Details

Time bar (total: 28.0s)

analyze3.1s (11.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
0%98.1%1.9%13
0%98.1%1.9%14
Compiler

Compiled 59 to 22 computations (62.7% saved)

sample638.0ms (2.3%)

Algorithm
intervals
Results
114.0ms408×body128nan
96.0ms68×body4096valid
67.0ms38×body8192valid
54.0ms49×body2048valid
40.0ms25×body1024valid
34.0ms160×body128invalid
12.0ms58×body128valid
6.0ms10×body512valid
5.0msbody2048invalid
3.0msbody256valid
1.0msbody4096invalid
1.0msbody512invalid
0.0msbody256invalid
Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify70.0ms (0.3%)

Algorithm
egg-herbie
Rules
599×times-frac_binary64
518×distribute-neg-frac_binary64
416×fma-def_binary64
304×associate-/l*_binary64
217×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02278
16474
229674
3310367
4421867
5536567

prune10.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
58.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
59.0b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
61.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 c0 (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 c0 (*.f64 w h)) (*.f64 (*.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (*.f64 w h)))) (*.f64 M M)))))
Compiler

Compiled 321 to 130 computations (59.5% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
12.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
12.8b
(*.f64 (*.f64 w h) (*.f64 D D))
13.2b
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
31.0b
(+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))

series1.7s (6%)

Counts
4 → 240
Calls

4 calls:

719.0ms
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
571.0ms
(+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))
355.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
41.0ms
(*.f64 (*.f64 w h) (*.f64 D D))

rewrite152.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
94×add-cbrt-cube_binary64
94×add-exp-log_binary64
51×cbrt-unprod_binary64
51×prod-exp_binary64
18×pow1_binary64
Counts
4 → 130
Calls

4 calls:

53.0ms
(+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))
50.0ms
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
15.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
6.0ms
(*.f64 (*.f64 w h) (*.f64 D D))

simplify361.0ms (1.3%)

Algorithm
egg-herbie
Rules
488×associate-/r*_binary64
478×associate-/l*_binary64
460×fma-def_binary64
295×associate-*l/_binary64
278×associate-*r/_binary64
Counts
370 → 279
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
047718780
1146516679
2488616625
3516016625

prune685.0ms (2.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New45013463
Fresh011
Picked101
Done000
Total45114465
Error
29.2b
Counts
465 → 14
Alt Table
StatusErrorProgram
59.7b
(*.f64 (sqrt.f64 (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))) (sqrt.f64 (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))))
59.9b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 2 (/.f64 (*.f64 (pow.f64 d 2) c0) (*.f64 (pow.f64 D 2) (*.f64 w h)))))
60.9b
(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (*.f64 w h)) (/.f64 (*.f64 d d) (*.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (*.f64 (pow.f64 d 4) (*.f64 c0 c0)) (*.f64 (*.f64 w h) (*.f64 w h))) (pow.f64 D 4)) (*.f64 M M))))) (/.f64 c0 (*.f64 2 w))))
60.3b
(/.f64 (*.f64 (pow.f64 d 2) (pow.f64 c0 2)) (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
62.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (/.f64 c0 (*.f64 w h)) (/.f64 (*.f64 d d) (*.f64 D D)) (sqrt.f64 (neg.f64 (*.f64 M M)))))
63.7b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (exp.f64 (+.f64 (+.f64 (log.f64 w) (log.f64 h)) (+.f64 (log.f64 D) (log.f64 D))))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
60.7b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 c0 (*.f64 d d)) (/.f64 1 (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
63.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (+.f64 (log.f64 d) (log.f64 d))) (log.f64 (*.f64 (*.f64 w h) (*.f64 D D))))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
47.7b
(*.f64 1/2 (/.f64 (*.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
42.4b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 w (*.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
35.5b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
60.4b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 w (*.f64 h (*.f64 D D)))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
61.1b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (exp.f64 (log.f64 (/.f64 (*.f64 (*.f64 d d) c0) (*.f64 (*.f64 D D) (*.f64 w h)))))) (*.f64 M M)))))
61.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 c0 (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 c0 (*.f64 w h)) (*.f64 (*.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (*.f64 w h)))) (*.f64 M M)))))
Compiler

Compiled 31788 to 7109 computations (77.6% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

NewErrorProgram
9.7b
(*.f64 (pow.f64 M 2) h)
14.8b
(*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))
16.1b
(/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series175.0ms (0.6%)

Counts
3 → 40
Calls

3 calls:

131.0ms
(/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
36.0ms
(*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))
9.0ms
(*.f64 (pow.f64 M 2) h)

rewrite31.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
141×add-exp-log_binary64
87×prod-exp_binary64
42×pow-exp_binary64
42×pow-to-exp_binary64
39×div-exp_binary64
Counts
3 → 133
Calls

3 calls:

8.0ms
(/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
6.0ms
(*.f64 (pow.f64 M 2) h)
6.0ms
(*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))

simplify128.0ms (0.5%)

Algorithm
egg-herbie
Rules
468×associate-*l/_binary64
391×associate-/l/_binary64
373×*-commutative_binary64
370×associate-*r/_binary64
310×fma-def_binary64
Counts
173 → 160
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01643095
13322730
213612677
341282571
449132571
550862571

prune504.0ms (1.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New14416160
Fresh31013
Picked101
Done000
Total14826174
Error
19.3b
Counts
174 → 26
Alt Table
StatusErrorProgram
54.4b
(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
32.9b
(*.f64 1/4 (*.f64 (/.f64 (pow.f64 D 2) (pow.f64 (*.f64 (cbrt.f64 d) (cbrt.f64 d)) 2)) (/.f64 (*.f64 (pow.f64 M 2) h) (pow.f64 (cbrt.f64 d) 2))))
52.6b
(*.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
59.7b
(*.f64 (sqrt.f64 (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))) (sqrt.f64 (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))))
59.9b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 2 (/.f64 (*.f64 (pow.f64 d 2) c0) (*.f64 (pow.f64 D 2) (*.f64 w h)))))
31.8b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 M (*.f64 M h))) (pow.f64 d 2)))
60.3b
(/.f64 (*.f64 (pow.f64 d 2) (pow.f64 c0 2)) (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
62.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (/.f64 c0 (*.f64 w h)) (/.f64 (*.f64 d d) (*.f64 D D)) (sqrt.f64 (neg.f64 (*.f64 M M)))))
47.0b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 (sqrt.f64 M) 2) (*.f64 h M))) (pow.f64 d 2)))
60.4b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 w (*.f64 h (*.f64 D D)))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
54.2b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
31.6b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d)) d))
63.7b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (exp.f64 (+.f64 (+.f64 (log.f64 w) (log.f64 h)) (+.f64 (log.f64 D) (log.f64 D))))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
58.2b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
63.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (+.f64 (log.f64 d) (log.f64 d))) (log.f64 (*.f64 (*.f64 w h) (*.f64 D D))))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
50.1b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (log.f64 (*.f64 (pow.f64 M 2) h))) (log.f64 (pow.f64 d 2)))))
47.7b
(*.f64 1/2 (/.f64 (*.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
33.3b
(*.f64 1/4 (/.f64 (*.f64 D (*.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
56.1b
(*.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
61.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 c0 (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 c0 (*.f64 w h)) (*.f64 (*.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (*.f64 w h)))) (*.f64 M M)))))
31.3b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 D D) d) (/.f64 (*.f64 h (*.f64 M M)) d)))
60.0b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
38.8b
(*.f64 1/4 (exp.f64 (-.f64 (log.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))) (log.f64 (pow.f64 d 2)))))
54.0b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
61.1b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (exp.f64 (log.f64 (/.f64 (*.f64 (*.f64 d d) c0) (*.f64 (*.f64 D D) (*.f64 w h)))))) (*.f64 M M)))))
35.0b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
Compiler

Compiled 5112 to 3145 computations (38.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
5.5b
(/.f64 (*.f64 h (*.f64 M M)) d)
7.6b
(/.f64 (*.f64 D D) d)
9.7b
(*.f64 h (*.f64 M M))
11.5b
(*.f64 (/.f64 (*.f64 D D) d) (/.f64 (*.f64 h (*.f64 M M)) d))

series310.0ms (1.1%)

Counts
4 → 132
Calls

4 calls:

220.0ms
(*.f64 (/.f64 (*.f64 D D) d) (/.f64 (*.f64 h (*.f64 M M)) d))
50.0ms
(/.f64 (*.f64 h (*.f64 M M)) d)
22.0ms
(/.f64 (*.f64 D D) d)
18.0ms
(*.f64 h (*.f64 M M))

rewrite70.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
77×add-cbrt-cube_binary64
77×add-exp-log_binary64
32×cbrt-unprod_binary64
32×prod-exp_binary64
22×cbrt-undiv_binary64
Counts
4 → 123
Calls

4 calls:

21.0ms
(*.f64 (/.f64 (*.f64 D D) d) (/.f64 (*.f64 h (*.f64 M M)) d))
10.0ms
(*.f64 h (*.f64 M M))
9.0ms
(/.f64 (*.f64 h (*.f64 M M)) d)
7.0ms
(/.f64 (*.f64 D D) d)

simplify216.0ms (0.8%)

Algorithm
egg-herbie
Rules
637×associate-/r*_binary64
534×associate-/r/_binary64
461×*-commutative_binary64
309×log-div_binary64
218×log-prod_binary64
Counts
255 → 160
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01704137
14003453
215763453
340693451
448653451
550263451

prune608.0ms (2.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New1528160
Fresh71825
Picked101
Done000
Total16026186
Error
17.1b
Counts
186 → 26
Alt Table
StatusErrorProgram
46.1b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 D D) d) (/.f64 (*.f64 (*.f64 (sqrt.f64 h) M) (*.f64 (sqrt.f64 h) M)) d)))
58.2b
(*.f64 1/4 (exp.f64 (+.f64 (log.f64 (/.f64 (*.f64 D D) d)) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
52.6b
(*.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
59.7b
(*.f64 (sqrt.f64 (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))) (sqrt.f64 (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))))
30.7b
(*.f64 1/4 (*.f64 (*.f64 h (/.f64 (*.f64 D D) d)) (/.f64 (*.f64 M M) d)))
59.9b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 2 (/.f64 (*.f64 (pow.f64 d 2) c0) (*.f64 (pow.f64 D 2) (*.f64 w h)))))
31.8b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 M (*.f64 M h))) (pow.f64 d 2)))
60.3b
(/.f64 (*.f64 (pow.f64 d 2) (pow.f64 c0 2)) (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
62.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (/.f64 c0 (*.f64 w h)) (/.f64 (*.f64 d d) (*.f64 D D)) (sqrt.f64 (neg.f64 (*.f64 M M)))))
31.3b
(*.f64 1/4 (*.f64 (*.f64 (/.f64 (*.f64 D D) d) (*.f64 (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d)) (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d)))) (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d))))
60.4b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 w (*.f64 h (*.f64 D D)))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
27.5b
(*.f64 1/4 (*.f64 (/.f64 D 1) (*.f64 (/.f64 D d) (/.f64 (*.f64 h (*.f64 M M)) d))))
63.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (+.f64 (log.f64 d) (log.f64 d))) (log.f64 (*.f64 (*.f64 w h) (*.f64 D D))))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
26.9b
(*.f64 1/4 (*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 h (*.f64 M M)) d))))
54.0b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
28.2b
(*.f64 1/4 (*.f64 (/.f64 D (/.f64 d D)) (/.f64 (*.f64 h (*.f64 M M)) d)))
33.3b
(*.f64 1/4 (/.f64 (*.f64 D (*.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
56.1b
(*.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
61.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 c0 (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 c0 (*.f64 w h)) (*.f64 (*.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (*.f64 w h)))) (*.f64 M M)))))
27.4b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 D D) d) (/.f64 (*.f64 (*.f64 h M) M) d)))
54.4b
(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
38.8b
(*.f64 1/4 (exp.f64 (-.f64 (log.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))) (log.f64 (pow.f64 d 2)))))
63.7b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (exp.f64 (+.f64 (+.f64 (log.f64 w) (log.f64 h)) (+.f64 (log.f64 D) (log.f64 D))))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
61.1b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (exp.f64 (log.f64 (/.f64 (*.f64 (*.f64 d d) c0) (*.f64 (*.f64 D D) (*.f64 w h)))))) (*.f64 M M)))))
35.0b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
60.0b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
Compiler

Compiled 5349 to 1859 computations (65.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.4b
(*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 h (*.f64 M M)) d)))
5.5b
(/.f64 (*.f64 h (*.f64 M M)) d)
6.8b
(*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 h (*.f64 M M)) d))
9.7b
(*.f64 h (*.f64 M M))

series2.4s (8.6%)

Counts
2 → 96
Calls

2 calls:

2.3s
(*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 h (*.f64 M M)) d))
158.0ms
(*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 h (*.f64 M M)) d)))

rewrite57.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
187×add-exp-log_binary64
153×add-cbrt-cube_binary64
92×cbrt-unprod_binary64
92×prod-exp_binary64
58×cbrt-undiv_binary64
Counts
2 → 143
Calls

2 calls:

16.0ms
(*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 h (*.f64 M M)) d)))
10.0ms
(*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 h (*.f64 M M)) d))

simplify158.0ms (0.6%)

Algorithm
egg-herbie
Rules
610×associate-/r/_binary64
350×associate-*r*_binary64
307×associate-*l/_binary64
307×times-frac_binary64
295×associate-*r/_binary64
Counts
239 → 209
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02497889
15884982
226264964
348784964
449654964

prune570.0ms (2%)

Pruning

30 alts after pruning (30 fresh and 0 done)

PrunedKeptTotal
New2588266
Fresh32225
Picked101
Done000
Total26230292
Error
16.1b
Counts
292 → 30
Alt Table
StatusErrorProgram
27.4b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 D D) d) (/.f64 (*.f64 (*.f64 h M) M) d)))
27.4b
(*.f64 1/4 (*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (*.f64 (/.f64 D (cbrt.f64 d)) (*.f64 h (*.f64 M M))) (/.f64 1 d))))
58.2b
(*.f64 1/4 (exp.f64 (+.f64 (log.f64 (/.f64 (*.f64 D D) d)) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
27.0b
(*.f64 1/4 (*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (*.f64 h (/.f64 D (cbrt.f64 d))) (/.f64 (*.f64 M M) d))))
52.6b
(*.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
59.7b
(*.f64 (sqrt.f64 (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))) (sqrt.f64 (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))))
30.7b
(*.f64 1/4 (*.f64 (*.f64 h (/.f64 (*.f64 D D) d)) (/.f64 (*.f64 M M) d)))
27.0b
(*.f64 1/4 (*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (/.f64 D (cbrt.f64 d)) (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d)) (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d))) (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d))))))
26.1b
(*.f64 1/4 (*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (*.f64 M M) (cbrt.f64 d)))))
59.9b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 2 (/.f64 (*.f64 (pow.f64 d 2) c0) (*.f64 (pow.f64 D 2) (*.f64 w h)))))
44.0b
(*.f64 1/4 (*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 (*.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h))) d))))
38.8b
(*.f64 1/4 (exp.f64 (-.f64 (log.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))) (log.f64 (pow.f64 d 2)))))
22.5b
(*.f64 1/4 (*.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 (*.f64 h M) M) d))))
31.8b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 M (*.f64 M h))) (pow.f64 d 2)))
60.3b
(/.f64 (*.f64 (pow.f64 d 2) (pow.f64 c0 2)) (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
62.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (/.f64 c0 (*.f64 w h)) (/.f64 (*.f64 d d) (*.f64 D D)) (sqrt.f64 (neg.f64 (*.f64 M M)))))
31.3b
(*.f64 1/4 (*.f64 (*.f64 (/.f64 (*.f64 D D) d) (*.f64 (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d)) (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d)))) (cbrt.f64 (/.f64 (*.f64 h (*.f64 M M)) d))))
60.4b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 w (*.f64 h (*.f64 D D)))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
27.5b
(*.f64 1/4 (*.f64 (/.f64 D 1) (*.f64 (/.f64 D d) (/.f64 (*.f64 h (*.f64 M M)) d))))
63.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (+.f64 (log.f64 d) (log.f64 d))) (log.f64 (*.f64 (*.f64 w h) (*.f64 D D))))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
26.9b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 (cbrt.f64 D) (cbrt.f64 D)) (cbrt.f64 d)) (*.f64 (/.f64 (cbrt.f64 D) (cbrt.f64 d)) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (*.f64 h (*.f64 M M)) d)))))
61.1b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (exp.f64 (log.f64 (/.f64 (*.f64 (*.f64 d d) c0) (*.f64 (*.f64 D D) (*.f64 w h)))))) (*.f64 M M)))))
30.9b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 M M) h) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 D (cbrt.f64 d)))) (*.f64 (cbrt.f64 d) d)))
56.1b
(*.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
61.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 c0 (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 c0 (*.f64 w h)) (*.f64 (*.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (*.f64 w h)))) (*.f64 M M)))))
54.4b
(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
63.7b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (exp.f64 (+.f64 (+.f64 (log.f64 w) (log.f64 h)) (+.f64 (log.f64 D) (log.f64 D))))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))
28.2b
(*.f64 1/4 (*.f64 (/.f64 D (/.f64 d D)) (/.f64 (*.f64 h (*.f64 M M)) d)))
35.0b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
60.0b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
Compiler

Compiled 9467 to 2112 computations (77.7% saved)

regimes1.6s (5.8%)

Accuracy

Total 6.1b remaining (25.7%)

Threshold costs 0b (0%)

Counts
115 → 3
Compiler

Compiled 45069 to 25243 computations (44% saved)

bsearch275.0ms (1%)

Steps
ItersRangePoint
9
2.2355640830677916e+134
3.6915694254620503e+143
3.6331476128764397e+143
4
-5.867333877531429e+105
-3.088264778914999e+105
-5.73365257904138e+105
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
if-if-or-not_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03082
14282
24282

end1.0ms (0%)

Compiler

Compiled 59 to 32 computations (45.8% saved)

sample14.1s (50.3%)

Algorithm
intervals
Results
2.9s2139×body4096valid
2.5s12075×body128nan
1.9s1191×body8192valid
1.4s1278×body2048valid
844.0ms4085×body128invalid
523.0ms624×body1024valid
483.0ms2316×body128valid
182.0ms307×body512valid
70.0ms145×body256valid
52.0ms50×body2048invalid
46.0ms57×body1024invalid
26.0ms43×body512invalid
19.0ms15×body4096invalid
8.0ms21×body256invalid
6.0msbody8192exit
Compiler

Compiled 1187 to 647 computations (45.5% saved)

Profiling

Loading profile data...