Details

Time bar (total: 6.2s)

analyze1.2s (20.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
2.3%97.4%0.2%9
3.5%96.2%0.2%10
9.5%90.2%0.2%11
14.3%85.4%0.2%12
22.4%77.4%0.2%13
29.7%70%0.2%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (18.4%)

Results
991.0ms8254×body128valid
88.0ms720×body128invalid
0.0msbody512valid
0.0msbody256valid
Compiler

Compiled 50 to 32 computations (36% saved)

simplify112.0ms (1.8%)

Algorithm
egg-herbie
Rules
1405×fma-def_binary64
906×div-sub_binary64
613×distribute-rgt-in_binary64
583×fma-neg_binary64
525×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01116
12214
24314
38214
416414
530414
665514
7159014
8304614
9278114
10295414
11302814
12311614
13428914
14518714

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
1.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
1.0b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
Compiler

Compiled 56 to 29 computations (48.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 z t) (-.f64 z a))
0.9b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series58.0ms (0.9%)

Counts
2 → 96
Calls

2 calls:

37.0ms
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
20.0ms
(/.f64 (-.f64 z t) (-.f64 z a))

rewrite10.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity_binary64
38×add-sqr-sqrt_binary64
25×times-frac_binary64
14×add-cube-cbrt_binary64
12×distribute-lft-out--_binary64
Counts
2 → 64
Calls

2 calls:

6.0ms
(/.f64 (-.f64 z t) (-.f64 z a))
0.0ms
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify84.0ms (1.4%)

Algorithm
egg-herbie
Rules
878×fma-def_binary64
685×times-frac_binary64
505×cancel-sign-sub-inv_binary64
356×sub-neg_binary64
161×+-commutative_binary64
Counts
160 → 135
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02714135
16994064
223963758
350753758

prune115.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1296135
Fresh000
Picked011
Done000
Total1297136
Error
0.0b
Counts
136 → 7
Alt Table
StatusErrorProgram
41.0b
(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (*.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (*.f64 y (*.f64 a (*.f64 a t))) (pow.f64 z 3)))))
7.5b
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
48.3b
(fma.f64 y (*.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 a))) (/.f64 (-.f64 z t) (-.f64 (sqrt.f64 z) (sqrt.f64 a)))) x)
1.0b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
1.3b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
23.8b
(fma.f64 (/.f64 y a) t x)
40.7b
(fma.f64 y (*.f64 (/.f64 (-.f64 z t) (-.f64 (pow.f64 z 3) (pow.f64 a 3))) (+.f64 (*.f64 z z) (+.f64 (*.f64 a a) (*.f64 z a)))) x)
Compiler

Compiled 3532 to 1181 computations (66.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
0.4b
(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
0.9b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
2.8b
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))

series492.0ms (7.9%)

Counts
4 → 168
Calls

4 calls:

286.0ms
(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
140.0ms
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))
43.0ms
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
22.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))

rewrite124.0ms (2%)

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity_binary64
248×cbrt-prod_binary64
247×add-sqr-sqrt_binary64
205×times-frac_binary64
96×distribute-lft-out--_binary64
Counts
4 → 284
Calls

4 calls:

35.0ms
(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
28.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
5.0ms
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))
0.0ms
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)

simplify331.0ms (5.3%)

Algorithm
egg-herbie
Rules
545×*-commutative_binary64
306×+-commutative_binary64
220×associate-+r+_binary64
215×fma-def_binary64
176×associate-*r*_binary64
Counts
452 → 482
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0149123923
1485023653
2499923653

prune870.0ms (14%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New6820682
Fresh055
Picked011
Done011
Total6827689
Error
0.0b
Counts
689 → 7
Alt Table
StatusErrorProgram
41.0b
(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (*.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (*.f64 y (*.f64 a (*.f64 a t))) (pow.f64 z 3)))))
7.5b
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
48.3b
(fma.f64 y (*.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 a))) (/.f64 (-.f64 z t) (-.f64 (sqrt.f64 z) (sqrt.f64 a)))) x)
1.0b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
1.3b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
23.8b
(fma.f64 (/.f64 y a) t x)
40.7b
(fma.f64 y (*.f64 (/.f64 (-.f64 z t) (-.f64 (pow.f64 z 3) (pow.f64 a 3))) (+.f64 (*.f64 z z) (+.f64 (*.f64 a a) (*.f64 z a)))) x)
Compiler

Compiled 48481 to 20016 computations (58.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 y (-.f64 z a))
0.0b
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
3.1b
(fma.f64 (/.f64 y (-.f64 z a)) z x)
5.4b
(/.f64 (*.f64 y t) (-.f64 z a))

series125.0ms (2%)

Counts
4 → 156
Calls

4 calls:

53.0ms
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
28.0ms
(/.f64 (*.f64 y t) (-.f64 z a))
25.0ms
(fma.f64 (/.f64 y (-.f64 z a)) z x)
19.0ms
(/.f64 y (-.f64 z a))

rewrite30.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity_binary64
58×add-sqr-sqrt_binary64
40×times-frac_binary64
36×add-cube-cbrt_binary64
33×prod-diff_binary64
Counts
4 → 141
Calls

4 calls:

7.0ms
(/.f64 (*.f64 y t) (-.f64 z a))
7.0ms
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
3.0ms
(/.f64 y (-.f64 z a))
0.0ms
(fma.f64 (/.f64 y (-.f64 z a)) z x)

simplify212.0ms (3.4%)

Algorithm
egg-herbie
Rules
540×cancel-sign-sub-inv_binary64
307×fma-neg_binary64
252×sub-neg_binary64
206×associate-/l*_binary64
189×times-frac_binary64
Counts
297 → 265
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03987851
19567082
234396648
347766648
449976648
548586648

prune197.0ms (3.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2641265
Fresh134
Picked011
Done022
Total2657272
Error
0b
Counts
272 → 7
Alt Table
StatusErrorProgram
48.3b
(fma.f64 y (*.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 a))) (/.f64 (-.f64 z t) (-.f64 (sqrt.f64 z) (sqrt.f64 a)))) x)
1.0b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
1.3b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
33.6b
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (*.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 t (sqrt.f64 (-.f64 z a)))))
23.8b
(fma.f64 (/.f64 y a) t x)
40.7b
(fma.f64 y (*.f64 (/.f64 (-.f64 z t) (-.f64 (pow.f64 z 3) (pow.f64 a 3))) (+.f64 (*.f64 z z) (+.f64 (*.f64 a a) (*.f64 z a)))) x)
7.5b
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
Compiler

Compiled 8646 to 1811 computations (79.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
3.2b
(fma.f64 (/.f64 y a) t x)

series14.0ms (0.2%)

Counts
1 → 48
Calls

1 calls:

14.0ms
(fma.f64 (/.f64 y a) t x)

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 (/.f64 y a) t x)

simplify85.0ms (1.4%)

Algorithm
egg-herbie
Rules
601×distribute-rgt-out_binary64
552×distribute-rgt-in_binary64
546×associate-*l/_binary64
522×distribute-lft-in_binary64
416×times-frac_binary64
Counts
58 → 22
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
021463
126446
251446
3134446
4445446
51651446
64002446
74440446
84739446
95000446
104982446

prune15.0ms (0.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New22022
Fresh033
Picked011
Done033
Total22729
Error
0b
Counts
29 → 7
Alt Table
StatusErrorProgram
48.3b
(fma.f64 y (*.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 a))) (/.f64 (-.f64 z t) (-.f64 (sqrt.f64 z) (sqrt.f64 a)))) x)
1.0b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
1.3b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
33.6b
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (*.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 t (sqrt.f64 (-.f64 z a)))))
23.8b
(fma.f64 (/.f64 y a) t x)
40.7b
(fma.f64 y (*.f64 (/.f64 (-.f64 z t) (-.f64 (pow.f64 z 3) (pow.f64 a 3))) (+.f64 (*.f64 z z) (+.f64 (*.f64 a a) (*.f64 z a)))) x)
7.5b
(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
Compiler

Compiled 388 to 137 computations (64.7% saved)

regimes804.0ms (12.9%)

Accuracy

Total 1.3b remaining (98.4%)

Threshold costs 0b (0%)

Counts
99 → 1
Compiler

Compiled 16472 to 9434 computations (42.7% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01014
11414
22214
32614
42814
52814

end99.0ms (1.6%)

Compiler

Compiled 194 to 104 computations (46.4% saved)

Profiling

Loading profile data...