Details

Time bar (total: 7.1s)

analyze1.2s (16.4%)

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)

sample58.0ms (0.8%)

Algorithm
intervals
Results
13.0ms256×body128valid
8.0ms164×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify9.0ms (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
32.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
32.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
35.3b
(+.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
4.2b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
10.8b
(/.f64 x (*.f64 y y))
24.3b
(/.f64 (*.f64 z z) (*.f64 t t))

series157.0ms (2.2%)

Counts
3 → 96
Calls

3 calls:

101.0ms
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
29.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
26.0ms
(/.f64 x (*.f64 y y))

rewrite10.0ms (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:

4.0ms
(/.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)))

simplify106.0ms (1.5%)

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

prune83.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New641175
Fresh101
Picked101
Done000
Total661177
Error
0.1b
Counts
77 → 11
Alt Table
StatusErrorProgram
48.3b
(fma.f64 x (/.f64 (sqrt.f64 x) (/.f64 (*.f64 y y) (sqrt.f64 x))) (/.f64 (*.f64 z z) (*.f64 t t)))
17.9b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
41.0b
(/.f64 (pow.f64 x 2) (pow.f64 y 2))
18.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
25.3b
(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)))
29.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (cbrt.f64 (pow.f64 (/.f64 z t) 6)))
25.4b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
25.1b
(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (*.f64 z z) (*.f64 t t)))
44.7b
(fma.f64 x (*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) y)) (/.f64 (*.f64 z z) (*.f64 t t)))
25.0b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 1840 to 509 computations (72.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))

series333.0ms (4.7%)

Counts
1 → 48
Calls

1 calls:

333.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (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
1 → 29
Calls

1 calls:

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

simplify92.0ms (1.3%)

Algorithm
egg-herbie
Rules
894×fma-def_binary64
358×distribute-rgt-out_binary64
262×sqr-pow_binary64
244×associate-*l/_binary64
213×associate-*r/_binary64
Counts
77 → 44
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0481634
11001440
22231309
36611295
424971216
541401215
648581028
749171028

prune52.0ms (0.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New37744
Fresh5510
Picked011
Done000
Total421355
Error
0.0b
Counts
55 → 13
Alt Table
StatusErrorProgram
41.0b
(/.f64 (pow.f64 x 2) (pow.f64 y 2))
18.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
1.3b
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)))
25.4b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
0.8b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))
32.4b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
17.9b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
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)))))
1.6b
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 5) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (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))))
1.1b
(*.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))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
25.0b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 1571 to 425 computations (72.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.3b
(*.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))))
0.3b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))
1.6b
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series497.0ms (7%)

Counts
3 → 96
Calls

3 calls:

309.0ms
(*.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))))
114.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))
73.0ms
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

rewrite19.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
28×pow1_binary64
16×add-sqr-sqrt_binary64
15×pow-prod-up_binary64
12×associate-*l*_binary64
11×sqrt-pow1_binary64
Counts
3 → 78
Calls

3 calls:

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

simplify123.0ms (1.7%)

Algorithm
egg-herbie
Rules
777×fma-def_binary64
751×times-frac_binary64
417×associate-/r*_binary64
388×associate-/l*_binary64
288×associate-*l/_binary64
Counts
174 → 133
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01985187
14764629
213844233
348484233
453224233

prune167.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1558163
Fresh7411
Picked101
Done011
Total16313176
Error
0b
Counts
176 → 13
Alt Table
StatusErrorProgram
1.3b
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)))
0.9b
(*.f64 (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))))
25.4b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
0.8b
(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)
0.6b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))))
1.1b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))))
0.8b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (fabs.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.7b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (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))))
17.9b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
0.5b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
18.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
1.2b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)))
Compiler

Compiled 6505 to 1760 computations (72.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
0.4b
(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)
1.6b
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series464.0ms (6.6%)

Counts
2 → 96
Calls

2 calls:

291.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
173.0ms
(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
add-exp-log_binary64
*-un-lft-identity_binary64
unpow-prod-down_binary64
add-cube-cbrt_binary64
Counts
2 → 55
Calls

2 calls:

5.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
1.0ms
(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)

simplify142.0ms (2%)

Algorithm
egg-herbie
Rules
727×fma-def_binary64
307×times-frac_binary64
246×associate-*r*_binary64
238×cancel-sign-sub-inv_binary64
228×unswap-sqr_binary64
Counts
151 → 135
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02795734
18215456
229135228
349105228
450675228

prune179.0ms (2.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1632165
Fresh3811
Picked011
Done011
Total16612178
Error
0b
Counts
178 → 12
Alt Table
StatusErrorProgram
1.3b
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)))
0.9b
(*.f64 (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))))
25.4b
(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
0.6b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
0.5b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
0.5b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/4) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/4)))
1.2b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)))
1.1b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))))
0.8b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (fabs.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.5b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
18.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
0.8b
(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)
Compiler

Compiled 6675 to 2901 computations (56.5% saved)

regimes1.6s (23.1%)

Accuracy

Total 0.4b remaining (89.5%)

Threshold costs 0.4b (89.5%)

Counts
150 → 1
Compiler

Compiled 48187 to 21852 computations (54.7% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01213
11413
21213

end0.0ms (0%)

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.7s (24.4%)

Algorithm
intervals
Results
520.0ms8000×body128valid
321.0ms5865×body128invalid
Compiler

Compiled 416 to 180 computations (56.7% saved)

Profiling

Loading profile data...