Details

Time bar (total: 14.1s)

analyze2.8s (19.8%)

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)

sample85.0ms (0.6%)

Algorithm
intervals
Results
18.0ms256×body128valid
18.0ms229×body128invalid
Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify230.0ms (1.6%)

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
4.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
4.9b
(*.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))
5.9b
(*.f64 (*.f64 c (fma.f64 b c a)) i)

series94.0ms (0.7%)

Counts
4 → 228
Calls

4 calls:

55.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))
20.0ms
(*.f64 (*.f64 c (fma.f64 b c a)) i)
10.0ms
(*.f64 c (fma.f64 b c a))
9.0ms
(fma.f64 x y (*.f64 z t))

rewrite15.0ms (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:

5.0ms
(*.f64 c (fma.f64 b c a))
4.0ms
(*.f64 (*.f64 c (fma.f64 b c a)) i)
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))

simplify122.0ms (0.9%)

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

prune197.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New14713160
Fresh000
Picked101
Done000
Total14813161
Error
0.3b
Counts
161 → 13
Alt Table
StatusErrorProgram
32.1b
(*.f64 2 (fma.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))) (neg.f64 (*.f64 (*.f64 c (fma.f64 b c a)) i))))
5.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 c (fma.f64 b c a)) (*.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 i))))
7.9b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (+.f64 (*.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
42.5b
(*.f64 2 (*.f64 t z))
12.4b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (+.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (*.f64 c (*.f64 i a)))))
33.3b
(*.f64 2 (-.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 x y (*.f64 z t))) (fma.f64 x y (*.f64 z t)))) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
31.9b
(*.f64 2 (*.f64 (sqrt.f64 (-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (*.f64 i (fma.f64 c b a))))) (sqrt.f64 (-.f64 (fma.f64 t z (*.f64 y x)) (*.f64 c (*.f64 i (fma.f64 c b a)))))))
37.0b
(*.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))))
27.7b
(*.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)))))))
5.4b
(*.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)))))))
5.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a)))))
34.0b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (fma.f64 b c a))) i)))
5.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) i)))
Compiler

Compiled 4461 to 1343 computations (69.9% 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 c (*.f64 i (fma.f64 c b a))))
0.6b
(*.f64 i (fma.f64 c b a))
4.7b
(*.f64 c (*.f64 i (fma.f64 c b a)))

series99.0ms (0.7%)

Counts
3 → 192
Calls

3 calls:

60.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))
23.0ms
(*.f64 c (*.f64 i (fma.f64 c b a)))
15.0ms
(*.f64 i (fma.f64 c b a))

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×fma-udef_binary64
10×add-sqr-sqrt_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
10×pow1_binary64
Counts
3 → 71
Calls

3 calls:

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

simplify143.0ms (1%)

Algorithm
egg-herbie
Rules
613×distribute-rgt-in_binary64
606×distribute-lft-in_binary64
552×fma-def_binary64
306×fma-neg_binary64
215×cancel-sign-sub-inv_binary64
Counts
263 → 138
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01544703
13323822
211633783
345223783
449773783
549313783

prune163.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1542156
Fresh5712
Picked011
Done000
Total15910169
Error
0b
Counts
169 → 10
Alt Table
StatusErrorProgram
37.0b
(*.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))))
2.4b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (fma.f64 c b a))))
32.1b
(*.f64 2 (fma.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))) (neg.f64 (*.f64 (*.f64 c (fma.f64 b c a)) i))))
7.9b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (+.f64 (*.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
5.4b
(*.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)))))))
5.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a)))))
7.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (+.f64 (*.f64 c (*.f64 i b)) (*.f64 a i)))))
34.0b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (fma.f64 b c a))) i)))
33.3b
(*.f64 2 (-.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 x y (*.f64 z t))) (fma.f64 x y (*.f64 z t)))) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
5.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) i)))
Compiler

Compiled 4137 to 1155 computations (72.1% saved)

localize12.0ms (0.1%)

Local error

Found 3 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 i) (fma.f64 c b a)))
4.3b
(*.f64 (*.f64 c i) (fma.f64 c b a))

series79.0ms (0.6%)

Counts
2 → 144
Calls

2 calls:

57.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (fma.f64 c b a)))
22.0ms
(*.f64 (*.f64 c i) (fma.f64 c b a))

rewrite9.0ms (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:

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

simplify134.0ms (1%)

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
01293996
13073155
210333116
336283108
448433108
547973108

prune110.0ms (0.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1220122
Fresh088
Picked011
Done011
Total12210132
Error
0b
Counts
132 → 10
Alt Table
StatusErrorProgram
37.0b
(*.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))))
2.4b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (fma.f64 c b a))))
32.1b
(*.f64 2 (fma.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))) (neg.f64 (*.f64 (*.f64 c (fma.f64 b c a)) i))))
7.9b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (+.f64 (*.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
5.4b
(*.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)))))))
5.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a)))))
7.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (+.f64 (*.f64 c (*.f64 i b)) (*.f64 a i)))))
34.0b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (fma.f64 b c a))) i)))
33.3b
(*.f64 2 (-.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 x y (*.f64 z t))) (fma.f64 x y (*.f64 z t)))) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
5.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) i)))
Compiler

Compiled 3381 to 966 computations (71.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
0.5b
(*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
5.9b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) i)
10.5b
(cbrt.f64 (*.f64 c (fma.f64 b c a)))

series185.0ms (1.3%)

Counts
4 → 156
Calls

4 calls:

74.0ms
(*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
53.0ms
(cbrt.f64 (*.f64 c (fma.f64 b c a)))
29.0ms
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) i)
29.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))

rewrite27.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
39×pow1_binary64
20×add-exp-log_binary64
16×pow1/3_binary64
13×pow-prod-down_binary64
13×add-sqr-sqrt_binary64
Counts
4 → 102
Calls

4 calls:

8.0ms
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) i)
6.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
4.0ms
(*.f64 (cbrt.f64 (*.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
2.0ms
(cbrt.f64 (*.f64 c (fma.f64 b c a)))

simplify181.0ms (1.3%)

Algorithm
egg-herbie
Rules
486×associate-*l*_binary64
474×times-frac_binary64
361×associate-/l*_binary64
343×associate-/r*_binary64
236×fma-def_binary64
Counts
258 → 297
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05317708
116526777
249756777
349366777

prune561.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4681469
Fresh167
Picked101
Done022
Total4709479
Error
0b
Counts
479 → 9
Alt Table
StatusErrorProgram
37.0b
(*.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))))
2.4b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (fma.f64 c b a))))
32.1b
(*.f64 2 (fma.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))) (neg.f64 (*.f64 (*.f64 c (fma.f64 b c a)) i))))
7.9b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (+.f64 (*.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
5.4b
(*.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)))))))
5.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a)))))
7.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (+.f64 (*.f64 c (*.f64 i b)) (*.f64 a i)))))
33.3b
(*.f64 2 (-.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 x y (*.f64 z t))) (fma.f64 x y (*.f64 z t)))) (*.f64 (*.f64 c (fma.f64 b c a)) i)))
16.1b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 c (fma.f64 b c a)) (*.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a)))) i)))
Compiler

Compiled 26081 to 11036 computations (57.7% saved)

regimes4.5s (31.7%)

Accuracy

Total 0.9b remaining (97.2%)

Threshold costs 0.9b (97.2%)

Counts
136 → 3
Compiler

Compiled 64317 to 38567 computations (40% saved)

bsearch12.0ms (0.1%)

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify14.0ms (0.1%)

Algorithm
egg-herbie
Rules
26×*-commutative_binary64
19×+-commutative_binary64
16×distribute-rgt-neg-in_binary64
16×sub-neg_binary64
14×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03590
16390
28590
311790
415390
517390
618190
718390
818390

end54.0ms (0.4%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 345 to 175 computations (49.3% saved)

sample4.2s (30.1%)

Algorithm
intervals
Results
1.2s8000×body128valid
1.1s7157×body128invalid
Compiler

Compiled 401 to 225 computations (43.9% saved)

Profiling

Loading profile data...