Details

Time bar (total: 21.2s)

analyze635.0ms (3%)

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%68.6%31.4%5
0%65.5%34.5%6
0%59.2%40.8%7
0%51.4%48.6%8
0%41.3%58.7%9
0%28.4%71.6%10
2.3%22.3%75.4%11
2.3%21%76.7%12
2.7%18%79.3%13
2.7%16.4%80.8%14
Compiler

Compiled 22 to 16 computations (27.3% saved)

sample82.0ms (0.4%)

Algorithm
intervals
Results
39.0ms256×body128valid
13.0ms156×body128nan
0.0msbody128invalid
Compiler

Compiled 48 to 36 computations (25% saved)

simplify232.0ms (1.1%)

Algorithm
egg-herbie
Rules
2140×distribute-rgt-in_binary64
556×associate--r+_binary64
551×associate-+l+_binary64
551×unsub-neg_binary64
546×associate-+r+_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01625
12923
27223
316023
442623
5109723
6199423
7198123
8195623
9197223
10198723
11203723
12204423
13224823
14265123
15244723
16245923
17246523
18246523
19255723
20464923
21472023
22480223
23487823
24764323

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
0.3b
(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))
Compiler

Compiled 118 to 76 computations (35.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
0.1b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
0.1b
(*.f64 (-.f64 a 1/2) (log.f64 t))
0.5b
(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

series1.7s (8%)

Counts
4 → 164
Calls

4 calls:

828.0ms
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
426.0ms
(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
339.0ms
(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
89.0ms
(*.f64 (-.f64 a 1/2) (log.f64 t))

rewrite69.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
93×*-un-lft-identity_binary64
48×pow1_binary64
45×add-sqr-sqrt_binary64
42×prod-diff_binary64
42×log-pow_binary64
Counts
4 → 176
Calls

4 calls:

21.0ms
(*.f64 (-.f64 a 1/2) (log.f64 t))
13.0ms
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
11.0ms
(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
9.0ms
(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)

simplify131.0ms (0.6%)

Algorithm
egg-herbie
Rules
450×associate--l+_binary64
371×associate-+l+_binary64
360×associate--r+_binary64
318×fma-def_binary64
286×sub-neg_binary64
Counts
340 → 368
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04697429
113966861
251566861

prune380.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New35711368
Fresh101
Picked101
Done000
Total35911370
Error
0.0b
Counts
370 → 11
Alt Table
StatusErrorProgram
0.2b
(+.f64 (+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t)) (*.f64 (-.f64 a 1/2) (log.f64 t)))
29.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (sqrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t))) (sqrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))))
34.9b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (-.f64 a 1/2) (sqrt.f64 (log.f64 t))) (sqrt.f64 (log.f64 t))))
0.8b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t))) (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))) (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))))
50.5b
(log.f64 (*.f64 (pow.f64 t (+.f64 a -1/2)) (/.f64 (*.f64 z (+.f64 y x)) (exp.f64 t))))
15.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (/.f64 (*.f64 (log.f64 t) (fma.f64 a a -1/4)) (+.f64 a 1/2)))
0.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (+.f64 (*.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t)))))
0.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (-.f64 a 1/2) (*.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t))))
19.1b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (cbrt.f64 (*.f64 (*.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) (*.f64 (-.f64 a 1/2) (log.f64 t))) (*.f64 (-.f64 a 1/2) (log.f64 t)))))
25.8b
(/.f64 (*.f64 (+.f64 (log.f64 (+.f64 y x)) (fma.f64 (log.f64 t) (+.f64 a -1/2) (-.f64 (log.f64 z) t))) (-.f64 (-.f64 (+.f64 (log.f64 z) (log.f64 (+.f64 y x))) t) (*.f64 (log.f64 t) (+.f64 a -1/2)))) (-.f64 (-.f64 (+.f64 (log.f64 z) (log.f64 (+.f64 y x))) t) (*.f64 (log.f64 t) (+.f64 a -1/2))))
0.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (cbrt.f64 (-.f64 a 1/2)) (cbrt.f64 (-.f64 a 1/2))) (*.f64 (cbrt.f64 (-.f64 a 1/2)) (log.f64 t))))
Compiler

Compiled 10772 to 4231 computations (60.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (log.f64 z) t)
0.1b
(+.f64 (+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t)) (*.f64 (-.f64 a 1/2) (log.f64 t)))
0.1b
(*.f64 (-.f64 a 1/2) (log.f64 t))
0.3b
(+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t))

series1.8s (8.6%)

Counts
3 → 119
Calls

3 calls:

1.4s
(+.f64 (+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t)) (*.f64 (-.f64 a 1/2) (log.f64 t)))
320.0ms
(+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t))
102.0ms
(-.f64 (log.f64 z) t)

rewrite80.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity_binary64
29×add-sqr-sqrt_binary64
27×add-cube-cbrt_binary64
25×associate-+r+_binary64
24×prod-diff_binary64
Counts
3 → 126
Calls

3 calls:

27.0ms
(+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t))
22.0ms
(+.f64 (+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t)) (*.f64 (-.f64 a 1/2) (log.f64 t)))
11.0ms
(-.f64 (log.f64 z) t)

simplify219.0ms (1%)

Algorithm
egg-herbie
Rules
562×fma-neg_binary64
365×associate--l+_binary64
362×associate-+l+_binary64
331×associate--r+_binary64
286×fma-def_binary64
Counts
245 → 280
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04135613
112555158
247905156
352965156

prune490.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3370337
Fresh01010
Picked011
Done000
Total33711348
Error
0.0b
Counts
348 → 11
Alt Table
StatusErrorProgram
0.2b
(+.f64 (+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t)) (*.f64 (-.f64 a 1/2) (log.f64 t)))
29.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (sqrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t))) (sqrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))))
34.9b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (-.f64 a 1/2) (sqrt.f64 (log.f64 t))) (sqrt.f64 (log.f64 t))))
0.8b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t))) (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))) (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))))
50.5b
(log.f64 (*.f64 (pow.f64 t (+.f64 a -1/2)) (/.f64 (*.f64 z (+.f64 y x)) (exp.f64 t))))
15.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (/.f64 (*.f64 (log.f64 t) (fma.f64 a a -1/4)) (+.f64 a 1/2)))
0.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (+.f64 (*.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t)))))
0.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (-.f64 a 1/2) (*.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t))))
19.1b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (cbrt.f64 (*.f64 (*.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) (*.f64 (-.f64 a 1/2) (log.f64 t))) (*.f64 (-.f64 a 1/2) (log.f64 t)))))
25.8b
(/.f64 (*.f64 (+.f64 (log.f64 (+.f64 y x)) (fma.f64 (log.f64 t) (+.f64 a -1/2) (-.f64 (log.f64 z) t))) (-.f64 (-.f64 (+.f64 (log.f64 z) (log.f64 (+.f64 y x))) t) (*.f64 (log.f64 t) (+.f64 a -1/2)))) (-.f64 (-.f64 (+.f64 (log.f64 z) (log.f64 (+.f64 y x))) t) (*.f64 (log.f64 t) (+.f64 a -1/2))))
0.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (cbrt.f64 (-.f64 a 1/2)) (cbrt.f64 (-.f64 a 1/2))) (*.f64 (cbrt.f64 (-.f64 a 1/2)) (log.f64 t))))
Compiler

Compiled 9518 to 3683 computations (61.3% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t)))
0.3b
(+.f64 (*.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t))))
0.5b
(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
0.6b
(cbrt.f64 t)

series2.7s (12.9%)

Counts
3 → 60
Calls

3 calls:

1.9s
(+.f64 (*.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t))))
704.0ms
(*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t)))
143.0ms
(cbrt.f64 t)

rewrite86.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
48×log-prod_binary64
36×distribute-lft-in_binary64
36×distribute-rgt-in_binary64
27×cbrt-prod_binary64
24×associate-+l+_binary64
Counts
3 → 105
Calls

3 calls:

58.0ms
(+.f64 (*.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t))))
11.0ms
(*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t)))
1.0ms
(cbrt.f64 t)

simplify185.0ms (0.9%)

Algorithm
egg-herbie
Rules
302×associate-+l+_binary64
282×associate-+r+_binary64
249×associate-*l*_binary64
231×cancel-sign-sub-inv_binary64
225×associate-*r*_binary64
Counts
165 → 191
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02112996
15542596
221892274
348672270
448852270

prune540.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2912293
Fresh459
Picked101
Done011
Total2968304
Error
0.0b
Counts
304 → 8
Alt Table
StatusErrorProgram
0.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (+.f64 (*.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (pow.f64 t 1/3)))))
0.2b
(+.f64 (+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t)) (*.f64 (-.f64 a 1/2) (log.f64 t)))
50.5b
(log.f64 (*.f64 (pow.f64 t (+.f64 a -1/2)) (/.f64 (*.f64 z (+.f64 y x)) (exp.f64 t))))
15.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (/.f64 (*.f64 (log.f64 t) (fma.f64 a a -1/4)) (+.f64 a 1/2)))
0.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (fma.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t)))))
0.8b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t))) (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))) (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))))
0.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (-.f64 a 1/2) (*.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t))))
0.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (cbrt.f64 (-.f64 a 1/2)) (cbrt.f64 (-.f64 a 1/2))) (*.f64 (cbrt.f64 (-.f64 a 1/2)) (log.f64 t))))
Compiler

Compiled 10593 to 4829 computations (54.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t)))
0.2b
(fma.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t))))
0.5b
(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
0.6b
(cbrt.f64 t)

series2.3s (11%)

Counts
1 → 24
Calls

1 calls:

2.3s
(fma.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t))))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

1.0ms
(fma.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t))))

simplify61.0ms (0.3%)

Algorithm
egg-herbie
Rules
664×distribute-rgt-in_binary64
627×distribute-lft-in_binary64
538×fma-def_binary64
536×fma-neg_binary64
137×associate-+l+_binary64
Counts
34 → 27
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
051865
1110575
2291457
31003368
44677368
55047368

prune335.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2080208
Fresh066
Picked011
Done011
Total2088216
Error
0.0b
Counts
216 → 8
Alt Table
StatusErrorProgram
0.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (+.f64 (*.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (pow.f64 t 1/3)))))
0.2b
(+.f64 (+.f64 (log.f64 (+.f64 x y)) (-.f64 (log.f64 z) t)) (*.f64 (-.f64 a 1/2) (log.f64 t)))
50.5b
(log.f64 (*.f64 (pow.f64 t (+.f64 a -1/2)) (/.f64 (*.f64 z (+.f64 y x)) (exp.f64 t))))
15.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (/.f64 (*.f64 (log.f64 t) (fma.f64 a a -1/4)) (+.f64 a 1/2)))
0.3b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (fma.f64 (+.f64 a -1/2) (*.f64 2 (log.f64 (cbrt.f64 t))) (*.f64 (+.f64 a -1/2) (log.f64 (cbrt.f64 t)))))
0.8b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t))) (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))) (cbrt.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)))))
0.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (-.f64 a 1/2) (*.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t))))
0.7b
(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (*.f64 (cbrt.f64 (-.f64 a 1/2)) (cbrt.f64 (-.f64 a 1/2))) (*.f64 (cbrt.f64 (-.f64 a 1/2)) (log.f64 t))))
Compiler

Compiled 7002 to 3120 computations (55.4% saved)

regimes5.3s (25%)

Accuracy

Total 0.3b remaining (90%)

Threshold costs 0.3b (90%)

Counts
209 → 1
Compiler

Compiled 72276 to 50672 computations (29.9% saved)

simplify9.0ms (0%)

Algorithm
egg-herbie
Rules
15×+-commutative_binary64
12×sub-neg_binary64
11×*-commutative_binary64
11×neg-sub0_binary64
11×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01943
12743
23943
35343
47943
59443
610643
711543
812143
912443
1012543
1112043

end9.0ms (0%)

Compiler

Compiled 99 to 54 computations (45.5% saved)

sample3.7s (17.3%)

Algorithm
intervals
Results
1.4s8000×body128valid
656.0ms4254×body128nan
5.0ms32×body128invalid
Compiler

Compiled 291 to 200 computations (31.3% saved)

Profiling

Loading profile data...