Details

Time bar (total: 22.7s)

analyze3.1s (13.5%)

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)

sample304.0ms (1.3%)

Algorithm
intervals
Results
51.0ms72×body4096valid
46.0ms42×body8192valid
34.0ms304×body128nan
27.0ms50×body2048valid
18.0ms118×body128invalid
14.0ms19×body1024valid
7.0ms59×body128valid
3.0msbody512valid
1.0msbody2048invalid
1.0msbody256valid
0.0msbody1024invalid
0.0msbody256invalid
Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify50.0ms (0.2%)

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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
59.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
59.8b
(*.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)))))
61.9b
(*.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)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
11.6b
(*.f64 (*.f64 w h) (*.f64 D D))
13.3b
(*.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)))))
16.4b
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
34.3b
(+.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))))

series1.1s (5%)

Counts
4 → 240
Calls

4 calls:

567.0ms
(*.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)))))
332.0ms
(+.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))))
214.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
23.0ms
(*.f64 (*.f64 w h) (*.f64 D D))

rewrite134.0ms (0.6%)

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:

45.0ms
(*.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)))))
41.0ms
(+.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))))
13.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
9.0ms
(*.f64 (*.f64 w h) (*.f64 D D))

simplify394.0ms (1.7%)

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

prune662.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New45310463
Fresh011
Picked101
Done000
Total45411465
Error
26.9b
Counts
465 → 11
Alt Table
StatusErrorProgram
63.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (cbrt.f64 (*.f64 (pow.f64 D 6) (*.f64 (pow.f64 w 3) (pow.f64 h 3))))) (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)))))
62.3b
(*.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)))))
61.1b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (cbrt.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))))) (cbrt.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)))))
50.3b
(*.f64 1/2 (/.f64 (*.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
60.1b
(*.f64 c0 (*.f64 (/.f64 1 (*.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
(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))))
32.4b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
63.9b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (log.f64 (*.f64 d d))) (+.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)))))
61.9b
(*.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)))))
40.7b
(*.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))))
60.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 2 (/.f64 (*.f64 (pow.f64 d 2) c0) (*.f64 (pow.f64 D 2) (*.f64 w h)))))
Compiler

Compiled 31462 to 6975 computations (77.8% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
6.7b
(*.f64 (pow.f64 M 2) h)
14.0b
(*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))
15.7b
(/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series1.7s (7.4%)

Counts
4 → 72
Calls

4 calls:

1.5s
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
136.0ms
(/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
34.0ms
(*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))
9.0ms
(*.f64 (pow.f64 M 2) h)

rewrite62.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
290×add-exp-log_binary64
190×prod-exp_binary64
78×div-exp_binary64
76×pow-exp_binary64
76×pow-to-exp_binary64
Counts
4 → 205
Calls

4 calls:

14.0ms
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
14.0ms
(/.f64 (*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
6.0ms
(*.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h))
4.0ms
(*.f64 (pow.f64 M 2) h)

simplify168.0ms (0.7%)

Algorithm
egg-herbie
Rules
506×*-commutative_binary64
444×associate-/l/_binary64
380×fma-def_binary64
373×associate-/r/_binary64
294×log-prod_binary64
Counts
277 → 231
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02175669
14225071
216725018
339364789
450064789

prune465.0ms (2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New21516231
Fresh2810
Picked101
Done000
Total21824242
Error
17.7b
Counts
242 → 24
Alt Table
StatusErrorProgram
32.2b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
63.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (cbrt.f64 (*.f64 (pow.f64 D 6) (*.f64 (pow.f64 w 3) (pow.f64 h 3))))) (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)))))
57.9b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
62.3b
(*.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)))))
30.7b
(*.f64 1/4 (/.f64 (*.f64 D (*.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
54.1b
(*.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
31.2b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 (*.f64 (cbrt.f64 D) (cbrt.f64 D)) 2) (*.f64 (pow.f64 (cbrt.f64 D) 2) (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
54.8b
(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (log.f64 (*.f64 (pow.f64 M 2) h))) (*.f64 (log.f64 d) 2))))
49.7b
(*.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
59.9b
(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))))
54.1b
(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 (*.f64 h 1/4)))))
27.9b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d)) d))
32.4b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 (*.f64 (pow.f64 M 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (cbrt.f64 h))) (pow.f64 d 2)))
63.9b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (log.f64 (*.f64 d d))) (+.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)))))
30.3b
(*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 M (*.f64 M h))) (pow.f64 d 2)))
28.6b
(*.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (*.f64 h (*.f64 M M)) d))))
61.1b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (cbrt.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))))) (cbrt.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)))))
57.5b
(*.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))))
61.9b
(*.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)))))
57.3b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
60.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 2 (/.f64 (*.f64 (pow.f64 d 2) c0) (*.f64 (pow.f64 D 2) (*.f64 w h)))))
60.1b
(*.f64 c0 (*.f64 (/.f64 1 (*.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))))))
29.7b
(*.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))))
43.2b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d)) (pow.f64 (sqrt.f64 d) 2)))
Compiler

Compiled 6654 to 4100 computations (38.4% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.3b
(/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d)) d)
6.7b
(*.f64 h (*.f64 M M))
7.0b
(/.f64 (*.f64 D D) d)
12.7b
(*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d))

series236.0ms (1%)

Counts
4 → 144
Calls

4 calls:

143.0ms
(/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d)) d)
72.0ms
(*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d))
12.0ms
(/.f64 (*.f64 D D) d)
8.0ms
(*.f64 h (*.f64 M M))

rewrite41.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
97×add-cbrt-cube_binary64
97×add-exp-log_binary64
46×cbrt-unprod_binary64
46×prod-exp_binary64
24×cbrt-undiv_binary64
Counts
4 → 124
Calls

4 calls:

9.0ms
(/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d)) d)
8.0ms
(*.f64 (*.f64 h (*.f64 M M)) (/.f64 (*.f64 D D) d))
6.0ms
(*.f64 h (*.f64 M M))
3.0ms
(/.f64 (*.f64 D D) d)

simplify166.0ms (0.7%)

Algorithm
egg-herbie
Rules
542×*-commutative_binary64
351×fma-def_binary64
241×fma-neg_binary64
224×unswap-sqr_binary64
219×associate-*l*_binary64
Counts
268 → 176
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01694803
13803954
217693954
331223917
446843896
549713896

prune400.0ms (1.8%)

Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New16313176
Fresh71623
Picked101
Done000
Total17129200
Error
14.6b
Counts
200 → 29
Alt Table
StatusErrorProgram
32.2b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
63.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (cbrt.f64 (*.f64 (pow.f64 D 6) (*.f64 (pow.f64 w 3) (pow.f64 h 3))))) (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)))))
57.9b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
62.3b
(*.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)))))
49.9b
(*.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (neg.f64 (log.f64 (/.f64 d h))))) d))
33.8b
(*.f64 1/4 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 M M) h) 3) (pow.f64 (/.f64 d D) 6))))
30.7b
(*.f64 1/4 (/.f64 (*.f64 D (*.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
54.1b
(*.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
49.7b
(*.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
59.9b
(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))))
54.1b
(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 (*.f64 h 1/4)))))
28.6b
(*.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (*.f64 h (*.f64 M M)) d))))
61.1b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (cbrt.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))))) (cbrt.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)))))
28.0b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 h) (*.f64 M M))) (/.f64 (*.f64 D D) d)) d))
57.5b
(*.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))))
42.7b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 h) M) (*.f64 (sqrt.f64 h) M)) (/.f64 (*.f64 D D) d)) d))
61.9b
(*.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)))))
25.8b
(*.f64 1/4 (*.f64 (*.f64 (*.f64 M M) h) (*.f64 (/.f64 D d) (/.f64 D d))))
25.7b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (/.f64 d D))) d))
53.7b
(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (+.f64 (log.f64 h) (log.f64 (*.f64 M M))) (-.f64 (log.f64 (*.f64 D D)) (log.f64 d)))) d))
43.2b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (sqrt.f64 d)) (/.f64 D (/.f64 (pow.f64 d 3/2) D))))
53.8b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (+.f64 (log.f64 h) (log.f64 (*.f64 M M))) (log.f64 (/.f64 (*.f64 D D) d))) (log.f64 d))))
60.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 2 (/.f64 (*.f64 (pow.f64 d 2) c0) (*.f64 (pow.f64 D 2) (*.f64 w h)))))
25.7b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 D d))))
60.1b
(*.f64 c0 (*.f64 (/.f64 1 (*.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))))))
41.0b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (sqrt.f64 d))) (/.f64 D (sqrt.f64 d))) d))
24.4b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d))
63.9b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (log.f64 (*.f64 d d))) (+.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)))))
25.6b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 h M) M) (/.f64 (*.f64 D D) d)) d))
Compiler

Compiled 5805 to 2105 computations (63.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.8b
(*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d)))
4.3b
(/.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d)
6.7b
(*.f64 h (*.f64 M M))
9.0b
(*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))))

series1.8s (7.8%)

Counts
3 → 144
Calls

3 calls:

1.5s
(*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))))
167.0ms
(/.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d)
100.0ms
(*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d)))

rewrite102.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
269×add-exp-log_binary64
219×add-cbrt-cube_binary64
145×cbrt-unprod_binary64
145×prod-exp_binary64
71×cbrt-undiv_binary64
Counts
3 → 184
Calls

3 calls:

28.0ms
(*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d)))
18.0ms
(/.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d)
9.0ms
(*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))))

simplify240.0ms (1.1%)

Algorithm
egg-herbie
Rules
579×associate-*l*_binary64
529×times-frac_binary64
375×associate-/l*_binary64
363×log-prod_binary64
344×associate-*r*_binary64
Counts
328 → 249
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
028710930
16426631
234926601
346756601
451396601

prune713.0ms (3.1%)

Pruning

34 alts after pruning (34 fresh and 0 done)

PrunedKeptTotal
New26814282
Fresh82028
Picked101
Done000
Total27734311
Error
14.5b
Counts
311 → 34
Alt Table
StatusErrorProgram
25.1b
(*.f64 1/4 (/.f64 (*.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))))) (/.f64 D (cbrt.f64 d))) d))
49.9b
(*.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (neg.f64 (log.f64 (/.f64 d h))))) d))
63.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (cbrt.f64 (*.f64 (pow.f64 D 6) (*.f64 (pow.f64 w 3) (pow.f64 h 3))))) (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)))))
24.1b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (*.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 (/.f64 D (cbrt.f64 d)) (cbrt.f64 d))))
62.3b
(*.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)))))
23.9b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) 1) (/.f64 (/.f64 D (cbrt.f64 d)) d)))
49.7b
(*.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
21.6b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 M h) M) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d))
24.4b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d)))) (cbrt.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))))) (cbrt.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))))) d))
59.9b
(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))))
54.1b
(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (*.f64 D M)) (log.f64 (*.f64 h 1/4)))))
58.8b
(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (+.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))))) (log.f64 (/.f64 D (cbrt.f64 d))))) d))
24.0b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 h (*.f64 (*.f64 M M) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d))))) (/.f64 D (cbrt.f64 d))) d))
25.6b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 h M) M) (/.f64 (*.f64 D D) d)) d))
26.7b
(*.f64 1/4 (/.f64 (pow.f64 (/.f64 (*.f64 D (*.f64 D (*.f64 (*.f64 M M) h))) d) 1) d))
42.9b
(*.f64 1/4 (/.f64 (/.f64 (/.f64 (*.f64 D (*.f64 D (*.f64 (*.f64 M M) h))) d) (sqrt.f64 d)) (sqrt.f64 d)))
61.1b
(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (cbrt.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))))) (cbrt.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)))))
57.5b
(*.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))))
42.7b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 h) M) (*.f64 (sqrt.f64 h) M)) (/.f64 (*.f64 D D) d)) d))
61.9b
(*.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)))))
25.8b
(*.f64 1/4 (*.f64 (*.f64 (*.f64 M M) h) (*.f64 (/.f64 D d) (/.f64 D d))))
51.1b
(*.f64 1/4 (/.f64 (*.f64 (exp.f64 (+.f64 (+.f64 (log.f64 h) (log.f64 (*.f64 M M))) (log.f64 (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))))) (/.f64 D (cbrt.f64 d))) d))
53.7b
(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (+.f64 (log.f64 h) (log.f64 (*.f64 M M))) (-.f64 (log.f64 (*.f64 D D)) (log.f64 d)))) d))
25.7b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (/.f64 d D))) d))
43.2b
(*.f64 1/4 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (sqrt.f64 d)) (/.f64 D (/.f64 (pow.f64 d 3/2) D))))
53.8b
(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (+.f64 (log.f64 h) (log.f64 (*.f64 M M))) (log.f64 (/.f64 (*.f64 D D) d))) (log.f64 d))))
60.3b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 2 (/.f64 (*.f64 (pow.f64 d 2) c0) (*.f64 (pow.f64 D 2) (*.f64 w h)))))
24.4b
(*.f64 1/4 (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d)) (cbrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d))) (cbrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d))))
33.6b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (exp.f64 (log.f64 (*.f64 h (*.f64 M M)))) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d))
54.1b
(*.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (*.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
60.1b
(*.f64 c0 (*.f64 (/.f64 1 (*.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 (*.f64 (*.f64 D (*.f64 (pow.f64 M 2) h)) (pow.f64 (/.f64 1 (pow.f64 d 2)) 1/3)) (/.f64 D (cbrt.f64 d))) d))
24.4b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 h (*.f64 M M)) (/.f64 D (*.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (*.f64 (cbrt.f64 D) (cbrt.f64 D)) (cbrt.f64 (*.f64 (cbrt.f64 d) (cbrt.f64 d))))) (/.f64 (cbrt.f64 D) (cbrt.f64 (cbrt.f64 d)))) d))
63.9b
(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (log.f64 (*.f64 d d))) (+.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)))))
Compiler

Compiled 10300 to 2327 computations (77.4% saved)

regimes2.1s (9.4%)

Accuracy

Total 8.7b remaining (34.1%)

Threshold costs 0b (0%)

Counts
143 → 1
Compiler

Compiled 49919 to 30555 computations (38.8% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01634
12134
22134

end1.0ms (0%)

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample8.7s (38.4%)

Algorithm
intervals
Results
1.7s2138×body4096valid
1.6s12168×body128nan
1.2s1152×body8192valid
774.0ms1274×body2048valid
527.0ms4067×body128invalid
434.0ms621×body1024valid
290.0ms2382×body128valid
124.0ms293×body512valid
36.0ms66×body2048invalid
31.0ms140×body256valid
21.0ms48×body1024invalid
11.0ms16×body4096invalid
9.0ms28×body512invalid
6.0ms22×body256invalid
2.0msbody8192exit
Compiler

Compiled 1313 to 720 computations (45.2% saved)

Profiling

Loading profile data...