Details

Time bar (total: 9.8s)

analyze1.3s (12.7%)

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)

sample4.2s (42.7%)

Results
2.5s4108×body2048valid
1.0s2094×body1024valid
364.0ms1022×body512valid
115.0ms508×body256valid
66.0ms524×body128valid
1.0msbody128invalid
Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify68.0ms (0.7%)

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
0.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.9b
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
Compiler

Compiled 53 to 36 computations (32.1% saved)

localize7.0ms (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))
0.9b
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series6.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

4.0ms
(/.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)))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
2 → 39
Calls

2 calls:

3.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
0.0ms
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

simplify74.0ms (0.8%)

Algorithm
egg-herbie
Rules
667×times-frac_binary64
628×fma-def_binary64
405×fma-neg_binary64
337×associate-/l*_binary64
292×associate-/r*_binary64
Counts
63 → 60
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01031379
12091264
25491261
314341259
445021259
550391259

prune50.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New57360
Fresh000
Picked101
Done000
Total58361
Error
0.9b
Counts
61 → 3
Alt Table
StatusErrorProgram
2.3b
(*.f64 (*.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
0.9b
(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
0.9b
(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
Compiler

Compiled 1303 to 942 computations (27.7% saved)

localize56.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
0.0b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
0.0b
(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
0.9b
(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series523.0ms (5.3%)

Counts
2 → 24
Calls

2 calls:

520.0ms
(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
2.0ms
(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
expm1-log1p-u_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 22
Calls

2 calls:

0.0ms
(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
0.0ms
(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

simplify115.0ms (1.2%)

Algorithm
egg-herbie
Rules
862×fma-neg_binary64
724×unswap-sqr_binary64
466×times-frac_binary64
417×unsub-neg_binary64
335×fma-def_binary64
Counts
46 → 33
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
036950
140873
250873
366873
491873
5133873
6225873
7462873
81063873
92763873
103925873
114716873
124964873

prune86.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New89493
Fresh022
Picked101
Done000
Total90696
Error
0.8b
Counts
96 → 6
Alt Table
StatusErrorProgram
0.9b
(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
2.3b
(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)))
3.4b
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
0.9b
(expm1.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))
2.3b
(*.f64 (*.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
1.8b
(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
Compiler

Compiled 2310 to 1717 computations (25.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))
0.0b
(log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))
0.0b
(expm1.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))
0.9b
(acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))

series1.1s (10.8%)

Counts
4 → 12
Calls

4 calls:

537.0ms
(expm1.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))
520.0ms
(log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))
2.0ms
(+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))
2.0ms
(acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-log-exp_binary64
add-exp-log_binary64
Counts
4 → 58
Calls

4 calls:

3.0ms
(+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))
2.0ms
(log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))
0.0ms
(acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))
0.0ms
(expm1.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))

simplify116.0ms (1.2%)

Algorithm
egg-herbie
Rules
747×fma-neg_binary64
651×fma-def_binary64
436×unswap-sqr_binary64
387×associate-+l+_binary64
355×distribute-rgt-in_binary64
Counts
70 → 88
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0731619
11241514
21841514
33401514
47791514
519221514
628271514
746451514
849501514

prune95.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New83588
Fresh325
Picked101
Done000
Total87794
Error
0.8b
Counts
94 → 7
Alt Table
StatusErrorProgram
0.9b
(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
0.9b
(expm1.f64 (log.f64 (*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
2.3b
(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)))
2.3b
(expm1.f64 (log.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (cbrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))) (cbrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
3.4b
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))) (cbrt.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))) (cbrt.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
2.3b
(*.f64 (*.f64 (cbrt.f64 (expm1.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))) (cbrt.f64 (expm1.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))))) (cbrt.f64 (expm1.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
2.3b
(expm1.f64 (log.f64 (+.f64 1 (*.f64 (*.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
Compiler

Compiled 2867 to 2177 computations (24.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))))
0.0b
(expm1.f64 (log.f64 (*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
0.0b
(*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))
0.9b
(acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))

series1.0s (10.6%)

Counts
3 → 36
Calls

3 calls:

527.0ms
(expm1.f64 (log.f64 (*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
513.0ms
(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))))
3.0ms
(*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))

rewrite38.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
34×pow1_binary64
27×add-sqr-sqrt_binary64
26×sqrt-prod_binary64
25×*-un-lft-identity_binary64
24×sqrt-div_binary64
Counts
3 → 111
Calls

3 calls:

11.0ms
(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))))
9.0ms
(*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))
1.0ms
(expm1.f64 (log.f64 (*.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))

simplify228.0ms (2.3%)

Algorithm
egg-herbie
Rules
684×fma-def_binary64
503×log-prod_binary64
416×distribute-rgt-in_binary64
357×distribute-lft-in_binary64
274×distribute-rgt-out_binary64
Counts
147 → 153
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01144669
11844257
24234209
310344059
428604047
535474037
645264037
750004037
848494037

prune301.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1881189
Fresh246
Picked101
Done000
Total1915196
Error
0.8b
Counts
196 → 5
Alt Table
StatusErrorProgram
0.9b
(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
2.3b
(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)))
3.6b
(expm1.f64 (log.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))))
3.4b
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))))) (cbrt.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))) (cbrt.f64 (log.f64 (+.f64 1 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
2.3b
(expm1.f64 (log.f64 (+.f64 1 (*.f64 (*.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 -5 v) 1) (fma.f64 v v -1))))))))
Compiler

Compiled 8248 to 6293 computations (23.7% saved)

regimes292.0ms (3%)

Accuracy

Total 0.0b remaining (2%)

Threshold costs 0.0b (2%)

Counts
55 → 1
Compiler

Compiled 8121 to 6203 computations (23.6% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01425
11725
21625

end184.0ms (1.9%)

Compiler

Compiled 269 to 205 computations (23.8% saved)

Profiling

Loading profile data...