Details

Time bar (total: 10.2s)

analyze2.0s (20.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.6%0.4%0
0%99.6%0.4%1
0%99.6%0.4%2
0%99.6%0.4%3
0%99.6%0.4%4
0%99.6%0.4%5
0%99.6%0.4%6
0%99.6%0.4%7
0%99.6%0.4%8
0%99.6%0.4%9
0%99.6%0.4%10
0%99.6%0.4%11
0%99.6%0.4%12
0%99.6%0.4%13
0%99.6%0.4%14
Compiler

Compiled 28 to 19 computations (32.1% saved)

sample121.0ms (1.2%)

Algorithm
intervals
Symmetry

(sort x y)

(sort z t)

Results
17.0ms256×body128valid
17.0ms242×body128invalid
Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify221.0ms (2.2%)

Algorithm
egg-herbie
Rules
1133×distribute-rgt-in_binary64
1066×distribute-lft-in_binary64
969×unsub-neg_binary64
583×fma-def_binary64
461×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01926
13724
29724
327724
479724
5180924
6253224
7278324
8312824
9340924
10331924
11332724
12333124
13346124
14362024
15362124
16362324
17362324
18507124

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
6.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
6.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
Compiler

Compiled 94 to 57 computations (39.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x y (*.f64 z t))
0.0b
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))
0.1b
(*.f64 c (fma.f64 b c a))
7.8b
(*.f64 (*.f64 c (fma.f64 b c a)) i)

series111.0ms (1.1%)

Counts
4 → 228
Calls

4 calls:

57.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))
24.0ms
(fma.f64 x y (*.f64 z t))
21.0ms
(*.f64 (*.f64 c (fma.f64 b c a)) i)
9.0ms
(*.f64 c (fma.f64 b c a))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
11×pow1_binary64
*-un-lft-identity_binary64
Counts
4 → 73
Calls

4 calls:

4.0ms
(*.f64 (*.f64 c (fma.f64 b c a)) i)
3.0ms
(*.f64 c (fma.f64 b c a))
3.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))
0.0ms
(fma.f64 x y (*.f64 z t))

simplify155.0ms (1.5%)

Algorithm
egg-herbie
Rules
578×fma-neg_binary64
563×distribute-rgt-in_binary64
556×distribute-lft-in_binary64
505×fma-def_binary64
242×cancel-sign-sub-inv_binary64
Counts
301 → 160
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01494992
13274027
210913988
345313988
449333988

prune242.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New15010160
Fresh000
Picked011
Done000
Total15011161
Error
0.0b
Counts
161 → 11
Alt Table
StatusErrorProgram
6.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
33.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (fma.f64 b c a)) (sqrt.f64 i)) (sqrt.f64 i))))
7.2b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))) (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))))
31.7b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (sqrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) (sqrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))))))
5.6b
(*.f64 2 (-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (*.f64 i (fma.f64 c b a)))))
24.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 c (fma.f64 b c a)) (*.f64 c (fma.f64 b c a))) (*.f64 c (fma.f64 b c a)))) i)))
5.5b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))))
14.6b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (+.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (*.f64 c (*.f64 i a)))))
5.9b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a))))) (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))))))
19.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (expm1.f64 (log1p.f64 (*.f64 (*.f64 c (fma.f64 b c a)) i)))))
6.4b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (*.f64 (cbrt.f64 (fma.f64 b c a)) (cbrt.f64 (fma.f64 b c a)))) (cbrt.f64 (fma.f64 b c a))) i)))
Compiler

Compiled 4358 to 1265 computations (71% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 i)
1.0b
(*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))
2.4b
(*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i))))
2.9b
(*.f64 (*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))

series654.0ms (6.4%)

Counts
4 → 156
Calls

4 calls:

333.0ms
(*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i))))
255.0ms
(*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))
33.0ms
(*.f64 (*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))
32.0ms
(cbrt.f64 i)

rewrite29.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
32×add-exp-log_binary64
32×pow1_binary64
22×add-cbrt-cube_binary64
19×cbrt-unprod_binary64
19×prod-exp_binary64
Counts
4 → 86
Calls

4 calls:

9.0ms
(*.f64 (*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))
8.0ms
(*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i))))
6.0ms
(*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))
1.0ms
(cbrt.f64 i)

simplify105.0ms (1%)

Algorithm
egg-herbie
Rules
937×fma-def_binary64
720×*-commutative_binary64
594×unswap-sqr_binary64
569×distribute-rgt-in_binary64
568×distribute-lft-in_binary64
Counts
242 → 146
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01423940
13203127
212762914
333742912
453312912

prune392.0ms (3.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1820182
Fresh099
Picked011
Done011
Total18211193
Error
0.0b
Counts
193 → 11
Alt Table
StatusErrorProgram
6.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
33.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (fma.f64 b c a)) (sqrt.f64 i)) (sqrt.f64 i))))
7.2b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))) (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))))
31.7b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (sqrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) (sqrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))))))
5.6b
(*.f64 2 (-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (*.f64 i (fma.f64 c b a)))))
24.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 c (fma.f64 b c a)) (*.f64 c (fma.f64 b c a))) (*.f64 c (fma.f64 b c a)))) i)))
5.5b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))))
14.6b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (+.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (*.f64 c (*.f64 i a)))))
5.9b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a))))) (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))))))
19.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (expm1.f64 (log1p.f64 (*.f64 (*.f64 c (fma.f64 b c a)) i)))))
6.4b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (*.f64 (cbrt.f64 (fma.f64 b c a)) (cbrt.f64 (fma.f64 b c a)))) (cbrt.f64 (fma.f64 b c a))) i)))
Compiler

Compiled 5917 to 1807 computations (69.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 t z (*.f64 y x))
0.0b
(-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (*.f64 i (fma.f64 c b a))))
0.8b
(*.f64 i (fma.f64 c b a))
5.4b
(*.f64 c (*.f64 i (fma.f64 c b a)))

series102.0ms (1%)

Counts
4 → 240
Calls

4 calls:

56.0ms
(-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (*.f64 i (fma.f64 c b a))))
19.0ms
(*.f64 c (*.f64 i (fma.f64 c b a)))
14.0ms
(fma.f64 t z (*.f64 y x))
12.0ms
(*.f64 i (fma.f64 c b a))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×fma-udef_binary64
11×add-sqr-sqrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
11×pow1_binary64
Counts
4 → 81
Calls

4 calls:

4.0ms
(*.f64 c (*.f64 i (fma.f64 c b a)))
3.0ms
(-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (*.f64 i (fma.f64 c b a))))
3.0ms
(*.f64 i (fma.f64 c b a))
0.0ms
(fma.f64 t z (*.f64 y x))

simplify175.0ms (1.7%)

Algorithm
egg-herbie
Rules
613×distribute-rgt-in_binary64
606×distribute-lft-in_binary64
552×fma-def_binary64
290×fma-neg_binary64
215×cancel-sign-sub-inv_binary64
Counts
321 → 155
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01575146
13394265
211664226
345334226
449904226
549264226

prune234.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1532155
Fresh268
Picked101
Done112
Total1579166
Error
0.0b
Counts
166 → 9
Alt Table
StatusErrorProgram
6.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
33.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (fma.f64 b c a)) (sqrt.f64 i)) (sqrt.f64 i))))
7.2b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))) (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))))
31.7b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (sqrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) (sqrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))))))
1.9b
(*.f64 2 (-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 (*.f64 c i) (fma.f64 c b a))))
9.0b
(*.f64 2 (-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (+.f64 (*.f64 c (*.f64 i b)) (*.f64 a i)))))
5.9b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a))))) (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))))))
19.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (expm1.f64 (log1p.f64 (*.f64 (*.f64 c (fma.f64 b c a)) i)))))
6.4b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (*.f64 (cbrt.f64 (fma.f64 b c a)) (cbrt.f64 (fma.f64 b c a)))) (cbrt.f64 (fma.f64 b c a))) i)))
Compiler

Compiled 4099 to 1111 computations (72.9% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 t z (*.f64 y x))
0.0b
(-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 (*.f64 c i) (fma.f64 c b a)))
5.9b
(*.f64 (*.f64 c i) (fma.f64 c b a))

series82.0ms (0.8%)

Counts
2 → 144
Calls

2 calls:

61.0ms
(-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 (*.f64 c i) (fma.f64 c b a)))
21.0ms
(*.f64 (*.f64 c i) (fma.f64 c b a))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
fma-udef_binary64
*-un-lft-identity_binary64
Counts
2 → 45
Calls

2 calls:

6.0ms
(*.f64 (*.f64 c i) (fma.f64 c b a))
3.0ms
(-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 (*.f64 c i) (fma.f64 c b a)))

simplify130.0ms (1.3%)

Algorithm
egg-herbie
Rules
663×fma-neg_binary64
516×fma-def_binary64
445×distribute-rgt-in_binary64
436×distribute-lft-in_binary64
295×*-commutative_binary64
Counts
189 → 104
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01283996
13083155
210333116
336283108
448433108
547973108

prune114.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1192121
Fresh167
Picked101
Done011
Total1219130
Error
0.0b
Counts
130 → 9
Alt Table
StatusErrorProgram
6.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
33.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (fma.f64 b c a)) (sqrt.f64 i)) (sqrt.f64 i))))
9.0b
(*.f64 2 (-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (+.f64 (*.f64 c (*.f64 i b)) (*.f64 a i)))))
31.7b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (sqrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) (sqrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))))))
32.6b
(*.f64 2 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 y x (*.f64 t z)) 3)) (*.f64 (*.f64 c i) (fma.f64 c b a))))
32.0b
(*.f64 2 (-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 (*.f64 (*.f64 c i) (sqrt.f64 (fma.f64 c b a))) (sqrt.f64 (fma.f64 c b a)))))
5.9b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a))))) (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))))))
19.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (expm1.f64 (log1p.f64 (*.f64 (*.f64 c (fma.f64 b c a)) i)))))
6.4b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (*.f64 (cbrt.f64 (fma.f64 b c a)) (cbrt.f64 (fma.f64 b c a)))) (cbrt.f64 (fma.f64 b c a))) i)))
Compiler

Compiled 3050 to 795 computations (73.9% saved)

regimes3.0s (29.3%)

Accuracy

Total 1.1b remaining (97.3%)

Threshold costs 0b (0%)

Counts
150 → 3
Compiler

Compiled 68083 to 41646 computations (38.8% saved)

bsearch6.0ms (0.1%)

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify95.0ms (0.9%)

Algorithm
egg-herbie
Rules
30×*-commutative_binary64
19×+-commutative_binary64
17×sub-neg_binary64
14×neg-sub0_binary64
14×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044130
177130
2105130
3127130
4155130
5171130
6179130
7183130
8184130
9184130

end25.0ms (0.2%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 485 to 220 computations (54.6% saved)

sample2.1s (20.3%)

Algorithm
intervals
Results
576.0ms8000×body128valid
510.0ms7218×body128invalid
Compiler

Compiled 422 to 234 computations (44.5% saved)

Profiling

Loading profile data...