Details

Time bar (total: 7.0s)

analyze1.9s (27.4%)

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
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
1.1%98.6%0.3%12
1.9%97.8%0.3%13
7%92.7%0.3%14
Compiler

Compiled 28 to 17 computations (39.3% saved)

sample32.0ms (0.5%)

Algorithm
1×intervals
Results
19.0ms256×body128valid
Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify96.0ms (1.4%)

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 (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
28.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶28.7b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
Compiler

Compiled 96 to 51 computations (46.9% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.3b
(fma.f64 (+.f64 x y) z (*.f64 t a))
✓2.0b
(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓26.9b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series190.0ms (2.7%)

Counts
3 → 204
Calls

3 calls:

150.0ms
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
27.0ms
(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
13.0ms
(fma.f64 (+.f64 x y) z (*.f64 t a))

rewrite12.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
33×*-un-lft-identity_binary64
15×times-frac_binary64
13×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
12×distribute-lft-out_binary64
Counts
3 → 59
Calls

3 calls:

7.0ms
(/.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 (+.f64 x y) z (*.f64 t a))
0.0ms
(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))

simplify168.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
591×associate-/l*_binary64
378×associate-/r*_binary64
286×+-commutative_binary64
241×associate-+r+_binary64
237×associate--l+_binary64
Counts
263 → 200
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067311356
1196111106
2507811106

prune189.0ms (2.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New18614200
Fresh000
Picked101
Done000
Total18714201
Error
2.6b
Counts
201 → 14
Alt Table
StatusErrorProgram
29.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
▶28.4b
(-.f64 (+.f64 a z) b)
44.6b
(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
42.0b
(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
44.7b
(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))
45.6b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
53.2b
(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
50.7b
(*.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
29.3b
(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (*.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (cbrt.f64 (+.f64 x (+.f64 y t))))
46.1b
(-.f64 (+.f64 (/.f64 (*.f64 y a) t) (+.f64 a (+.f64 (/.f64 (*.f64 z x) t) (/.f64 (*.f64 y z) t)))) (+.f64 (/.f64 (*.f64 a x) t) (+.f64 (/.f64 (*.f64 a y) t) (/.f64 (*.f64 y b) t))))
43.0b
a
45.5b
(*.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
28.7b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
44.3b
z
Compiler

Compiled 10845 to 3255 computations (70% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (+.f64 a z) b)

series5.0ms (0.1%)

Counts
1 → 9
Calls

1 calls:

5.0ms
(-.f64 (+.f64 a z) b)

rewrite9.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
23×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×prod-diff_binary64
10×add-cube-cbrt_binary64
6×add-log-exp_binary64
Counts
1 → 37
Calls

1 calls:

6.0ms
(-.f64 (+.f64 a z) b)

simplify79.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
886×times-frac_binary64
653×associate-+l+_binary64
560×fma-neg_binary64
391×*-commutative_binary64
293×associate-*l*_binary64
Counts
46 → 51
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
071676
1135385
2446346
31951345
43407345
54746345
65579345

prune45.0ms (0.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New46551
Fresh11213
Picked101
Done000
Total481765
Error
2.6b
Counts
65 → 17
Alt Table
StatusErrorProgram
29.3b
(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (*.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (cbrt.f64 (+.f64 x (+.f64 y t))))
30.7b
(+.f64 a z)
46.1b
(-.f64 (+.f64 (/.f64 (*.f64 y a) t) (+.f64 a (+.f64 (/.f64 (*.f64 z x) t) (/.f64 (*.f64 y z) t)))) (+.f64 (/.f64 (*.f64 a x) t) (+.f64 (/.f64 (*.f64 a y) t) (/.f64 (*.f64 y b) t))))
40.9b
(-.f64 z b)
29.1b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 a z) b)) (cbrt.f64 (-.f64 (+.f64 a z) b))) (cbrt.f64 (-.f64 (+.f64 a z) b)))
45.5b
(*.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
44.6b
(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
42.0b
(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
44.7b
(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))
45.6b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
53.2b
(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
50.7b
(*.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
▶28.4b
(+.f64 a (-.f64 z b))
29.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
44.2b
(expm1.f64 (log1p.f64 (-.f64 (+.f64 a z) b)))
28.7b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
44.3b
z
Compiler

Compiled 1551 to 630 computations (59.4% saved)

localize4.0ms (0.1%)

prune18.0ms (0.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New000
Fresh01616
Picked011
Done000
Total01717
Error
2.6b
Counts
17 → 17
Alt Table
StatusErrorProgram
29.3b
(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (*.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (cbrt.f64 (+.f64 x (+.f64 y t))))
30.7b
(+.f64 a z)
46.1b
(-.f64 (+.f64 (/.f64 (*.f64 y a) t) (+.f64 a (+.f64 (/.f64 (*.f64 z x) t) (/.f64 (*.f64 y z) t)))) (+.f64 (/.f64 (*.f64 a x) t) (+.f64 (/.f64 (*.f64 a y) t) (/.f64 (*.f64 y b) t))))
40.9b
(-.f64 z b)
29.1b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 a z) b)) (cbrt.f64 (-.f64 (+.f64 a z) b))) (cbrt.f64 (-.f64 (+.f64 a z) b)))
45.5b
(*.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
44.6b
(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
42.0b
(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
44.7b
(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))
45.6b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
53.2b
(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
50.7b
(*.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
✓28.4b
(+.f64 a (-.f64 z b))
29.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
44.2b
(expm1.f64 (log1p.f64 (-.f64 (+.f64 a z) b)))
▶28.7b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
44.3b
z
Compiler

Compiled 879 to 452 computations (48.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.3b
(fma.f64 z (+.f64 x y) (*.f64 a t))
✓2.0b
(fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))
✓26.9b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))

series190.0ms (2.7%)

Counts
3 → 204
Calls

3 calls:

147.0ms
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
27.0ms
(fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))
16.0ms
(fma.f64 z (+.f64 x y) (*.f64 a t))

rewrite11.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
33×*-un-lft-identity_binary64
15×times-frac_binary64
13×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
12×distribute-lft-out_binary64
Counts
3 → 59
Calls

3 calls:

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

simplify163.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
591×associate-/l*_binary64
378×associate-/r*_binary64
286×+-commutative_binary64
241×associate-+r+_binary64
237×associate--l+_binary64
Counts
263 → 187
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067211356
1196111106
2507811106

prune142.0ms (2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

PrunedKeptTotal
New1861187
Fresh11415
Picked011
Done011
Total18717204
Error
2.6b
Counts
204 → 17
Alt Table
StatusErrorProgram
29.3b
(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (*.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (cbrt.f64 (+.f64 x (+.f64 y t))))
30.7b
(+.f64 a z)
46.1b
(-.f64 (+.f64 (/.f64 (*.f64 y a) t) (+.f64 a (+.f64 (/.f64 (*.f64 z x) t) (/.f64 (*.f64 y z) t)))) (+.f64 (/.f64 (*.f64 a x) t) (+.f64 (/.f64 (*.f64 a y) t) (/.f64 (*.f64 y b) t))))
40.9b
(-.f64 z b)
29.1b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 a z) b)) (cbrt.f64 (-.f64 (+.f64 a z) b))) (cbrt.f64 (-.f64 (+.f64 a z) b)))
45.5b
(*.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
28.8b
(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))))
44.6b
(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
42.0b
(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
44.7b
(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))
45.6b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
53.2b
(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
50.7b
(*.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
✓28.4b
(+.f64 a (-.f64 z b))
29.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
44.2b
(expm1.f64 (log1p.f64 (-.f64 (+.f64 a z) b)))
✓28.7b
(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
Compiler

Compiled 10177 to 3040 computations (70.1% saved)

regimes2.6s (37.1%)

Accuracy

Total 4.3b remaining (57.6%)

Threshold costs 0b (0%)

Counts
96 → 3
Compiler

Compiled 19829 to 9967 computations (49.7% saved)

bsearch4.0ms (0.1%)

Compiler

Compiled 27 to 16 computations (40.7% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
13×+-commutative_binary64
7×*-commutative_binary64
6×sub-neg_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035108
158108
270108
376108
479108
578108

end1.0ms (0%)

Compiler

Compiled 79 to 31 computations (60.8% saved)

sample1.1s (15.6%)

Algorithm
1×intervals
Results
556.0ms7998×body128valid
0.0ms1×body1024valid
0.0ms1×body256valid
Compiler

Compiled 578 to 294 computations (49.1% saved)

Profiling

Loading profile data...