Details

Time bar (total: 8.4s)

analyze1.3s (15.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
6.2%93.6%0.2%9
9.4%90.4%0.2%10
14%83.4%2.5%11
18.7%78.2%3.1%12
28.1%65.5%6.4%13
30.7%59.4%9.9%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample2.0s (23.7%)

Results
1.1s8256×body128valid
834.0ms6003×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
associate-/l*_binary64
associate-*r/_binary64
associate-/r/_binary64
fma-def_binary64
associate-/r*_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01222
12520
24520
35520
45520
55520

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
28.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
29.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
34.2b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 107 to 55 computations (48.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
5.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
9.0b
(/.f64 x (*.f64 y y))
18.9b
(/.f64 (*.f64 z z) (*.f64 t t))

series146.0ms (1.7%)

Counts
3 → 96
Calls

3 calls:

98.0ms
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
25.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
23.0ms
(/.f64 x (*.f64 y y))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
cbrt-undiv_binary64
div-exp_binary64
*-un-lft-identity_binary64
Counts
3 → 56
Calls

3 calls:

6.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
3.0ms
(/.f64 x (*.f64 y y))
0.0ms
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))

simplify112.0ms (1.3%)

Algorithm
egg-herbie
Rules
652×times-frac_binary64
469×unswap-sqr_binary64
438×associate-/l*_binary64
258×associate-*l/_binary64
229×associate-/r*_binary64
Counts
152 → 75
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01062182
12241962
26561913
325971888
443921885
549441885
649651885

prune88.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New651075
Fresh101
Picked101
Done000
Total671077
Error
0.1b
Counts
77 → 10
Alt Table
StatusErrorProgram
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
16.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
41.5b
(fma.f64 x (*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) y)) (/.f64 (*.f64 z z) (*.f64 t t)))
16.8b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
24.2b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
39.6b
(/.f64 (pow.f64 x 2) (pow.f64 y 2))
29.0b
(fma.f64 x (*.f64 x (/.f64 1 (*.f64 y y))) (/.f64 (*.f64 z z) (*.f64 t t)))
22.3b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
25.9b
(fma.f64 x (/.f64 x (*.f64 y y)) (cbrt.f64 (pow.f64 (/.f64 z t) 6)))
22.1b
(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 1786 to 483 computations (73% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (/.f64 z t) (/.f64 x y))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))

series294.0ms (3.5%)

Counts
2 → 96
Calls

2 calls:

254.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
40.0ms
(hypot.f64 (/.f64 z t) (/.f64 x y))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
pow1_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
hypot-udef_binary64
Counts
2 → 39
Calls

2 calls:

3.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
0.0ms
(hypot.f64 (/.f64 z t) (/.f64 x y))

simplify80.0ms (1%)

Algorithm
egg-herbie
Rules
928×associate-/l*_binary64
772×associate-/r*_binary64
212×fma-def_binary64
151×unswap-sqr_binary64
148×associate-/r/_binary64
Counts
135 → 87
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01173714
13423389
213143211
352683211

prune142.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1218129
Fresh279
Picked101
Done000
Total12415139
Error
0.0b
Counts
139 → 15
Alt Table
StatusErrorProgram
16.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
17.8b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (sqrt.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (/.f64 (*.f64 z z) (*.f64 t t)))))
14.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (*.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
1.2b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
22.3b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
1.2b
(*.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
41.5b
(fma.f64 x (*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) y)) (/.f64 (*.f64 z z) (*.f64 t t)))
16.8b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
24.2b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
1.7b
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
0.6b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.4b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 x y) (/.f64 x y)))
29.0b
(fma.f64 x (*.f64 x (/.f64 1 (*.f64 y y))) (/.f64 (*.f64 z z) (*.f64 t t)))
22.1b
(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 4423 to 1559 computations (64.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 x y) (/.f64 x y)))
0.3b
(*.f64 (/.f64 z t) (/.f64 z t))
0.3b
(*.f64 (/.f64 x y) (/.f64 x y))

series149.0ms (1.8%)

Counts
3 → 96
Calls

3 calls:

91.0ms
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 x y) (/.f64 x y)))
30.0ms
(*.f64 (/.f64 x y) (/.f64 x y))
28.0ms
(*.f64 (/.f64 z t) (/.f64 z t))

rewrite41.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
83×add-sqr-sqrt_binary64
80×times-frac_binary64
59×*-un-lft-identity_binary64
59×add-cube-cbrt_binary64
27×add-cbrt-cube_binary64
Counts
3 → 161
Calls

3 calls:

9.0ms
(*.f64 (/.f64 z t) (/.f64 z t))
8.0ms
(*.f64 (/.f64 x y) (/.f64 x y))
6.0ms
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 x y) (/.f64 x y)))

simplify134.0ms (1.6%)

Algorithm
egg-herbie
Rules
876×times-frac_binary64
778×fma-def_binary64
271×associate-*r/_binary64
261×associate-*l/_binary64
249×fma-neg_binary64
Counts
257 → 242
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02594168
17613735
224413417
345393417
451613417

prune287.0ms (3.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2357242
Fresh6814
Picked101
Done000
Total24215257
Error
0b
Counts
257 → 15
Alt Table
StatusErrorProgram
14.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (*.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
16.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
3.0b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (/.f64 (*.f64 x (/.f64 x y)) y))
29.0b
(fma.f64 x (*.f64 x (/.f64 1 (*.f64 y y))) (/.f64 (*.f64 z z) (*.f64 t t)))
3.5b
(+.f64 (*.f64 z (*.f64 (/.f64 1 t) (/.f64 z t))) (*.f64 (/.f64 x y) (/.f64 x y)))
22.3b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
1.2b
(*.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
24.2b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
31.0b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (*.f64 x (/.f64 (sqrt.f64 x) y)) (/.f64 (sqrt.f64 x) y)))
2.5b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) (/.f64 x y))))
32.7b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (*.f64 (/.f64 x y) (/.f64 1 (sqrt.f64 y))) (/.f64 x (sqrt.f64 y))))
0.6b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
2.6b
(+.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (*.f64 (/.f64 z (cbrt.f64 t)) (/.f64 z t))) (*.f64 (/.f64 x y) (/.f64 x y)))
3.9b
(+.f64 (/.f64 (*.f64 z (/.f64 z t)) t) (*.f64 (/.f64 x y) (/.f64 x y)))
Compiler

Compiled 6278 to 1423 computations (77.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (/.f64 z t) (/.f64 x y))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
0.5b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
1.5b
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series310.0ms (3.7%)

Counts
3 → 120
Calls

3 calls:

206.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
63.0ms
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))
40.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))

rewrite27.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
36×pow1_binary64
32×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
15×pow-prod-up_binary64
15×sqrt-pow1_binary64
Counts
3 → 97
Calls

3 calls:

12.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
6.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
1.0ms
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

simplify119.0ms (1.4%)

Algorithm
egg-herbie
Rules
960×associate-/r*_binary64
363×fma-def_binary64
200×cancel-sign-sub-inv_binary64
194×unswap-sqr_binary64
169×associate-/r/_binary64
Counts
217 → 165
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02025798
15205228
219055086
352975086

prune347.0ms (4.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New3210321
Fresh01414
Picked011
Done000
Total32115336
Error
0b
Counts
336 → 15
Alt Table
StatusErrorProgram
14.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (*.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
16.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
3.0b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (/.f64 (*.f64 x (/.f64 x y)) y))
29.0b
(fma.f64 x (*.f64 x (/.f64 1 (*.f64 y y))) (/.f64 (*.f64 z z) (*.f64 t t)))
3.5b
(+.f64 (*.f64 z (*.f64 (/.f64 1 t) (/.f64 z t))) (*.f64 (/.f64 x y) (/.f64 x y)))
22.3b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
1.2b
(*.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
24.2b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
31.0b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (*.f64 x (/.f64 (sqrt.f64 x) y)) (/.f64 (sqrt.f64 x) y)))
2.5b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) (/.f64 x y))))
32.7b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (*.f64 (/.f64 x y) (/.f64 1 (sqrt.f64 y))) (/.f64 x (sqrt.f64 y))))
0.6b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
2.6b
(+.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (*.f64 (/.f64 z (cbrt.f64 t)) (/.f64 z t))) (*.f64 (/.f64 x y) (/.f64 x y)))
3.9b
(+.f64 (/.f64 (*.f64 z (/.f64 z t)) t) (*.f64 (/.f64 x y) (/.f64 x y)))
Compiler

Compiled 12237 to 3640 computations (70.3% saved)

regimes2.6s (31.1%)

Accuracy

Total 0.4b remaining (92.3%)

Threshold costs 0.4b (92.3%)

Counts
215 → 1
Compiler

Compiled 59328 to 30299 computations (48.9% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01413
11613
21313

end150.0ms (1.8%)

Compiler

Compiled 397 to 191 computations (51.9% saved)

Profiling

Loading profile data...