Details

Time bar (total: 8.1s)

analyze1.2s (14.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
0%100%0%4
0%100%0%5
0%100%0%6
0%100%0%7
0%100%0%8
0%100%0%9
0%100%0%10
0%100%0%11
0%100%0%12
3%46.9%50%13
3.1%46.8%50%14
Compiler

Compiled 16 to 11 computations (31.3% saved)

sample3.9s (47.6%)

Results
2.3s4010×body2048valid
892.0ms2136×body1024valid
339.0ms1087×body512valid
105.0ms501×body256valid
65.0ms521×body128valid
1.0msbody4096valid
1.0msbody128invalid
Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify72.0ms (0.9%)

Algorithm
egg-herbie
Rules
686×div-sub_binary64
546×sub-neg_binary64
397×neg-mul-1_binary64
344×neg-sub0_binary64
311×associate-/r*_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01019
13119
27217
320317
453217
5134017
6271017
7374817
8464317
9498117

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.6b
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
Compiler

Compiled 53 to 36 computations (32.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
0.6b
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series5.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

3.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
2.0ms
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite56.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
891×log1p-expm1-u_binary64
891×expm1-log1p-u_binary64
98×add-sqr-sqrt_binary64
91×add-cbrt-cube_binary64
90×add-log-exp_binary64
Counts
2 → 69
Calls

2 calls:

54.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
54.0ms
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01032
119932
2227732
3549132
000
100

simplify76.0ms (0.9%)

Algorithm
egg-herbie
Rules
649×cancel-sign-sub-inv_binary64
494×fma-def_binary64
460×sub-neg_binary64
309×distribute-rgt-out_binary64
286×unswap-sqr_binary64
Counts
93 → 84
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040380
1113362
2316359
3829359
42262359
54207359
64609359
74995359

prune83.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New79584
Fresh000
Picked101
Done000
Total80585
Error
0.6b
Counts
85 → 5
Alt Table
StatusErrorProgram
2.5b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (*.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) (*.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) (*.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (*.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))))
2.1b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 1))) (fma.f64 (neg.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 1 (*.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 1)))
0.6b
(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
0.9b
(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
1.5b
(pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)
Compiler

Compiled 2777 to 2033 computations (26.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
0.0b
(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
0.0b
(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
0.6b
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series316.0ms (3.9%)

Counts
2 → 24
Calls

2 calls:

314.0ms
(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
2.0ms
(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

rewrite84.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
471×log-prod_binary64
272×pow2_binary64
190×pow1/3_binary64
187×expm1-udef_binary64
187×log1p-udef_binary64
Counts
2 → 70
Calls

2 calls:

82.0ms
(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
82.0ms
(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01236
121536
2244836
3492536
000
100

simplify133.0ms (1.6%)

Algorithm
egg-herbie
Rules
862×fma-neg_binary64
850×unsub-neg_binary64
557×sub-neg_binary64
476×distribute-neg-in_binary64
388×neg-sub0_binary64
Counts
94 → 72
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011432
118432
225432
334432
452432
579432
6134432
7270432
8527432
91633432
102720432
113905432
124474432
134642432
144925432
154845432

prune145.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1533156
Fresh314
Picked101
Done000
Total1574161
Error
0.6b
Counts
161 → 4
Alt Table
StatusErrorProgram
2.5b
(exp.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)) (log.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
0.9b
(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
2.5b
(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) 2) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2) (*.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2))))
0.6b
(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
Compiler

Compiled 4764 to 3547 computations (25.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
0.0b
(log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
0.0b
(expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
0.6b
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series1.0s (12.6%)

Counts
3 → 36
Calls

3 calls:

702.0ms
(log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
316.0ms
(expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
2.0ms
(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))

rewrite65.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
509×log-prod_binary64
204×pow1/3_binary64
202×expm1-udef_binary64
202×log1p-udef_binary64
187×pow3_binary64
Counts
3 → 97
Calls

3 calls:

61.0ms
(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
61.0ms
(log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
61.0ms
(expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01457
123657
2263857
3496657
000
100

simplify141.0ms (1.7%)

Algorithm
egg-herbie
Rules
862×fma-neg_binary64
850×unsub-neg_binary64
557×sub-neg_binary64
476×distribute-neg-in_binary64
388×neg-sub0_binary64
Counts
133 → 100
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
013720
121684
229684
338684
456684
583684
6138684
7274684
8531684
91637684
102724684
113909684
124478684
134646684
144929684
154849684

prune149.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1342136
Fresh123
Picked011
Done000
Total1355140
Error
0.6b
Counts
140 → 5
Alt Table
StatusErrorProgram
2.5b
(exp.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)) (log.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
0.9b
(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
3.0b
(exp.f64 (fma.f64 (*.f64 (cbrt.f64 (+.f64 1 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (+.f64 1 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (+.f64 1 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) -1))
0.6b
(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
3.0b
(exp.f64 (expm1.f64 (pow.f64 (cbrt.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) 3)))
Compiler

Compiled 4877 to 3631 computations (25.5% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.6b
(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series2.0ms (0%)

Counts
1 → 0
Calls

1 calls:

2.0ms
(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite96.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
667×log1p-expm1-u_binary64
667×expm1-log1p-u_binary64
152×prod-diff_binary64
138×expm1-udef_binary64
138×log1p-udef_binary64
Counts
1 → 35
Calls

1 calls:

95.0ms
(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
116414
2170814
3493714
4495414
5494214
000
100

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Counts
35 → 35
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
100

prune41.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New34135
Fresh123
Picked101
Done011
Total36440
Error
0.6b
Counts
40 → 4
Alt Table
StatusErrorProgram
3.0b
(exp.f64 (fma.f64 (*.f64 (cbrt.f64 (+.f64 1 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (+.f64 1 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (+.f64 1 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) -1))
1.9b
(pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 3)
0.6b
(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
3.0b
(exp.f64 (expm1.f64 (pow.f64 (cbrt.f64 (log1p.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) 3)))
Compiler

Compiled 1053 to 791 computations (24.9% saved)

regimes424.0ms (5.2%)

Accuracy

Total 0.0b remaining (2.3%)

Threshold costs 0.0b (2.3%)

Counts
77 → 1
Compiler

Compiled 8451 to 6366 computations (24.7% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01425
11725
21625

end111.0ms (1.4%)

Compiler

Compiled 138 to 107 computations (22.5% saved)

Profiling

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