Details

Time bar (total: 5.7s)

analyze103.0ms (1.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%6.2%93.8%0
0%6.2%93.8%1
3.1%3.1%93.8%2
3.1%3.1%93.8%3
4.7%1.6%93.8%4
4.7%1.6%93.8%5
5.5%0.8%93.8%6
5.5%0.8%93.8%7
5.8%0.4%93.8%8
5.8%0.4%93.8%9
6%0.2%93.8%10
6%0.2%93.8%11
6.1%0.1%93.8%12
6.1%0.1%93.8%13
6.2%0%93.8%14
Compiler

Compiled 36 to 30 computations (16.7% saved)

sample1.8s (32.2%)

Results
1.8s8256×body128valid
Compiler

Compiled 72 to 60 computations (16.7% saved)

preprocess75.0ms (1.3%)

Algorithm
egg-herbie
Rules
545×*-commutative_binary64
493×associate-*l*_binary64
470×sqr-pow_binary64
416×unswap-sqr_binary64
325×associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02848
15948
211048
320748
449548
5151248
6205648
7270148
8282048
9299448
10321348
11354548
12400548
13460448
022
Stop Event
saturated
node limit
Compiler

Compiled 21 to 19 computations (9.5% saved)

simplify53.0ms (0.9%)

Algorithm
egg-herbie
Rules
818×unswap-sqr_binary64
500×sqr-pow_binary64
281×cube-prod_binary64
277×*-commutative_binary64
242×pow-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02024
13824
26524
311424
425524
573924
6100724
7133724
8262124
9272324
10288424
11309324
12340024
13382824
14439224
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.3b
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
0.3b
(+.f64 (*.f64 (*.f64 (/.f64 1 6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (*.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
Compiler

Compiled 112 to 98 computations (12.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2))))
0.2b
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.2b
(*.f64 (PI.f64) u2)
0.3b
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)

series172.0ms (3%)

Counts
4 → 36
Calls

15 calls:

46.0ms
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u2
inf
46.0ms
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u2
-inf
20.0ms
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u1
0
12.0ms
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u1
-inf
11.0ms
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u1
inf

rewrite55.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
575×prod-diff_binary64
276×log1p-udef_binary64
156×add-sqr-sqrt_binary64
147×add-log-exp_binary64
146×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01650
132450
2363550
Stop Event
node limit
Counts
4 → 76

simplify39.0ms (0.7%)

Algorithm
egg-herbie
Rules
715×fma-neg_binary64
432×distribute-rgt-neg-in_binary64
423×distribute-lft-neg-in_binary64
387×associate-*l*_binary64
351×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
089952
1231900
2643838
32796824
Stop Event
node limit
Counts
112 → 101

prune133.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New938101
Fresh101
Picked101
Done000
Total958103
Error
0b
Counts
103 → 8
Alt Table
StatusErrorProgram
0.5b
(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)))
0.3b
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
1.1b
(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)) 3)
0.8b
(pow.f64 (pow.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2) 3) 1/3)
0.6b
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (exp.f64 (log.f64 (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))))) 1/2)
0.5b
(/.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) 3) 1/8) (+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))))) (-.f64 1/4 (*.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) 1/2))))
0.6b
(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2) 3))
0.6b
(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)) 2)
Compiler

Compiled 2502 to 1917 computations (23.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (neg.f64 (log.f64 u1)))
0.2b
(*.f64 (PI.f64) u2)
0.3b
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
0.4b
(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

series253.0ms (4.5%)

Counts
3 → 44
Calls

12 calls:

114.0ms
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u2
inf
47.0ms
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u2
-inf
13.0ms
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u1
inf
12.0ms
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u1
-inf
11.0ms
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
u1
0

rewrite51.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
575×prod-diff_binary64
167×add-sqr-sqrt_binary64
158×log1p-expm1-u_binary64
158×expm1-log1p-u_binary64
157×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01743
134937
2403737
Stop Event
node limit
Counts
3 → 64

simplify41.0ms (0.7%)

Algorithm
egg-herbie
Rules
546×fma-neg_binary64
476×distribute-rgt-neg-in_binary64
458×distribute-lft-neg-in_binary64
445×associate-*l*_binary64
426×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0721102
11931070
25591024
326671018
Stop Event
node limit
Counts
108 → 84

prune80.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New98199
Fresh347
Picked011
Done000
Total1016107
Error
0b
Counts
107 → 6
Alt Table
StatusErrorProgram
0.5b
(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)))
0.3b
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
0.6b
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (exp.f64 (log.f64 (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))))) 1/2)
0.5b
(/.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) 3) 1/8) (+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))))) (-.f64 1/4 (*.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) 1/2))))
0.2b
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)
0.6b
(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)) 2)
Compiler

Compiled 2418 to 1723 computations (28.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64))))))
0.1b
(sqrt.f64 (neg.f64 (log.f64 u1)))
0.2b
(*.f64 u2 (PI.f64))
0.3b
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)

series154.0ms (2.7%)

Counts
3 → 48
Calls

12 calls:

52.0ms
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)
u2
-inf
49.0ms
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)
u2
inf
14.0ms
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)
u1
0
13.0ms
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)
u1
-inf
12.0ms
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)
u1
inf

rewrite51.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
575×prod-diff_binary64
168×add-sqr-sqrt_binary64
158×log1p-expm1-u_binary64
158×expm1-log1p-u_binary64
157×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01751
134949
2405349
Stop Event
node limit
Counts
3 → 51

simplify45.0ms (0.8%)

Algorithm
egg-herbie
Rules
917×fma-neg_binary64
631×associate-*l*_binary64
568×associate-*r*_binary64
247×fma-def_binary64
238×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0801210
12201166
27111108
336641104
Stop Event
node limit
Counts
99 → 74

prune94.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1020102
Fresh044
Picked011
Done011
Total1026108
Error
0b
Counts
108 → 6
Alt Table
StatusErrorProgram
0.5b
(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)))
0.3b
(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) (*.f64 1/6 (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
0.6b
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (exp.f64 (log.f64 (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))))) 1/2)
0.5b
(/.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) 3) 1/8) (+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))))) (-.f64 1/4 (*.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64)))))) 1/2))))
0.2b
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)
0.6b
(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)) 2)
Compiler

Compiled 2593 to 1802 computations (30.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 u2 (*.f64 2 (PI.f64)))
0.3b
(log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2))
0.3b
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)
0.3b
(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)))

series1.1s (19.7%)

Counts
4 → 84
Calls

21 calls:

180.0ms
(log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2))
u2
inf
179.0ms
(log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2))
u2
-inf
171.0ms
(log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2))
u1
inf
154.0ms
(log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2))
u1
-inf
148.0ms
(log.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2))
u1
0

rewrite59.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
484×prod-diff_binary64
282×log1p-udef_binary64
160×add-sqr-sqrt_binary64
150×add-log-exp_binary64
150×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01882
134082
2371182
Stop Event
node limit
Counts
4 → 84

simplify52.0ms (0.9%)

Algorithm
egg-herbie
Rules
666×times-frac_binary64
540×associate-/l*_binary64
315×associate-/r*_binary64
307×fma-def_binary64
248×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01332748
13802567
212142445
Stop Event
node limit
Counts
168 → 92

prune83.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New91192
Fresh123
Picked101
Done112
Total94498
Error
0b
Counts
98 → 4
Alt Table
StatusErrorProgram
0.6b
(fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (exp.f64 (log.f64 (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))))) 1/2)
0.2b
(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (*.f64 (sqrt.f64 2) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))) 1/2)
0.3b
(fma.f64 1/6 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (cos.f64 (*.f64 (PI.f64) (*.f64 2 u2)))) 1/2)
0.6b
(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (*.f64 1/6 (cos.f64 (*.f64 u2 (*.f64 2 (PI.f64))))) 1/2)) 2)
Compiler

Compiled 2605 to 2029 computations (22.1% saved)

regimes972.0ms (17.2%)

Accuracy

Total 0.2b remaining (95.2%)

Threshold costs 0.2b (95.2%)

Counts
78 → 1
Compiler

Compiled 17818 to 15773 computations (11.5% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01728
12528
22728
32828
Stop Event
saturated

end94.0ms (1.7%)

Stop Event
fuel
Compiler

Compiled 113 to 101 computations (10.6% saved)

Profiling

Loading profile data...