-copysign: 18.0ms (0% of total)
ival-fma: 17.0ms (0% of total)
ival-log2: 14.0ms (0% of total)
ival-cosh: 12.0ms (0% of total)
ival-tanh: 10.0ms (0% of total)
ival-<: 5.0ms (0% of total)
ival->: 5.0ms (0% of total)

bsearch3.4min (2.5%)

Algorithm
5398×binary-search
649×left-value
Stop Event
130×predicate-same
5267×narrow-enough
1×predicate-failed
Results
1.9min619895×0valid
20.3s36666×1valid
5.5s27359×0invalid
3.6s5515×2valid
902.0ms1284×3valid
109.0ms532×1invalid
40.0ms287×0unsamplable
101.0ms185×2invalid
1.0ms1×5exit
Compiler

Compiled 1254569 to 939921 computations (25.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.6min
ival-mult: 34.0s (34.5% of total)
ival-sub: 15.8s (16.1% of total)
ival-div: 11.7s (11.9% of total)
ival-add: 11.2s (11.3% of total)
ival-sin: 5.0s (5% of total)
ival-pow: 4.1s (4.2% of total)
ival-cos: 2.9s (3% of total)
ival-sqrt: 2.8s (2.8% of total)
backward-pass: 2.6s (2.6% of total)
ival-log: 2.2s (2.2% of total)
ival-exp: 1.7s (1.7% of total)
const: 1.4s (1.4% of total)
ival-neg: 898.0ms (0.9% of total)
ival-tan: 892.0ms (0.9% of total)
ival-atan2: 390.0ms (0.4% of total)
ival-fabs: 238.0ms (0.2% of total)
ival-atan: 207.0ms (0.2% of total)
ival-acos: 174.0ms (0.2% of total)
ival-pi: 118.0ms (0.1% of total)
ival-asin: 92.0ms (0.1% of total)
ival-fmod: 78.0ms (0.1% of total)
ival-cbrt: 28.0ms (0% of total)
ival-tanh: 21.0ms (0% of total)
ival->=: 18.0ms (0% of total)
ival-if: 17.0ms (0% of total)
ival-copysign: 9.0ms (0% of total)
ival-hypot: 6.0ms (0% of total)
ival-cosh: 4.0ms (0% of total)
ival-sinh: 4.0ms (0% of total)

series3.3min (2.5%)

Counts
21249 → 473665
Calls

115143 calls:

TimeVariablePointExpression
3.9s
hi
@-inf
(/ (+ x (- (* lo (/ (- x lo) hi)) lo)) hi)
3.3s
hi
@0
(* lo (- (/ 1 hi) (/ x (pow hi 2))))
955.0ms
x
@-inf
(+ (/ 1 lo) (/ (* hi (- (/ 1 lo) (/ x (pow lo 2)))) lo))
500.0ms
dY.v
@inf
(log (+ 1 (sqrt (fmax (pow (sqrt (+ (* (* dX.w (floor d)) (* dX.w (floor d))) (* (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h))))) (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h)))))))) 2) (+ (* (pow (floor d) 2) (pow dY.w 2)) (/ (- (pow (* (floor w) dY.u) 4) (pow (* (floor h) dY.v) 4)) (- (pow (* (floor w) dY.u) 2) (pow (* (floor h) dY.v) 2))))))))
494.0ms
c0
@0
(* c0 (/ (log (pow (pow (exp -1/2) M) (sqrt -1))) w))

preprocess2.5min (1.9%)

Algorithm
542×egg-herbie
Rules
254384×fma-define
252110×fma-neg
118944×unsub-neg
101039×sub-neg
94642×distribute-lft-in
Stop Event
294×saturated
248×node limit
Compiler

Compiled 408496 to 225444 computations (44.8% saved)

analyze2.1min (1.6%)

Algorithm
545×search
2×random
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%84.4%15.6%0%0%0%0
39.4%33.3%51.2%15.6%0%0%0%1
45.1%37.7%46%15.6%0%0.7%0%2
54.3%44.3%37.3%15.7%0%2.7%0%3
61%49.2%31.4%15.8%0%3.6%0%4
67.2%53.9%26.3%15.8%0%4%0%5
71.1%56.7%23%15.8%0%4.3%0%6
75.1%59.5%19.7%15.9%0%4.8%0.1%7
77.1%60.8%18.1%15.9%0%5.2%0.1%8
79.7%62.6%15.9%15.9%0%5.5%0.1%9
81.2%63.5%14.7%16%0%5.7%0.1%10
83.5%65.2%12.9%16%0%5.8%0.1%11
84.6%65.8%12%16%0%6.1%0.1%12
Compiler

Compiled 13446 to 8689 computations (35.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-mult: 20.1s (26.6% of total)
ival-div: 9.0s (12% of total)
ival-pow: 8.1s (10.7% of total)
ival-add: 5.6s (7.5% of total)
ival-sub: 5.6s (7.5% of total)
ival-<=: 4.3s (5.7% of total)
ival-sqrt: 3.6s (4.8% of total)
ival-sin: 3.0s (4% of total)
ival-fabs: 2.9s (3.9% of total)
ival-cos: 2.5s (3.3% of total)
const: 1.2s (1.6% of total)
ival-log: 1.0s (1.3% of total)
ival-tan: 998.0ms (1.3% of total)
ival-floor: 880.0ms (1.2% of total)
ival-exp: 878.0ms (1.2% of total)
ival-if: 723.0ms (1% of total)
ival-==: 720.0ms (1% of total)
ival-and: 669.0ms (0.9% of total)
ival-fmax: 631.0ms (0.8% of total)
ival-neg: 535.0ms (0.7% of total)
ival-pi: 485.0ms (0.6% of total)
ival-<: 384.0ms (0.5% of total)
ival-atan2: 274.0ms (0.4% of total)
ival-log2: 179.0ms (0.2% of total)
backward-pass: 175.0ms (0.2% of total)
ival-atan: 130.0ms (0.2% of total)
ival-acos: 125.0ms (0.2% of total)
ival->: 122.0ms (0.2% of total)
ival->=: 101.0ms (0.1% of total)
ival-asin: 92.0ms (0.1% of total)
ival-fmod: 92.0ms (0.1% of total)
ival-cosh: 80.0ms (0.1% of total)
ival-sinh: 31.0ms (0% of total)
ival-or: 22.0ms (0% of total)
ival-cbrt: 19.0ms (0% of total)
ival-tanh: 8.0ms (0% of total)
ival-fmin: 6.0ms (0% of total)
ival-atanh: 1.0ms (0% of total)
ival-asinh: 0.0ms (0% of total)
ival-hypot: 0.0ms (0% of total)
ival-fma: 0.0ms (0% of total)
ival-acosh: 0.0ms (0% of total)

end5.5s (0.1%)

Calls

1 calls:

TimeVariablePointExpression
3.0ms
angle
@0
(sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2)))

Profiling

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