Details

Time bar (total: 14.8s)

analyze2.9s (19.4%)

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)

sample2.7s (18.1%)

Symmetry

(sort M D)

Results
1.7s8256×body128valid
896.0ms4646×body128invalid
Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify28.0ms (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
11.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
11.8b
(*.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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
2.4b
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
7.0b
(/.f64 (*.f64 M D) (*.f64 2 d))
11.8b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series621.0ms (4.2%)

Counts
4 → 204
Calls

4 calls:

237.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
194.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
176.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
14.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))

rewrite90.0ms (0.6%)

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
Counts
4 → 123
Calls

4 calls:

87.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
87.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
87.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
87.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01880
138480
2493280
3608680
000
100

simplify221.0ms (1.5%)

Algorithm
egg-herbie
Rules
668×fma-def_binary64
276×unswap-sqr_binary64
262×times-frac_binary64
248×associate-*r*_binary64
246×associate-/r*_binary64
Counts
327 → 242
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03108076
18108010
234707948
349427780
449847780
549597780

prune255.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2339242
Fresh000
Picked101
Done000
Total2349243
Error
5.3b
Counts
243 → 9
Alt Table
StatusErrorProgram
11.8b
(*.f64 w0 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
61.6b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4))))
12.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (*.f64 (*.f64 M 1/2) (/.f64 D d)) 2) (/.f64 h l)))))
61.7b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
61.6b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
11.9b
w0
9.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))))))
11.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
61.7b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
Compiler

Compiled 9303 to 5633 computations (39.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.4b
(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)))))
5.7b
(/.f64 l (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))
6.8b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)
7.0b
(/.f64 (*.f64 M D) (*.f64 2 d))

series517.0ms (3.5%)

Counts
3 → 156
Calls

3 calls:

266.0ms
(/.f64 l (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))
131.0ms
(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)))))
120.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)

rewrite83.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
544×prod-diff_binary64
182×add-sqr-sqrt_binary64
172×log1p-expm1-u_binary64
172×expm1-log1p-u_binary64
170×add-log-exp_binary64
Counts
3 → 82
Calls

3 calls:

81.0ms
(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)))))
81.0ms
(/.f64 l (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))
81.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01762
137059
2483059
3589059
000
100

simplify113.0ms (0.8%)

Algorithm
egg-herbie
Rules
624×associate-*l/_binary64
317×associate-/r/_binary64
264×fma-def_binary64
232×unswap-sqr_binary64
216×distribute-neg-frac_binary64
Counts
238 → 144
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01865336
15065302
220845284
354765284

prune319.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1993202
Fresh178
Picked101
Done000
Total20110211
Error
4.3b
Counts
211 → 10
Alt Table
StatusErrorProgram
11.8b
(*.f64 w0 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
61.6b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4))))
12.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (*.f64 (*.f64 M 1/2) (/.f64 D d)) 2) (/.f64 h l)))))
9.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)) 2)) (/.f64 l (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))))))))
61.6b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
11.9b
w0
35.3b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (*.f64 (/.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (sqrt.f64 h))) (/.f64 l (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (sqrt.f64 h))))))))
35.8b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (pow.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (sqrt.f64 h)) 2))))))
11.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
61.7b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
Compiler

Compiled 7193 to 4630 computations (35.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.4b
(sqrt.f64 (-.f64 1 (/.f64 1 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)) 2)) (/.f64 l (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)))))))
6.8b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)
7.0b
(/.f64 (*.f64 M D) (*.f64 2 d))
26.9b
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))

series2.4s (16.1%)

Counts
2 → 96
Calls

2 calls:

2.2s
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))
161.0ms
(sqrt.f64 (-.f64 1 (/.f64 1 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)) 2)) (/.f64 l (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)))))))

rewrite68.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
220×add-sqr-sqrt_binary64
209×log1p-expm1-u_binary64
209×expm1-log1p-u_binary64
205×add-cbrt-cube_binary64
205×add-log-exp_binary64
Counts
2 → 48
Calls

2 calls:

66.0ms
(sqrt.f64 (-.f64 1 (/.f64 1 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)) 2)) (/.f64 l (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)))))))
66.0ms
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02145
145845
2488445
3499945
000
100

simplify126.0ms (0.9%)

Algorithm
egg-herbie
Rules
697×fma-def_binary64
254×unswap-sqr_binary64
246×cancel-sign-sub-inv_binary64
221×fma-neg_binary64
205×distribute-neg-frac_binary64
Counts
144 → 122
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02724416
17104306
224304224
347814220
451674220

prune507.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3170317
Fresh099
Picked011
Done000
Total31710327
Error
4.3b
Counts
327 → 10
Alt Table
StatusErrorProgram
11.8b
(*.f64 w0 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
61.6b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4))))
12.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (*.f64 (*.f64 M 1/2) (/.f64 D d)) 2) (/.f64 h l)))))
9.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)) 2)) (/.f64 l (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))))))))
61.6b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
11.9b
w0
35.3b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (*.f64 (/.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (sqrt.f64 h))) (/.f64 l (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (sqrt.f64 h))))))))
35.8b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (pow.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (sqrt.f64 h)) 2))))))
11.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
61.7b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
Compiler

Compiled 14413 to 9788 computations (32.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.7b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
2.4b
(sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))))
7.0b
(/.f64 (*.f64 M D) (*.f64 2 d))
11.9b
(/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))

series566.0ms (3.8%)

Counts
3 → 168
Calls

3 calls:

246.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
195.0ms
(/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))
124.0ms
(sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))))

rewrite83.0ms (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
Counts
3 → 79
Calls

3 calls:

80.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h)))))
80.0ms
(sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))))
80.0ms
(/.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 l h))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01870
138770
2488570
3575070
000
100

simplify160.0ms (1.1%)

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
Counts
247 → 197
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03077716
18017650
234497588
354387588

prune353.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2523255
Fresh358
Picked101
Done011
Total2569265
Error
3.9b
Counts
265 → 9
Alt Table
StatusErrorProgram
6.5b
(*.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))))))
61.6b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 l (*.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
10.1b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (pow.f64 (cbrt.f64 (/.f64 l h)) 2)) (/.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (cbrt.f64 (/.f64 l h)))))))
61.7b
(*.f64 D (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4)) w0))
12.2b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (*.f64 (/.f64 D d) (*.f64 M 1/2)) 2) (/.f64 l h)))))
11.9b
w0
61.6b
(*.f64 w0 (*.f64 D (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 l (*.f64 d d))) -1/4))))
9.5b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h)) 2)) (/.f64 l (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) h))))))))
35.8b
(*.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (pow.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (sqrt.f64 h)) 2))))))
Compiler

Compiled 9621 to 5735 computations (40.4% saved)

regimes2.5s (17%)

Accuracy

Total 2.1b remaining (25.3%)

Threshold costs 0b (0%)

Counts
148 → 1
Compiler

Compiled 65711 to 49512 computations (24.7% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01939
13039
24139
35239
46639
57439
67939
78139
88039

end155.0ms (1.1%)

Remove

(sort M D)

Compiler

Compiled 373 to 261 computations (30% saved)

Profiling

Loading profile data...