Details

Time bar (total: 20.6s)

analyze2.7s (13%)

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)

sample2.9s (13.9%)

Symmetry

(sort x y)

(sort z t)

Results
1.4s8256×body128valid
1.3s7439×body128invalid
Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify219.0ms (1.1%)

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
6.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
6.5b
(*.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)

localize12.0ms (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))
7.4b
(*.f64 (*.f64 c (fma.f64 b c a)) i)

series279.0ms (1.4%)

Counts
4 → 228
Calls

4 calls:

239.0ms
(-.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)
12.0ms
(*.f64 c (fma.f64 b c a))
8.0ms
(fma.f64 x y (*.f64 z t))

rewrite87.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
367×fma-def_binary64
294×expm1-udef_binary64
294×log1p-udef_binary64
174×fma-neg_binary64
164×egg-rr
Counts
4 → 164
Calls

4 calls:

82.0ms
(fma.f64 x y (*.f64 z t))
82.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))
82.0ms
(*.f64 c (fma.f64 b c a))
82.0ms
(*.f64 (*.f64 c (fma.f64 b c a)) i)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01548
131148
2387248
3528948
000
100

simplify569.0ms (2.8%)

Algorithm
egg-herbie
Rules
932×fma-neg_binary64
891×distribute-rgt-neg-in_binary64
739×cube-prod_binary64
707×distribute-lft-neg-in_binary64
670×fabs-mul_binary64
Counts
392 → 201
Iterations

Useful iterations: 10 (0.0ms)

IterNodesCost
0473604
11132908
22752827
35722827
417772827
526702827
632672827
737032827
841612827
942492827
1043442675
1133482675
1234902675
1341212675
1444132675
1545692675
1648462675
1749122675

prune236.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New19011201
Fresh000
Picked101
Done000
Total19111202
Error
0.3b
Counts
202 → 11
Alt Table
StatusErrorProgram
32.5b
(*.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) 2))
4.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a)))))
10.9b
(*.f64 2 (fma.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) 2) (fma.f64 (neg.f64 (*.f64 (fma.f64 c b a) i)) c (*.f64 (*.f64 c (fma.f64 c b a)) i))))
6.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (pow.f64 (cbrt.f64 (*.f64 c (fma.f64 c b a))) 3) i)))
9.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (+.f64 (*.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
6.5b
(*.f64 2 (fma.f64 x y (-.f64 (*.f64 z t) (*.f64 (*.f64 c (fma.f64 c b a)) i))))
21.5b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (pow.f64 c 2) (*.f64 i b))))
23.7b
(*.f64 2 (fma.f64 t z (*.f64 y x)))
43.6b
(*.f64 2 (fma.f64 (-.f64 (pow.f64 (fma.f64 x y (*.f64 z t)) 3) (pow.f64 (*.f64 (*.f64 c (fma.f64 c b a)) i) 3)) (/.f64 1 (fma.f64 (*.f64 (*.f64 c (fma.f64 c b a)) i) (fma.f64 (*.f64 c (fma.f64 c b a)) i (fma.f64 x y (*.f64 z t))) (pow.f64 (fma.f64 x y (*.f64 z t)) 2))) (fma.f64 (neg.f64 (*.f64 (fma.f64 c b a) i)) c (*.f64 (*.f64 c (fma.f64 c b a)) i))))
22.0b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 c (fma.f64 c b a)) 3)) i)))
7.6b
(*.f64 2 (*.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) 2)))
Compiler

Compiled 6348 to 1625 computations (74.4% saved)

localize12.0ms (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))))
1.0b
(*.f64 i (fma.f64 c b a))
3.7b
(*.f64 c (*.f64 i (fma.f64 c b a)))

series78.0ms (0.4%)

Counts
3 → 192
Calls

3 calls:

48.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))
18.0ms
(*.f64 c (*.f64 i (fma.f64 c b a)))
12.0ms
(*.f64 i (fma.f64 c b a))

rewrite194.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
369×fma-def_binary64
294×expm1-udef_binary64
294×log1p-udef_binary64
174×fma-neg_binary64
163×add-sqr-sqrt_binary64
Counts
3 → 146
Calls

3 calls:

189.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))
189.0ms
(*.f64 i (fma.f64 c b a))
189.0ms
(*.f64 c (*.f64 i (fma.f64 c b a)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01540
131140
2387940
3529840
000
100

simplify366.0ms (1.8%)

Algorithm
egg-herbie
Rules
926×fma-neg_binary64
891×distribute-rgt-neg-in_binary64
739×cube-prod_binary64
707×distribute-lft-neg-in_binary64
670×fabs-mul_binary64
Counts
338 → 183
Iterations

Useful iterations: 10 (0.0ms)

IterNodesCost
0513283
11212587
22792587
35682587
417762587
526702587
632672587
737032587
841612587
942492587
1043442435
1133482435
1234902435
1341212435
1444132435
1545692435
1648462435
1749122435

prune239.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2034207
Fresh4610
Picked101
Done000
Total20810218
Error
0.0b
Counts
218 → 10
Alt Table
StatusErrorProgram
5.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (pow.f64 (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) 3)))
32.5b
(*.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) 2))
7.6b
(*.f64 2 (*.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) 2)))
33.1b
(*.f64 2 (fma.f64 (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))) (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))) (fma.f64 (neg.f64 (fma.f64 c b a)) (*.f64 c i) (*.f64 c (*.f64 i (fma.f64 c b a))))))
9.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (+.f64 (*.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
6.5b
(*.f64 2 (fma.f64 x y (-.f64 (*.f64 z t) (*.f64 (*.f64 c (fma.f64 c b a)) i))))
21.5b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (pow.f64 c 2) (*.f64 i b))))
23.7b
(*.f64 2 (fma.f64 t z (*.f64 y x)))
2.6b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i)))))
8.0b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (+.f64 (*.f64 c (*.f64 i b)) (*.f64 a i)))))
Compiler

Compiled 6327 to 1570 computations (75.2% saved)

localize16.0ms (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)) (fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i))))
2.5b
(fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i)))
4.4b
(*.f64 a (*.f64 c i))

series91.0ms (0.4%)

Counts
3 → 180
Calls

3 calls:

62.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i))))
21.0ms
(fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i)))
8.0ms
(*.f64 a (*.f64 c i))

rewrite77.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
310×expm1-udef_binary64
310×log1p-udef_binary64
171×add-sqr-sqrt_binary64
158×log1p-expm1-u_binary64
158×expm1-log1p-u_binary64
Counts
3 → 80
Calls

3 calls:

75.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i))))
75.0ms
(fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i)))
75.0ms
(*.f64 a (*.f64 c i))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01651
132843
2407543
3500443
000
100

simplify327.0ms (1.6%)

Algorithm
egg-herbie
Rules
1019×distribute-rgt-neg-in_binary64
923×fma-neg_binary64
702×fabs-mul_binary64
648×distribute-lft-neg-in_binary64
640×cancel-sign-sub-inv_binary64
Counts
260 → 110
Iterations

Useful iterations: 10 (0.0ms)

IterNodesCost
0423172
1992824
22482708
35312476
416652476
525542476
631702476
736192476
840772476
941622476
1042592324
1133232324
1232422324
1337572324
1444862324
1548392324

prune157.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1331134
Fresh189
Picked011
Done000
Total13410144
Error
0.0b
Counts
144 → 10
Alt Table
StatusErrorProgram
5.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (pow.f64 (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) 3)))
32.5b
(*.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) 2))
3.7b
(*.f64 2 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))) 3))
33.1b
(*.f64 2 (fma.f64 (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))) (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))) (fma.f64 (neg.f64 (fma.f64 c b a)) (*.f64 c i) (*.f64 c (*.f64 i (fma.f64 c b a))))))
9.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (+.f64 (*.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
6.5b
(*.f64 2 (fma.f64 x y (-.f64 (*.f64 z t) (*.f64 (*.f64 c (fma.f64 c b a)) i))))
21.5b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (pow.f64 c 2) (*.f64 i b))))
23.7b
(*.f64 2 (fma.f64 t z (*.f64 y x)))
2.6b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i)))))
8.0b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (+.f64 (*.f64 c (*.f64 i b)) (*.f64 a i)))))
Compiler

Compiled 3957 to 1153 computations (70.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))
0.7b
(pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))) 3)
0.7b
(cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a))))
5.8b
(*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a))

series5.5s (26.6%)

Counts
4 → 336
Calls

4 calls:

4.5s
(pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))) 3)
905.0ms
(cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a))))
62.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))
20.0ms
(*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a))

rewrite63.0ms (0.3%)

Algorithm
batch-egg-rewrite
Rules
200×add-sqr-sqrt_binary64
191×log1p-expm1-u_binary64
191×expm1-log1p-u_binary64
185×add-cbrt-cube_binary64
185×add-log-exp_binary64
Counts
4 → 154
Calls

4 calls:

58.0ms
(-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))
58.0ms
(pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))) 3)
58.0ms
(cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a))))
58.0ms
(*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01976
139476
2498076
000
100

simplify609.0ms (3%)

Algorithm
egg-herbie
Rules
927×fma-def_binary64
fma-neg_binary64
Counts
490 → 422
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04918137439016821
15850137439016821

prune2.0s (9.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New4220422
Fresh088
Picked011
Done011
Total42210432
Error
0.0b
Counts
432 → 10
Alt Table
StatusErrorProgram
5.2b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (pow.f64 (cbrt.f64 (*.f64 c (*.f64 i (fma.f64 c b a)))) 3)))
32.5b
(*.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 c b a)) i))) 2))
3.7b
(*.f64 2 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))) 3))
33.1b
(*.f64 2 (fma.f64 (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))) (sqrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (*.f64 i (fma.f64 c b a))))) (fma.f64 (neg.f64 (fma.f64 c b a)) (*.f64 c i) (*.f64 c (*.f64 i (fma.f64 c b a))))))
9.8b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (+.f64 (*.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
6.5b
(*.f64 2 (fma.f64 x y (-.f64 (*.f64 z t) (*.f64 (*.f64 c (fma.f64 c b a)) i))))
21.5b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (pow.f64 c 2) (*.f64 i b))))
23.7b
(*.f64 2 (fma.f64 t z (*.f64 y x)))
2.6b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (fma.f64 (*.f64 c b) (*.f64 c i) (*.f64 a (*.f64 c i)))))
8.0b
(*.f64 2 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 c (+.f64 (*.f64 c (*.f64 i b)) (*.f64 a i)))))
Compiler

Compiled 86992 to 56451 computations (35.1% saved)

regimes3.7s (17.9%)

Accuracy

Total 1.1b remaining (98.2%)

Threshold costs 0b (0%)

Counts
164 → 3
Compiler

Compiled 75542 to 46741 computations (38.1% saved)

bsearch7.0ms (0%)

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify12.0ms (0.1%)

Algorithm
egg-herbie
Rules
29×*-commutative_binary64
18×+-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
042116
178116
2110116
3131116
4157116
5172116
6180116
7184116
8185116
9184116

end186.0ms (0.9%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 823 to 430 computations (47.8% saved)

Profiling

Loading profile data...