Details

Time bar (total: 15.6s)

analyze3.4s (21.9%)

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
5.1%94.6%0.3%13
7%92.7%0.3%14
Compiler

Compiled 25 to 19 computations (24% saved)

sample120.0ms (0.8%)

Algorithm
intervals
Symmetry

(sort M D)

Results
39.0ms256×body128valid
8.0ms86×body128nan
4.0ms40×body128invalid
Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify31.0ms (0.2%)

Algorithm
egg-herbie
Rules
645×distribute-neg-frac_binary64
581×distribute-rgt-neg-in_binary64
418×associate-/l*_binary64
372×cancel-sign-sub-inv_binary64
263×associate-/l/_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01827
14227
211127
372327
4285527
5499427

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
15.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
15.1b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
Compiler

Compiled 72 to 54 computations (25% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
4.2b
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.4b
(/.f64 (*.f64 M D) (*.f64 2 d))
11.1b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series843.0ms (5.4%)

Counts
4 → 204
Calls

4 calls:

355.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
256.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
214.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
17.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))

rewrite33.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
67×add-exp-log_binary64
38×add-sqr-sqrt_binary64
27×prod-exp_binary64
23×add-cbrt-cube_binary64
19×associate-*r*_binary64
Counts
4 → 124
Calls

4 calls:

9.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
7.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
4.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
3.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

simplify179.0ms (1.2%)

Algorithm
egg-herbie
Rules
517×times-frac_binary64
399×associate-*l*_binary64
365×associate-/l*_binary64
342×associate-/r*_binary64
258×associate-*r/_binary64
Counts
328 → 314
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
051611209
1126210441
2498810441

prune420.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New30311314
Fresh000
Picked101
Done000
Total30411315
Error
3.1b
Counts
315 → 11
Alt Table
StatusErrorProgram
58.2b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (*.f64 M w0)))
11.6b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l)))))
59.1b
(*.f64 -1 (*.f64 (sqrt.f64 (neg.f64 (*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) h) (*.f64 (pow.f64 d 2) l))))) (*.f64 w0 M)))
13.2b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l))))))
57.2b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
61.1b
(/.f64 (*.f64 (sqrt.f64 (neg.f64 (*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 h (pow.f64 M 2))) l)))) w0) d)
23.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 1/4 (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (*.f64 (*.f64 M M) h) l))))))
15.1b
(*.f64 (*.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
15.9b
(*.f64 w0 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l)))) 3)))
59.9b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
14.0b
w0
Compiler

Compiled 12210 to 7367 computations (39.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.2b
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l))))
5.1b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)
5.4b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.7b
(*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l))

series596.0ms (3.8%)

Counts
3 → 156
Calls

3 calls:

233.0ms
(*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l))
187.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)
175.0ms
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l))))

rewrite33.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
152×add-exp-log_binary64
87×prod-exp_binary64
36×div-exp_binary64
25×pow-exp_binary64
21×add-sqr-sqrt_binary64
Counts
3 → 115
Calls

3 calls:

8.0ms
(*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l))
8.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)
4.0ms
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l))))

simplify210.0ms (1.3%)

Algorithm
egg-herbie
Rules
575×fma-def_binary64
322×unswap-sqr_binary64
296×cancel-sign-sub-inv_binary64
255×associate-*l*_binary64
241×associate-*r*_binary64
Counts
271 → 222
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03547915
17957298
230267215
348777215
449907215

prune400.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2583261
Fresh3710
Picked101
Done000
Total26210272
Error
2.4b
Counts
272 → 10
Alt Table
StatusErrorProgram
10.3b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 M D) (*.f64 2 d))) (cbrt.f64 (/.f64 (*.f64 M D) (*.f64 2 d)))) 2) (*.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 M D) (*.f64 2 d))) 2) h)) (/.f64 1 l)))))
57.2b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
61.1b
(/.f64 (*.f64 (sqrt.f64 (neg.f64 (*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 h (pow.f64 M 2))) l)))) w0) d)
11.4b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) h) (/.f64 1 l)))))
15.1b
(*.f64 (*.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
9.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l)))))
59.9b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
58.2b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (*.f64 M w0)))
59.1b
(*.f64 -1 (*.f64 (sqrt.f64 (neg.f64 (*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) h) (*.f64 (pow.f64 d 2) l))))) (*.f64 w0 M)))
14.0b
w0
Compiler

Compiled 9192 to 5946 computations (35.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.2b
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l))))
5.1b
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)
5.4b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.7b
(*.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l))

series484.0ms (3.1%)

Counts
3 → 156
Calls

3 calls:

274.0ms
(*.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l))
182.0ms
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l))))
28.0ms
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

rewrite137.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
872×add-exp-log_binary64
529×prod-exp_binary64
462×add-cbrt-cube_binary64
269×cbrt-unprod_binary64
242×div-exp_binary64
Counts
3 → 269
Calls

3 calls:

19.0ms
(*.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l))
8.0ms
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l))))
6.0ms
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

simplify320.0ms (2.1%)

Algorithm
egg-herbie
Rules
716×associate-*l/_binary64
514×times-frac_binary64
383×associate-/r*_binary64
311×associate-/l*_binary64
279×sqr-pow_binary64
Counts
425 → 378
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
056412888
1140211707
2426911456
3382310988
4518910988

prune549.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New4542456
Fresh189
Picked101
Done000
Total45610466
Error
2.2b
Counts
466 → 10
Alt Table
StatusErrorProgram
58.2b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (*.f64 M w0)))
8.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d))) l)))))
57.2b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
61.1b
(/.f64 (*.f64 (sqrt.f64 (neg.f64 (*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 h (pow.f64 M 2))) l)))) w0) d)
11.4b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) h) (/.f64 1 l)))))
15.1b
(*.f64 (*.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
12.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (*.f64 (*.f64 M D) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) 1) (*.f64 (*.f64 2 d) l)))))
59.9b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
59.1b
(*.f64 -1 (*.f64 (sqrt.f64 (neg.f64 (*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) h) (*.f64 (pow.f64 d 2) l))))) (*.f64 w0 M)))
14.0b
w0
Compiler

Compiled 19090 to 10425 computations (45.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
5.1b
(*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d)))
5.4b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.4b
(/.f64 (*.f64 D M) (*.f64 2 d))
5.5b
(/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d))) l)

series101.0ms (0.6%)

Counts
3 → 144
Calls

3 calls:

55.0ms
(/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d))) l)
27.0ms
(*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d)))
15.0ms
(/.f64 (*.f64 D M) (*.f64 2 d))

rewrite24.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
58×add-cbrt-cube_binary64
58×add-exp-log_binary64
22×cbrt-unprod_binary64
22×prod-exp_binary64
18×cbrt-undiv_binary64
Counts
3 → 86
Calls

3 calls:

6.0ms
(/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d))) l)
6.0ms
(*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d)))
4.0ms
(/.f64 (*.f64 D M) (*.f64 2 d))

simplify132.0ms (0.8%)

Algorithm
egg-herbie
Rules
543×*-commutative_binary64
287×times-frac_binary64
270×associate--l+_binary64
260×fma-def_binary64
241×associate-/l*_binary64
Counts
230 → 137
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01573753
13993255
219793253
329343252
447093252
550413252

prune289.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1751176
Fresh099
Picked101
Done000
Total17610186
Error
2.2b
Counts
186 → 10
Alt Table
StatusErrorProgram
8.8b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d))) l)) (cbrt.f64 (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d))) l))) (cbrt.f64 (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 2 d))) l)))))))
15.1b
(*.f64 (*.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
57.2b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
61.1b
(/.f64 (*.f64 (sqrt.f64 (neg.f64 (*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) (*.f64 h (pow.f64 M 2))) l)))) w0) d)
11.4b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) h) (/.f64 1 l)))))
12.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (*.f64 (*.f64 M D) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) 1) (*.f64 (*.f64 2 d) l)))))
59.9b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
58.2b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (*.f64 M w0)))
59.1b
(*.f64 -1 (*.f64 (sqrt.f64 (neg.f64 (*.f64 1/4 (/.f64 (*.f64 (pow.f64 D 2) h) (*.f64 (pow.f64 d 2) l))))) (*.f64 w0 M)))
14.0b
w0
Compiler

Compiled 5637 to 3049 computations (45.9% saved)

regimes4.7s (30.3%)

Accuracy

Total 4.1b remaining (49.9%)

Threshold costs 0b (0%)

Counts
208 → 2
Compiler

Compiled 104466 to 75595 computations (27.6% saved)

bsearch16.0ms (0.1%)

Compiler

Compiled 24 to 18 computations (25% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03994
16494
29394
312594
414694
515794
616094
715994

end7.0ms (0%)

Compiler

Compiled 204 to 132 computations (35.3% saved)

sample2.4s (15.6%)

Algorithm
intervals
Results
893.0ms8000×body128valid
389.0ms3133×body128nan
143.0ms1285×body128invalid
Compiler

Compiled 386 to 273 computations (29.3% saved)

Profiling

Loading profile data...