Details

Time bar (total: 15.0s)

analyze1.3s (8.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
12.5%87.2%0.3%7
12.5%87.2%0.3%8
18.7%81%0.3%9
21.8%77.9%0.3%10
21.8%77.9%0.3%11
21.8%77.9%0.3%12
37.4%62.3%0.3%13
37.4%62.3%0.3%14
Compiler

Compiled 24 to 15 computations (37.5% saved)

sample1.2s (8.1%)

Infinites
4.9% of outputs are infinite.
Results
1.1s8256×body128valid
Compiler

Compiled 71 to 44 computations (38% saved)

simplify77.0ms (0.5%)

Algorithm
egg-herbie
Rules
920×times-frac_binary64
593×fma-def_binary64
507×div-sub_binary64
484×sub-neg_binary64
470×neg-mul-1_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01523
12521
25021
39321
415721
527021
642321
772421
8134121
9389821
10440021
11495221

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
21.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
21.7b
(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
Compiler

Compiled 80 to 41 computations (48.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 z (-.f64 t a))
0.8b
(fma.f64 x y (*.f64 z (-.f64 t a)))
21.5b
(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

series197.0ms (1.3%)

Counts
3 → 168
Calls

3 calls:

176.0ms
(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
15.0ms
(fma.f64 x y (*.f64 z (-.f64 t a)))
6.0ms
(*.f64 z (-.f64 t a))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt_binary64
29×*-un-lft-identity_binary64
27×add-cube-cbrt_binary64
18×prod-diff_binary64
13×distribute-lft-in_binary64
Counts
3 → 89
Calls

3 calls:

6.0ms
(*.f64 z (-.f64 t a))
2.0ms
(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
0.0ms
(fma.f64 x y (*.f64 z (-.f64 t a)))

simplify152.0ms (1%)

Algorithm
egg-herbie
Rules
911×associate-/l*_binary64
492×fma-def_binary64
259×+-commutative_binary64
206×associate-+r+_binary64
151×*-commutative_binary64
Counts
257 → 217
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07659527
123148862
252348862

prune273.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2098217
Fresh000
Picked011
Done000
Total2099218
Error
0.2b
Counts
218 → 9
Alt Table
StatusErrorProgram
43.0b
(/.f64 (fma.f64 x y (*.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))
39.0b
(/.f64 x (-.f64 1 z))
43.8b
(-.f64 (fma.f64 (/.f64 a z) (/.f64 y (*.f64 b b)) (+.f64 (fma.f64 (/.f64 y b) (/.f64 x z) (/.f64 (*.f64 t y) (*.f64 b b))) (/.f64 t b))) (+.f64 (fma.f64 (/.f64 y (*.f64 b b)) (/.f64 t z) (/.f64 a b)) (/.f64 (*.f64 a y) (*.f64 b b))))
21.7b
(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
40.0b
(*.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (/.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)))
27.1b
(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
21.7b
(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
45.7b
(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (fma.f64 (/.f64 a (*.f64 y y)) (/.f64 (*.f64 b (*.f64 z z)) (pow.f64 (-.f64 1 z) 2)) (fma.f64 (/.f64 z (/.f64 (*.f64 y y) z)) (/.f64 (*.f64 x (*.f64 b b)) (pow.f64 (-.f64 1 z) 3)) (/.f64 x (-.f64 1 z))))) (fma.f64 (/.f64 z y) (/.f64 (*.f64 b x) (pow.f64 (-.f64 1 z) 2)) (fma.f64 (/.f64 a y) (/.f64 z (-.f64 1 z)) (/.f64 (*.f64 t (*.f64 b (*.f64 z z))) (*.f64 (*.f64 y y) (pow.f64 (-.f64 1 z) 2))))))
42.6b
(/.f64 (fma.f64 x y (*.f64 (*.f64 z (sqrt.f64 (-.f64 t a))) (sqrt.f64 (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))
Compiler

Compiled 11452 to 4364 computations (61.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 z (-.f64 t a))
0.6b
(/.f64 1 (fma.f64 z (-.f64 b y) y))
0.8b
(fma.f64 x y (*.f64 z (-.f64 t a)))
20.9b
(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

series212.0ms (1.4%)

Counts
2 → 108
Calls

2 calls:

176.0ms
(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
35.0ms
(/.f64 1 (fma.f64 z (-.f64 b y) y))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×times-frac_binary64
19×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
15×add-exp-log_binary64
Counts
2 → 71
Calls

2 calls:

5.0ms
(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
2.0ms
(/.f64 1 (fma.f64 z (-.f64 b y) y))

simplify165.0ms (1.1%)

Algorithm
egg-herbie
Rules
788×associate-/l*_binary64
519×fma-def_binary64
318×+-commutative_binary64
239×associate-+r+_binary64
177×sub-neg_binary64
Counts
179 → 236
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
081210485
126149766
253119766

prune330.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3230323
Fresh077
Picked011
Done011
Total3239332
Error
0.2b
Counts
332 → 9
Alt Table
StatusErrorProgram
43.0b
(/.f64 (fma.f64 x y (*.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))
39.0b
(/.f64 x (-.f64 1 z))
43.8b
(-.f64 (fma.f64 (/.f64 a z) (/.f64 y (*.f64 b b)) (+.f64 (fma.f64 (/.f64 y b) (/.f64 x z) (/.f64 (*.f64 t y) (*.f64 b b))) (/.f64 t b))) (+.f64 (fma.f64 (/.f64 y (*.f64 b b)) (/.f64 t z) (/.f64 a b)) (/.f64 (*.f64 a y) (*.f64 b b))))
21.7b
(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
40.0b
(*.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (/.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)))
27.1b
(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
21.7b
(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
45.7b
(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (fma.f64 (/.f64 a (*.f64 y y)) (/.f64 (*.f64 b (*.f64 z z)) (pow.f64 (-.f64 1 z) 2)) (fma.f64 (/.f64 z (/.f64 (*.f64 y y) z)) (/.f64 (*.f64 x (*.f64 b b)) (pow.f64 (-.f64 1 z) 3)) (/.f64 x (-.f64 1 z))))) (fma.f64 (/.f64 z y) (/.f64 (*.f64 b x) (pow.f64 (-.f64 1 z) 2)) (fma.f64 (/.f64 a y) (/.f64 z (-.f64 1 z)) (/.f64 (*.f64 t (*.f64 b (*.f64 z z))) (*.f64 (*.f64 y y) (pow.f64 (-.f64 1 z) 2))))))
42.6b
(/.f64 (fma.f64 x y (*.f64 (*.f64 z (sqrt.f64 (-.f64 t a))) (sqrt.f64 (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))
Compiler

Compiled 15580 to 6337 computations (59.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
7.4b
(/.f64 a (pow.f64 (-.f64 y b) 2))
10.5b
(fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))
12.0b
(fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b)))
12.9b
(fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))

series491.0ms (3.3%)

Counts
4 → 188
Calls

4 calls:

150.0ms
(fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))
133.0ms
(fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))
127.0ms
(fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b)))
79.0ms
(/.f64 a (pow.f64 (-.f64 y b) 2))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity_binary64
31×add-sqr-sqrt_binary64
30×times-frac_binary64
23×add-cube-cbrt_binary64
20×unpow-prod-down_binary64
Counts
4 → 89
Calls

4 calls:

5.0ms
(/.f64 a (pow.f64 (-.f64 y b) 2))
0.0ms
(fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))
0.0ms
(fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b)))
0.0ms
(fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))

simplify186.0ms (1.2%)

Algorithm
egg-herbie
Rules
494×associate-+r+_binary64
367×fma-neg_binary64
312×associate-/l*_binary64
305×associate-+l+_binary64
284×times-frac_binary64
Counts
277 → 232
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
050210158
112939496
248999496
352179496

prune303.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2293232
Fresh246
Picked101
Done022
Total2329241
Error
0.2b
Counts
241 → 9
Alt Table
StatusErrorProgram
42.6b
(/.f64 (fma.f64 x y (*.f64 (*.f64 z (sqrt.f64 (-.f64 t a))) (sqrt.f64 (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))
38.7b
(-.f64 (-.f64 (/.f64 (*.f64 a y) (*.f64 (pow.f64 b 2) z)) (+.f64 (/.f64 a b) (/.f64 (*.f64 a y) (pow.f64 b 2)))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
40.0b
(*.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (/.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)))
21.7b
(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
27.1b
(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (*.f64 1 (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))))
27.4b
(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))) (cbrt.f64 (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))) (cbrt.f64 (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))))
21.7b
(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
45.7b
(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (fma.f64 (/.f64 a (*.f64 y y)) (/.f64 (*.f64 b (*.f64 z z)) (pow.f64 (-.f64 1 z) 2)) (fma.f64 (/.f64 z (/.f64 (*.f64 y y) z)) (/.f64 (*.f64 x (*.f64 b b)) (pow.f64 (-.f64 1 z) 3)) (/.f64 x (-.f64 1 z))))) (fma.f64 (/.f64 z y) (/.f64 (*.f64 b x) (pow.f64 (-.f64 1 z) 2)) (fma.f64 (/.f64 a y) (/.f64 z (-.f64 1 z)) (/.f64 (*.f64 t (*.f64 b (*.f64 z z))) (*.f64 (*.f64 y y) (pow.f64 (-.f64 1 z) 2))))))
39.0b
(/.f64 x (-.f64 1 z))
Compiler

Compiled 14088 to 4817 computations (65.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
7.4b
(/.f64 a (pow.f64 (-.f64 y b) 2))
10.5b
(fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))
12.0b
(fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b)))
12.9b
(fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))

prune306.0ms (2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2320232
Fresh066
Picked011
Done022
Total2329241
Error
0.2b
Counts
241 → 9
Alt Table
StatusErrorProgram
42.6b
(/.f64 (fma.f64 x y (*.f64 (*.f64 z (sqrt.f64 (-.f64 t a))) (sqrt.f64 (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))
38.7b
(-.f64 (-.f64 (/.f64 (*.f64 a y) (*.f64 (pow.f64 b 2) z)) (+.f64 (/.f64 a b) (/.f64 (*.f64 a y) (pow.f64 b 2)))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
40.0b
(*.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (/.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)))
21.7b
(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
27.1b
(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (*.f64 1 (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))))
27.4b
(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))) (cbrt.f64 (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))) (cbrt.f64 (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))))
21.7b
(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
45.7b
(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (fma.f64 (/.f64 a (*.f64 y y)) (/.f64 (*.f64 b (*.f64 z z)) (pow.f64 (-.f64 1 z) 2)) (fma.f64 (/.f64 z (/.f64 (*.f64 y y) z)) (/.f64 (*.f64 x (*.f64 b b)) (pow.f64 (-.f64 1 z) 3)) (/.f64 x (-.f64 1 z))))) (fma.f64 (/.f64 z y) (/.f64 (*.f64 b x) (pow.f64 (-.f64 1 z) 2)) (fma.f64 (/.f64 a y) (/.f64 z (-.f64 1 z)) (/.f64 (*.f64 t (*.f64 b (*.f64 z z))) (*.f64 (*.f64 y y) (pow.f64 (-.f64 1 z) 2))))))
39.0b
(/.f64 x (-.f64 1 z))
Compiler

Compiled 14180 to 5103 computations (64% saved)

regimes9.4s (62.7%)

Accuracy

Total 6.8b remaining (91.9%)

Threshold costs 0b (0%)

Counts
268 → 3
Compiler

Compiled 85082 to 42176 computations (50.4% saved)

bsearch57.0ms (0.4%)

Steps
ItersRangePoint
10
6.056414359012005e+23
1.9456650516811163e+38
2.74295821737516e+27
7
-9.002148442170877e+54
-4.245054404745136e+53
-4.310313169511819e+53
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
041136
161136
280136
397136
4107136
5111136
6112136
7112136

end186.0ms (1.2%)

Compiler

Compiled 612 to 288 computations (52.9% saved)

Profiling

Loading profile data...