Details

Time bar (total: 11.2s)

analyze2.8s (25%)

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)

sample2.3s (20.6%)

Symmetry

(sort M D)

Results
1.5s8256×body128valid
773.0ms4491×body128invalid
Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify24.0ms (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
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01827
14227
211127
372327
4285527
5499427
Stop Event
node limit
Counts
1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
15.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
15.0b
(*.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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.9b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
5.3b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.9b
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
11.0b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series507.0ms (4.5%)

Counts
4 → 204
Calls

4 calls:

202.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
185.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
107.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
12.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))

rewrite87.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
593×prod-diff_binary64
190×add-sqr-sqrt_binary64
179×log1p-expm1-u_binary64
179×expm1-log1p-u_binary64
177×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01880
138480
2493280
3608680
Stop Event
node limit
Counts
4 → 119
Calls

4 calls:

85.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
85.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
85.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
85.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify206.0ms (1.8%)

Algorithm
egg-herbie
Rules
668×fma-def_binary64
276×unswap-sqr_binary64
262×times-frac_binary64
248×associate-*r*_binary64
246×associate-/r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03108076
18108010
234707948
349427780
449847780
549597780
Stop Event
node limit
Counts
323 → 238

prune284.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New22513238
Fresh000
Picked101
Done000
Total22613239
Error
7.5b
Counts
239 → 13
Alt Table
StatusErrorProgram
15.1b
(*.f64 w0 (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
61.1b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4))))
15.1b
(*.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))) 3))))
60.0b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
15.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
61.3b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
16.1b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) w0)) 3)
59.8b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
34.2b
(fma.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 (*.f64 M M) h) w0)) (*.f64 l (*.f64 d d))) -1/8 w0)
15.3b
(*.f64 w0 (exp.f64 (*.f64 (log1p.f64 (neg.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) 1/2)))
14.3b
w0
31.3b
(*.f64 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 M M) h)) (*.f64 l (*.f64 d d))) -1/4 1)) w0)
61.7b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 M M) h)) l) -1/4)) d))
Compiler

Compiled 9439 to 5735 computations (39.2% saved)

localize1.0ms (0%)

prune17.0ms (0.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New000
Fresh01212
Picked011
Done000
Total01313
Error
7.5b
Counts
13 → 13
Alt Table
StatusErrorProgram
15.1b
(*.f64 w0 (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
61.1b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4))))
15.1b
(*.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))) 3))))
60.0b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
15.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
61.3b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
16.1b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) w0)) 3)
59.8b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
34.2b
(fma.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 (*.f64 M M) h) w0)) (*.f64 l (*.f64 d d))) -1/8 w0)
15.3b
(*.f64 w0 (exp.f64 (*.f64 (log1p.f64 (neg.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) 1/2)))
14.3b
w0
31.3b
(*.f64 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 M M) h)) (*.f64 l (*.f64 d d))) -1/4 1)) w0)
61.7b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 M M) h)) l) -1/4)) d))
Compiler

Compiled 649 to 456 computations (29.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.9b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
5.3b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.9b
(sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))))
11.2b
(/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))

series494.0ms (4.4%)

Counts
3 → 168
Calls

3 calls:

223.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
167.0ms
(/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))
104.0ms
(sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))))

rewrite71.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
413×prod-diff_binary64
192×add-sqr-sqrt_binary64
181×log1p-expm1-u_binary64
181×expm1-log1p-u_binary64
179×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01870
138770
2488570
3575070
Stop Event
node limit
Counts
3 → 76
Calls

3 calls:

69.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
69.0ms
(sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))))
69.0ms
(/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))

simplify168.0ms (1.5%)

Algorithm
egg-herbie
Rules
646×fma-def_binary64
503×cancel-sign-sub-inv_binary64
276×unswap-sqr_binary64
262×times-frac_binary64
246×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03077716
18017650
234497588
354387588
Stop Event
node limit
Counts
244 → 194

prune434.0ms (3.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2483251
Fresh3811
Picked101
Done011
Total25212264
Error
6.3b
Counts
264 → 12
Alt Table
StatusErrorProgram
15.3b
(*.f64 w0 (exp.f64 (*.f64 (log1p.f64 (neg.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) 1/2)))
13.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 1) (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 l h))))))
9.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l) (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 1 h))))))
14.3b
w0
15.1b
(*.f64 w0 (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
60.0b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
16.8b
(*.f64 w0 (sqrt.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)) 3)))))
61.3b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
16.1b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) w0)) 3)
59.8b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
34.2b
(fma.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 (*.f64 M M) h) w0)) (*.f64 l (*.f64 d d))) -1/8 w0)
61.7b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 M M) h)) l) -1/4)) d))
Compiler

Compiled 9931 to 5962 computations (40% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.8b
(/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 1 h))
3.3b
(/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l)
5.3b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.9b
(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l) (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 1 h)))))

series172.0ms (1.5%)

Counts
3 → 144
Calls

3 calls:

107.0ms
(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l) (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 1 h)))))
40.0ms
(/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l)
24.0ms
(/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 1 h))

rewrite74.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
211×prod-diff_binary64
192×add-sqr-sqrt_binary64
181×log1p-expm1-u_binary64
181×expm1-log1p-u_binary64
179×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01765
138450
2481050
3522550
Stop Event
node limit
Counts
3 → 101
Calls

3 calls:

72.0ms
(/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 1 h))
72.0ms
(/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l)
72.0ms
(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l) (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 1 h)))))

simplify84.0ms (0.8%)

Algorithm
egg-herbie
Rules
607×associate-*l/_binary64
264×associate-/r/_binary64
254×fma-def_binary64
245×unswap-sqr_binary64
203×distribute-neg-frac_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01904032
15163994
220863976
353923976
Stop Event
node limit
Counts
245 → 160

prune409.0ms (3.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2713274
Fresh2810
Picked101
Done011
Total27412286
Error
6.3b
Counts
286 → 12
Alt Table
StatusErrorProgram
9.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l) (/.f64 (*.f64 (/.f64 1/2 d) (*.f64 M D)) (/.f64 1 h))))))
60.0b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
15.1b
(*.f64 w0 (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
10.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) l) (/.f64 (*.f64 (/.f64 D d) (*.f64 M 1/2)) (/.f64 1 h))))))
10.9b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 M D)) 2) l) (/.f64 (cbrt.f64 (*.f64 M D)) (*.f64 2 d))) (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 1 h))))))
61.3b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
16.1b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) w0)) 3)
59.8b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
34.2b
(fma.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 (*.f64 M M) h) w0)) (*.f64 l (*.f64 d d))) -1/8 w0)
15.3b
(*.f64 w0 (exp.f64 (*.f64 (log1p.f64 (neg.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) 1/2)))
14.3b
w0
61.7b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) (*.f64 (*.f64 M M) h)) l) -1/4)) d))
Compiler

Compiled 9889 to 5981 computations (39.5% saved)

regimes2.7s (24.4%)

Accuracy

Total 2.3b remaining (27.4%)

Threshold costs 0b (0%)

Counts
151 → 1
Compiler

Compiled 68191 to 50533 computations (25.9% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02242
13442
24242
35042
45842
56942
67642
78142
88342
98242
Stop Event
saturated

end277.0ms (2.5%)

Remove

(sort M D)

Compiler

Compiled 466 to 325 computations (30.3% saved)

Profiling

Loading profile data...