Details

Time bar (total: 7.6s)

analyze1.3s (17.1%)

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)

sample1.9s (25.6%)

Results
1.1s8256×body128valid
806.0ms6149×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

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
29.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
29.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
32.3b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 107 to 55 computations (48.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
3.2b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
9.9b
(/.f64 x (*.f64 y y))
21.9b
(/.f64 (*.f64 z z) (*.f64 t t))

series174.0ms (2.3%)

Counts
3 → 96
Calls

3 calls:

112.0ms
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
33.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
28.0ms
(/.f64 x (*.f64 y y))

rewrite12.0ms (0.2%)

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:

4.0ms
(/.f64 x (*.f64 y y))
4.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
0.0ms
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))

simplify105.0ms (1.4%)

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

prune77.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New631275
Fresh101
Picked101
Done000
Total651277
Error
0.1b
Counts
77 → 12
Alt Table
StatusErrorProgram
42.8b
(fma.f64 x (cbrt.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 y y) (*.f64 y y)) (*.f64 y y)))) (/.f64 (*.f64 z z) (*.f64 t t)))
37.6b
(/.f64 (pow.f64 x 2) (pow.f64 y 2))
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
16.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
24.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
17.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
22.2b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
28.8b
(fma.f64 x (/.f64 x (*.f64 y y)) (cbrt.f64 (pow.f64 (/.f64 z t) 6)))
22.2b
(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (*.f64 z z) (*.f64 t t)))
39.1b
(fma.f64 x (*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) y)) (/.f64 (*.f64 z z) (*.f64 t t)))
22.5b
(fma.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 x) y)) (/.f64 (*.f64 z z) (*.f64 t t)))
29.3b
(fma.f64 x (*.f64 (*.f64 (cbrt.f64 (/.f64 x (*.f64 y y))) (cbrt.f64 (/.f64 x (*.f64 y y)))) (cbrt.f64 (/.f64 x (*.f64 y y)))) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 1924 to 541 computations (71.9% 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)))

series332.0ms (4.4%)

Counts
2 → 96
Calls

2 calls:

275.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
57.0ms
(hypot.f64 (/.f64 z t) (/.f64 x y))

rewrite5.0ms (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))

simplify75.0ms (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

prune124.0ms (1.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1218129
Fresh5611
Picked101
Done000
Total12714141
Error
0.0b
Counts
141 → 14
Alt Table
StatusErrorProgram
1.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
24.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
35.1b
(cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 6))
17.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
0.7b
(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) 1)
22.2b
(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (*.f64 z z) (*.f64 t t)))
16.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
22.2b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
16.5b
(*.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)))))
0.7b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))
0.5b
(*.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))))
37.6b
(/.f64 (pow.f64 x 2) (pow.f64 y 2))
1.7b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.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))))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (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)))
Compiler

Compiled 4361 to 1527 computations (65% saved)

localize7.0ms (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 x y) (/.f64 x y))
0.3b
(*.f64 (/.f64 z t) (/.f64 z t))

series198.0ms (2.6%)

Counts
3 → 96
Calls

3 calls:

111.0ms
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 x y) (/.f64 x y)))
58.0ms
(*.f64 (/.f64 z t) (/.f64 z t))
29.0ms
(*.f64 (/.f64 x y) (/.f64 x y))

rewrite38.0ms (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))
7.0ms
(*.f64 (/.f64 x y) (/.f64 x y))
6.0ms
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 x y) (/.f64 x y)))

simplify122.0ms (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

prune249.0ms (3.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New2348242
Fresh4913
Picked101
Done000
Total23917256
Error
0b
Counts
256 → 17
Alt Table
StatusErrorProgram
1.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
24.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
35.1b
(cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 6))
17.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
4.3b
(+.f64 (/.f64 (*.f64 z (/.f64 z t)) t) (*.f64 (/.f64 x y) (/.f64 x y)))
22.2b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
32.7b
(+.f64 (*.f64 (*.f64 (/.f64 z t) (/.f64 (sqrt.f64 z) 1)) (/.f64 (sqrt.f64 z) t)) (*.f64 (/.f64 x y) (/.f64 x y)))
16.5b
(*.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)))))
0.7b
(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) 1)
22.2b
(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (*.f64 z z) (*.f64 t t)))
3.0b
(+.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))))
0.7b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))
17.4b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (/.f64 (*.f64 x x) (*.f64 y y)))
43.9b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 y)) (*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 y)) (/.f64 x y))))
1.0b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (/.f64 x y))))
3.5b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (/.f64 (*.f64 x (/.f64 x y)) y))
2.3b
(+.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)))
Compiler

Compiled 6370 to 1477 computations (76.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (/.f64 z t) (/.f64 x y))
0.7b
(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)
1.5b
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series469.0ms (6.2%)

Counts
2 → 48
Calls

2 calls:

397.0ms
(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)
72.0ms
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
unpow-prod-down_binary64
*-un-lft-identity_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64
Counts
2 → 40
Calls

2 calls:

2.0ms
(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)
1.0ms
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

simplify77.0ms (1%)

Algorithm
egg-herbie
Rules
550×times-frac_binary64
476×unswap-sqr_binary64
257×associate-/l*_binary64
254×associate-/r*_binary64
249×associate-*r*_binary64
Counts
88 → 68
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01272348
12802206
27662131
336592030
449842030

prune305.0ms (4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1100110
Fresh01616
Picked011
Done000
Total11017127
Error
0b
Counts
127 → 17
Alt Table
StatusErrorProgram
1.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
24.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
35.1b
(cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 6))
17.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
4.3b
(+.f64 (/.f64 (*.f64 z (/.f64 z t)) t) (*.f64 (/.f64 x y) (/.f64 x y)))
22.2b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
32.7b
(+.f64 (*.f64 (*.f64 (/.f64 z t) (/.f64 (sqrt.f64 z) 1)) (/.f64 (sqrt.f64 z) t)) (*.f64 (/.f64 x y) (/.f64 x y)))
16.5b
(*.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)))))
0.7b
(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) 1)
22.2b
(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (*.f64 z z) (*.f64 t t)))
3.0b
(+.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))))
0.7b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))
17.4b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (/.f64 (*.f64 x x) (*.f64 y y)))
43.9b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 y)) (*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 y)) (/.f64 x y))))
1.0b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (/.f64 x y))))
3.5b
(+.f64 (*.f64 (/.f64 z t) (/.f64 z t)) (/.f64 (*.f64 x (/.f64 x y)) y))
2.3b
(+.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)))
Compiler

Compiled 3147 to 1646 computations (47.7% saved)

regimes1.7s (22.6%)

Accuracy

Total 0.4b remaining (92%)

Threshold costs 0.4b (92%)

Counts
155 → 1
Compiler

Compiled 41927 to 21670 computations (48.3% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
*-rgt-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11622
21522

end229.0ms (3%)

Compiler

Compiled 455 to 220 computations (51.6% saved)

Profiling

Loading profile data...