Details

Time bar (total: 13.0s)

analyze3.0s (23.2%)

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
4.3%95.4%0.3%13
6.6%93.1%0.3%14
Compiler

Compiled 25 to 19 computations (24% saved)

sample2.5s (19.5%)

Symmetry

(sort M D)

Results
1.6s8256×body128valid
869.0ms4625×body128invalid
Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify27.0ms (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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
13.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
13.8b
(*.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)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.2b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
2.8b
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.6b
(/.f64 (*.f64 M D) (*.f64 2 d))
11.9b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series788.0ms (6.1%)

Counts
4 → 204
Calls

4 calls:

360.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
239.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
173.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
15.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))

rewrite36.0ms (0.3%)

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:

10.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
6.0ms
(*.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))))

simplify164.0ms (1.3%)

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

prune378.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New30311314
Fresh000
Picked101
Done000
Total30411315
Error
3.6b
Counts
315 → 11
Alt Table
StatusErrorProgram
61.8b
(*.f64 w0 (*.f64 M (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
13.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
9.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
61.2b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4))))
8.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) l))))
13.8b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
58.9b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (*.f64 M w0)))
61.3b
(*.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)))
26.0b
(-.f64 w0 (*.f64 1/8 (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (*.f64 (*.f64 (*.f64 M M) h) w0) l))))
12.3b
w0
61.4b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 M M) h)) l) -1/4)) d))
Compiler

Compiled 12232 to 7361 computations (39.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.8b
(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) l)))
4.6b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.0b
(/.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) l)
6.1b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)

series692.0ms (5.3%)

Counts
3 → 156
Calls

3 calls:

291.0ms
(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) l)))
248.0ms
(/.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) l)
153.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)

rewrite25.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
54×add-exp-log_binary64
22×prod-exp_binary64
19×add-sqr-sqrt_binary64
16×div-exp_binary64
12×*-un-lft-identity_binary64
Counts
3 → 84
Calls

3 calls:

7.0ms
(/.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) l)
7.0ms
(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h) l)))
6.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)

simplify154.0ms (1.2%)

Algorithm
egg-herbie
Rules
315×fma-def_binary64
298×unswap-sqr_binary64
288×distribute-neg-frac_binary64
241×cancel-sign-sub-inv_binary64
191×times-frac_binary64
Counts
240 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03347367
17646748
229856661
349956661

prune405.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2263229
Fresh2810
Picked101
Done000
Total22911240
Error
2.9b
Counts
240 → 11
Alt Table
StatusErrorProgram
61.8b
(*.f64 w0 (*.f64 M (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
7.8b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l))))
9.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
61.2b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4))))
8.2b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
8.7b
(*.f64 w0 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2)) l)))) (sqrt.f64 (cbrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2)) l))))))
58.9b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (*.f64 M w0)))
61.3b
(*.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)))
26.0b
(-.f64 w0 (*.f64 1/8 (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (*.f64 (*.f64 (*.f64 M M) h) w0) l))))
12.3b
w0
61.4b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 M M) h)) l) -1/4)) d))
Compiler

Compiled 8027 to 5081 computations (36.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.8b
(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l)))
4.6b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.0b
(/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l)
6.2b
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

series450.0ms (3.5%)

Counts
3 → 156
Calls

3 calls:

247.0ms
(/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l)
175.0ms
(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l)))
28.0ms
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

rewrite70.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
226×add-cbrt-cube_binary64
226×add-exp-log_binary64
108×cbrt-unprod_binary64
108×prod-exp_binary64
79×cbrt-undiv_binary64
Counts
3 → 135
Calls

3 calls:

15.0ms
(/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) 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)) l)))
6.0ms
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

simplify188.0ms (1.4%)

Algorithm
egg-herbie
Rules
584×associate-/l*_binary64
484×associate-*l*_binary64
455×associate-/r*_binary64
414×associate-*l/_binary64
390×associate-*r/_binary64
Counts
291 → 254
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04589762
112058761
247038697
349968697

prune444.0ms (3.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New3275332
Fresh4610
Picked101
Done000
Total33211343
Error
2.5b
Counts
343 → 11
Alt Table
StatusErrorProgram
60.8b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 M (*.f64 M h)) (*.f64 l (*.f64 d d))) -1/4))))
58.9b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (*.f64 M w0)))
10.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 1/2 (/.f64 (*.f64 D (*.f64 M h)) d))) l))))
12.3b
w0
61.8b
(*.f64 w0 (*.f64 M (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
8.2b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
7.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) l)))))
60.8b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 M (*.f64 M h))) l) -1/4)) d))
61.5b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 h (*.f64 D D)) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
26.0b
(-.f64 w0 (*.f64 1/8 (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (*.f64 (*.f64 (*.f64 M M) h) w0) l))))
9.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
Compiler

Compiled 13310 to 7230 computations (45.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.8b
(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) l))))
4.6b
(/.f64 (*.f64 D M) (*.f64 d 2))
6.2b
(*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2)))
6.2b
(/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) l)

series273.0ms (2.1%)

Counts
4 → 192
Calls

4 calls:

176.0ms
(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) l))))
53.0ms
(/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) l)
29.0ms
(*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2)))
15.0ms
(/.f64 (*.f64 D M) (*.f64 d 2))

rewrite32.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
59×add-cbrt-cube_binary64
59×add-exp-log_binary64
22×cbrt-unprod_binary64
22×prod-exp_binary64
18×cbrt-undiv_binary64
Counts
4 → 103
Calls

4 calls:

8.0ms
(*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2)))
7.0ms
(/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) l)
4.0ms
(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) l))))
4.0ms
(/.f64 (*.f64 D M) (*.f64 d 2))

simplify218.0ms (1.7%)

Algorithm
egg-herbie
Rules
488×times-frac_binary64
397×fma-def_binary64
360×associate-/l*_binary64
285×associate-*r*_binary64
272×associate-/r*_binary64
Counts
295 → 194
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03547220
19246696
244046678
349936678
449976678

prune318.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2232225
Fresh2810
Picked011
Done000
Total22511236
Error
2.5b
Counts
236 → 11
Alt Table
StatusErrorProgram
8.2b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
7.6b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (/.f64 (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l))))))
7.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (/.f64 (*.f64 h (/.f64 (*.f64 D M) (*.f64 d 2))) l)))))
60.3b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D M) (*.f64 D (*.f64 h M))) l) -1/4)) d))
60.8b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 M (*.f64 M h)) (*.f64 l (*.f64 d d))) -1/4))))
58.9b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (*.f64 M w0)))
10.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 1/2 (/.f64 (*.f64 D (*.f64 M h)) d))) l))))
12.3b
w0
61.8b
(*.f64 w0 (*.f64 M (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
61.5b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 h (*.f64 D D)) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
26.0b
(-.f64 w0 (*.f64 1/8 (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (*.f64 (*.f64 (*.f64 M M) h) w0) l))))
Compiler

Compiled 8686 to 4874 computations (43.9% saved)

regimes2.4s (18.4%)

Accuracy

Total 4.7b remaining (55%)

Threshold costs 0b (0%)

Counts
123 → 2
Compiler

Compiled 59848 to 43006 computations (28.1% saved)

bsearch5.0ms (0%)

Compiler

Compiled 15 to 12 computations (20% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Rules
23×*-commutative_binary64
14×+-commutative_binary64
14×sub-neg_binary64
13×neg-sub0_binary64
13×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03692
16192
28492
310692
413192
514292
614892
715092
814992

end323.0ms (2.5%)

Compiler

Compiled 535 to 355 computations (33.6% saved)

Profiling

Loading profile data...