Details

Time bar (total: 10.8s)

analyze928.0ms (8.6%)

Algorithm
1×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
12.5%87.2%0.3%5
12.5%87.2%0.3%6
12.5%87.2%0.3%7
18.7%81%0.3%8
28%71.7%0.3%9
28%71.7%0.3%10
42.1%57.6%0.3%11
42.1%57.6%0.3%12
42.1%57.6%0.3%13
49.1%50.6%0.3%14
Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.1s (10.2%)

Infinites
0% of outputs are infinite.
Results
1.0s8255×body128valid
0.0ms1×body512valid
Compiler

Compiled 83 to 50 computations (39.8% saved)

simplify95.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
765×sub-neg_binary64
731×fma-neg_binary64
652×neg-mul-1_binary64
505×fma-def_binary64
495×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01729
13729
28529
319427
448627
5100327
6192027
7340627
8407827
9443127
10491927
11508527

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
22.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶22.8b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
22.9b
(/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))
Compiler

Compiled 150 to 83 computations (44.7% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓1.8b
(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓22.7b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series167.0ms (1.5%)

Counts
2 → 144
Calls

2 calls:

140.0ms
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
26.0ms
(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))

rewrite9.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
32×*-un-lft-identity_binary64
15×times-frac_binary64
12×distribute-lft-out_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
Counts
2 → 49
Calls

2 calls:

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

simplify135.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
591×associate-/l*_binary64
378×associate-/r*_binary64
283×+-commutative_binary64
239×associate-+r+_binary64
237×associate--l+_binary64
Counts
193 → 174
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
066010618
1194610391
2501010391

prune175.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New16410174
Fresh101
Picked101
Done000
Total16610176
Error
2.9b
Counts
176 → 10
Alt Table
StatusErrorProgram
▶22.9b
(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
29.3b
(-.f64 (+.f64 a z) b)
43.0b
(/.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))) (/.f64 (+.f64 x (+.f64 y t)) (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))))
23.0b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
22.9b
(*.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
41.3b
(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
39.5b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 (+.f64 t x) y)) 3))
43.9b
z
33.4b
(/.f64 (+.f64 (*.f64 z (+.f64 x y)) (*.f64 y (-.f64 a b))) (+.f64 x (+.f64 y t)))
44.6b
a
Compiler

Compiled 9947 to 3024 computations (69.6% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
1.8b
(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓22.8b
(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

series1.7s (15.2%)

Counts
2 → 144
Calls

2 calls:

1.5s
(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))
141.0ms
(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))

rewrite37.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
148×*-un-lft-identity_binary64
132×times-frac_binary64
68×add-sqr-sqrt_binary64
68×add-cube-cbrt_binary64
48×distribute-lft-out_binary64
Counts
2 → 141
Calls

2 calls:

11.0ms
(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
6.0ms
(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

simplify390.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
600×associate-/l*_binary64
436×times-frac_binary64
336×fma-def_binary64
77×sub-neg_binary64
46×sqr-pow_binary64
Counts
285 → 297
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0278446779
1561746779

prune753.0ms (6.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3460346
Fresh099
Picked011
Done000
Total34610356
Error
2.9b
Counts
356 → 10
Alt Table
StatusErrorProgram
✓22.9b
(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
29.3b
(-.f64 (+.f64 a z) b)
43.0b
(/.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))) (/.f64 (+.f64 x (+.f64 y t)) (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))))
23.0b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
▶22.9b
(*.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
41.3b
(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
39.5b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 (+.f64 t x) y)) 3))
43.9b
z
33.4b
(/.f64 (+.f64 (*.f64 z (+.f64 x y)) (*.f64 y (-.f64 a b))) (+.f64 x (+.f64 y t)))
44.6b
a
Compiler

Compiled 53970 to 20620 computations (61.8% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (+.f64 x (+.f64 y t)))
1.8b
(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓22.8b
(*.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))

series159.0ms (1.5%)

Counts
2 → 108
Calls

2 calls:

133.0ms
(*.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
25.0ms
(/.f64 1 (+.f64 x (+.f64 y t)))

rewrite20.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
58×*-un-lft-identity_binary64
32×times-frac_binary64
29×add-sqr-sqrt_binary64
22×add-cube-cbrt_binary64
21×distribute-lft-out_binary64
Counts
2 → 89
Calls

2 calls:

9.0ms
(*.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
5.0ms
(/.f64 1 (+.f64 x (+.f64 y t)))

simplify150.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
671×associate-/l*_binary64
456×associate-/r*_binary64
306×+-commutative_binary64
245×associate-+r+_binary64
176×fma-def_binary64
Counts
197 → 229
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
074511101
1228910838
2501610838

prune252.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2780278
Fresh088
Picked011
Done011
Total27810288
Error
2.9b
Counts
288 → 10
Alt Table
StatusErrorProgram
✓22.9b
(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
29.3b
(-.f64 (+.f64 a z) b)
43.0b
(/.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))) (/.f64 (+.f64 x (+.f64 y t)) (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))))
▶23.0b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
✓22.9b
(*.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
41.3b
(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
39.5b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 (+.f64 t x) y)) 3))
43.9b
z
33.4b
(/.f64 (+.f64 (*.f64 z (+.f64 x y)) (*.f64 y (-.f64 a b))) (+.f64 x (+.f64 y t)))
44.6b
a
Compiler

Compiled 13554 to 4352 computations (67.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓7.1b
(/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))
✓7.4b
(/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))
✓8.0b
(/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))
✓8.3b
(/.f64 (*.f64 y b) (+.f64 y (+.f64 t x)))

series195.0ms (1.8%)

Counts
4 → 156
Calls

4 calls:

50.0ms
(/.f64 (*.f64 y b) (+.f64 y (+.f64 t x)))
49.0ms
(/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))
48.0ms
(/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))
48.0ms
(/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))

rewrite30.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
52×*-un-lft-identity_binary64
24×distribute-lft-out_binary64
24×add-cbrt-cube_binary64
24×add-exp-log_binary64
20×associate-/r*_binary64
Counts
4 → 116
Calls

4 calls:

7.0ms
(/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))
6.0ms
(/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))
6.0ms
(/.f64 (*.f64 y b) (+.f64 y (+.f64 t x)))
6.0ms
(/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))

simplify146.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
935×associate-/l*_binary64
268×associate-/r/_binary64
234×sub-neg_binary64
228×associate-/l/_binary64
204×+-commutative_binary64
Counts
272 → 337
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
077510628
1230210300
2510710300

prune370.0ms (3.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3307337
Fresh437
Picked101
Done022
Total33512347
Error
1.1b
Counts
347 → 12
Alt Table
StatusErrorProgram
✓22.9b
(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
17.8b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (+.f64 (*.f64 a (/.f64 t (+.f64 y (+.f64 t x)))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
29.3b
(-.f64 (+.f64 a z) b)
✓22.9b
(*.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
43.9b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 (/.f64 z (sqrt.f64 (+.f64 y (+.f64 t x)))) x) (sqrt.f64 (+.f64 y (+.f64 t x)))) (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
41.3b
(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
42.3b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 (/.f64 y (sqrt.f64 (+.f64 y (+.f64 t x)))) b) (sqrt.f64 (+.f64 y (+.f64 t x)))))
21.0b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b)))
21.3b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (*.f64 y (/.f64 b (+.f64 y (+.f64 t x)))))
22.0b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (*.f64 y (/.f64 a (+.f64 y (+.f64 t x))))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
30.2b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 z (+.f64 (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y a) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
43.0b
(/.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))) (/.f64 (+.f64 x (+.f64 y t)) (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))))
Compiler

Compiled 24166 to 5058 computations (79.1% saved)

regimes3.8s (35%)

Accuracy

Total 6.2b remaining (82.1%)

Threshold costs 0b (0%)

Counts
184 → 3
Compiler

Compiled 40738 to 21482 computations (47.3% saved)

bsearch9.0ms (0.1%)

Compiler

Compiled 27 to 16 computations (40.7% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
17×+-commutative_binary64
11×*-commutative_binary64
7×sub-neg_binary64
4×neg-sub0_binary64
4×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041154
167154
283154
391154
495154
595154

end187.0ms (1.7%)

Compiler

Compiled 734 to 299 computations (59.3% saved)

Profiling

Loading profile data...