Details

Time bar (total: 7.5s)

analyze1.1s (14.6%)

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)

sample61.0ms (0.8%)

Algorithm
intervals
Results
19.0ms256×body128valid
9.0ms175×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% 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

prune9.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
30.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
30.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
34.4b
(+.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
4.4b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
8.5b
(/.f64 x (*.f64 y y))
22.2b
(/.f64 (*.f64 z z) (*.f64 t t))

series180.0ms (2.4%)

Counts
3 → 96
Calls

3 calls:

123.0ms
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
32.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
24.0ms
(/.f64 x (*.f64 y y))

rewrite13.0ms (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:

5.0ms
(/.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)))

simplify110.0ms (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

prune77.0ms (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
15.5b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
43.5b
(/.f64 (pow.f64 x 2) (pow.f64 y 2))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
24.5b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
24.4b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
25.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 (*.f64 t t) z)))
28.4b
(fma.f64 x (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 y (/.f64 (cbrt.f64 x) y))) (/.f64 (*.f64 z z) (*.f64 t t)))
30.1b
(fma.f64 x (*.f64 x (/.f64 1 (*.f64 y y))) (/.f64 (*.f64 z z) (*.f64 t t)))
24.8b
(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)))
16.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
Compiler

Compiled 1800 to 483 computations (73.2% 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)))

series334.0ms (4.4%)

Counts
2 → 96
Calls

2 calls:

280.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
53.0ms
(hypot.f64 (/.f64 z t) (/.f64 x y))

rewrite8.0ms (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:

6.0ms
(*.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))

simplify74.0ms (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

prune109.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1236129
Fresh459
Picked011
Done000
Total12712139
Error
0.0b
Counts
139 → 12
Alt Table
StatusErrorProgram
15.5b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
43.5b
(/.f64 (pow.f64 x 2) (pow.f64 y 2))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
1.3b
(*.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))))
24.4b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
25.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 (*.f64 t t) z)))
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))))
30.1b
(fma.f64 x (*.f64 x (/.f64 1 (*.f64 y y))) (/.f64 (*.f64 z z) (*.f64 t t)))
1.3b
(*.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)))
0.7b
(*.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)))))
16.8b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3)))
0.9b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))
Compiler

Compiled 4204 to 1485 computations (64.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(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)))
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))))
1.3b
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series477.0ms (6.3%)

Counts
3 → 96
Calls

3 calls:

294.0ms
(*.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))))
109.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))
74.0ms
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

rewrite17.0ms (0.2%)

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))))
4.0ms
(*.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)))

simplify120.0ms (1.6%)

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
01985037
14764509
213844233
348484233
453224233

prune260.0ms (3.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2845289
Fresh3710
Picked101
Done011
Total28813301
Error
0.0b
Counts
301 → 13
Alt Table
StatusErrorProgram
0.7b
(*.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))))))
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 (sqrt.f64 (cbrt.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)))))
16.8b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3)))
0.8b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (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)))
1.3b
(*.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))))
24.4b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
25.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 (*.f64 t t) z)))
30.1b
(fma.f64 x (*.f64 x (/.f64 1 (*.f64 y y))) (/.f64 (*.f64 z z) (*.f64 t t)))
1.3b
(*.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)))
0.6b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
1.2b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
15.5b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
Compiler

Compiled 11783 to 3501 computations (70.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(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)))
0.3b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
1.3b
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series270.0ms (3.6%)

Counts
1 → 48
Calls

1 calls:

270.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×add-exp-log_binary64
11×prod-exp_binary64
10×add-cbrt-cube_binary64
10×pow1_binary64
associate-*l*_binary64
Counts
1 → 28
Calls

1 calls:

7.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))))

simplify113.0ms (1.5%)

Algorithm
egg-herbie
Rules
555×associate-/l*_binary64
345×associate-/r*_binary64
305×fma-def_binary64
299×sqr-pow_binary64
276×associate-/l/_binary64
Counts
76 → 43
Iterations

Useful iterations: 7 (0.0ms)

IterNodesCost
0652180
11171596
22301321
33851317
410231295
530901295
634761295
744331259
848761259
948951259

prune711.0ms (9.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New2841285
Fresh11011
Picked011
Done011
Total28513298
Error
0.0b
Counts
298 → 13
Alt Table
StatusErrorProgram
0.7b
(*.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))))))
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 (sqrt.f64 (cbrt.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)))))
16.8b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3)))
0.8b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
15.5b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
1.2b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
1.3b
(*.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))))
24.4b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
25.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 (*.f64 t t) z)))
30.1b
(fma.f64 x (*.f64 x (/.f64 1 (*.f64 y y))) (/.f64 (*.f64 z z) (*.f64 t t)))
0.6b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
1.2b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
Compiler

Compiled 11961 to 3897 computations (67.4% saved)

regimes2.0s (26.3%)

Accuracy

Total 0.4b remaining (89.6%)

Threshold costs 0.4b (89.6%)

Counts
170 → 1
Compiler

Compiled 51031 to 24160 computations (52.7% 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)

sample1.5s (19.3%)

Algorithm
intervals
Results
449.0ms8000×body128valid
364.0ms5947×body128invalid
Compiler

Compiled 444 to 179 computations (59.7% saved)

Profiling

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