Details

Time bar (total: 9.5s)

analyze3.5s (37.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
12.5%87.3%0.2%9
12.5%87.3%0.2%10
18.7%81.1%0.2%11
18.7%81.1%0.2%12
18.7%81.1%0.2%13
20.5%79.3%0.2%14
Compiler

Compiled 35 to 24 computations (31.4% saved)

sample67.0ms (0.7%)

Algorithm
1×intervals
Results
32.0ms251×body128valid
2.0ms4×body1024invalid
2.0ms3×body1024valid
2.0ms4×body512invalid
1.0ms6×body128invalid
1.0ms2×body256invalid
0.0ms1×body512valid
0.0ms1×body256valid
Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify53.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
605×exp-prod_binary64
532×exp-sum_binary64
375×associate-*l*_binary64
303×associate-*r*_binary64
251×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02245
15845
212543
336143
4114143
5404443
6512143

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
16.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶16.4b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 99 to 66 computations (33.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.2b
(/.f64 (*.f64 K (+.f64 m n)) 2)
33.9b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite149.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Error
16.0b
Rules
17×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
10×add-exp-log_binary64
10×add-cube-cbrt_binary64
9×add-cbrt-cube_binary64
Counts
4 → 72
Calls

4 calls:

22.0ms
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
9.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
6.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
Compiler

Compiled 2576 to 1283 computations (50.2% saved)

series241.0ms (2.6%)

Error
1.0b
Counts
4 → 78
Calls

4 calls:

76.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
52.0ms
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
46.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
33.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
Compiler

Compiled 5569 to 3730 computations (33% saved)

simplify125.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
453×distribute-rgt-in_binary64
411×distribute-lft-in_binary64
303×exp-sum_binary64
241×sub-neg_binary64
222×cancel-sign-sub-inv_binary64
Counts
150 → 133
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03144941
17524778
221424721
353694721

prune80.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1294133
Fresh000
Picked101
Done000
Total1304134
Error
0.9b
Counts
134 → 4
Alt Table
StatusErrorProgram
16.4b
(*.f64 (cos.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 (+.f64 m n) K) 2)) (cbrt.f64 (/.f64 (*.f64 (+.f64 m n) K) 2))) (cbrt.f64 (/.f64 (*.f64 (+.f64 m n) K) 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.4b
(*.f64 (log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.4b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (+.f64 m n)) (sqrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶1.1b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 2376 to 1212 computations (49% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite116.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Error
0.9b
Rules
17×*-un-lft-identity_binary64
17×add-sqr-sqrt_binary64
10×add-log-exp_binary64
6×unpow-prod-down_binary64
6×add-cube-cbrt_binary64
Counts
3 → 59
Calls

3 calls:

20.0ms
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
12.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
Compiler

Compiled 1989 to 1016 computations (48.9% saved)

series387.0ms (4.1%)

Error
0.9b
Counts
3 → 93
Calls

3 calls:

141.0ms
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
123.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
61.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
Compiler

Compiled 5854 to 3891 computations (33.5% saved)

simplify144.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
746×exp-sum_binary64
548×sub-neg_binary64
360×exp-diff_binary64
295×times-frac_binary64
236×associate--r+_binary64
Counts
152 → 136
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03775682
110495430
230365430
351765430

prune79.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1360136
Fresh033
Picked011
Done000
Total1364140
Error
0.9b
Counts
140 → 4
Alt Table
StatusErrorProgram
16.4b
(*.f64 (cos.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 (+.f64 m n) K) 2)) (cbrt.f64 (/.f64 (*.f64 (+.f64 m n) K) 2))) (cbrt.f64 (/.f64 (*.f64 (+.f64 m n) K) 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶16.4b
(*.f64 (log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.4b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (+.f64 m n)) (sqrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓1.1b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 2054 to 1024 computations (50.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M)))
0.2b
(/.f64 (*.f64 (+.f64 m n) K) 2)
0.6b
(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M))))
33.9b
(cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M))

rewrite155.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Error
0.9b
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
12×cos-sum_binary64
9×add-cbrt-cube_binary64
Counts
4 → 71
Calls

4 calls:

12.0ms
(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M)))
10.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M))
8.0ms
(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M))))
6.0ms
(/.f64 (*.f64 (+.f64 m n) K) 2)
Compiler

Compiled 2850 to 1462 computations (48.7% saved)

series243.0ms (2.6%)

Error
0.9b
Counts
4 → 54
Calls

4 calls:

101.0ms
(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M))))
46.0ms
(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M)))
41.0ms
(/.f64 (*.f64 (+.f64 m n) K) 2)
39.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) K) 2) M))
Compiler

Compiled 4342 to 3029 computations (30.2% saved)

simplify190.0ms (2%)

Algorithm
1×egg-herbie
Rules
585×associate-/r/_binary64
348×associate-*l*_binary64
318×cancel-sign-sub-inv_binary64
304×associate-*r*_binary64
275×distribute-rgt-neg-in_binary64
Counts
125 → 114
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02243963
14153777
29963777
330223775
449253775
550003775
649603775

prune99.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1104114
Fresh202
Picked101
Done011
Total1135118
Error
0.9b
Counts
118 → 5
Alt Table
StatusErrorProgram
16.1b
(*.f64 (log.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 (/.f64 (+.f64 n m) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 K (cbrt.f64 2))) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.2b
(*.f64 (log.f64 (*.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶16.1b
(*.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓1.1b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.4b
(*.f64 (log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (/.f64 (+.f64 n m) (sqrt.f64 2))) (sqrt.f64 2)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 2427 to 1397 computations (42.4% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b
(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))
0.9b
(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))
33.9b
(cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))
33.9b
(cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))

rewrite240.0ms (2.5%)

Algorithm
1×rewrite-expression-head
Error
0.9b
Rules
32×cos-sum_binary64
16×log-div_binary64
16×sqrt-div_binary64
16×exp-diff_binary64
16×distribute-lft-in_binary64
Counts
4 → 90
Calls

4 calls:

12.0ms
(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))
10.0ms
(cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))
9.0ms
(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))
8.0ms
(cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))
Compiler

Compiled 5180 to 3081 computations (40.5% saved)

series425.0ms (4.5%)

Error
0.9b
Counts
4 → 54
Calls

4 calls:

133.0ms
(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))
126.0ms
(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))
52.0ms
(cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))
47.0ms
(cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))
Compiler

Compiled 6579 to 4585 computations (30.3% saved)

simplify235.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
471×cancel-sign-sub-inv_binary64
339×distribute-rgt-in_binary64
308×distribute-lft-in_binary64
270×distribute-rgt-neg-in_binary64
241×distribute-lft-neg-in_binary64
Counts
144 → 114
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02667194
13536878
26776238
317696226
442416226
550036226

prune93.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1131114
Fresh123
Picked101
Done011
Total1154119
Error
0.9b
Counts
119 → 4
Alt Table
StatusErrorProgram
16.1b
(*.f64 (log.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 (/.f64 (+.f64 n m) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 K (cbrt.f64 2))) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.1b
(*.f64 (+.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M))))) 3)) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 1/2 (+.f64 n m))) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓1.1b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.4b
(*.f64 (log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (/.f64 (+.f64 n m) (sqrt.f64 2))) (sqrt.f64 2)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 2380 to 1416 computations (40.5% saved)

regimes845.0ms (8.9%)

Accuracy

Total 0.2b remaining (13.5%)

Threshold costs 0.2b (13.5%)

Compiler

Compiled 20462 to 14418 computations (29.5% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01731
12831
24531
36031
46931
57231
67231

end7.0ms (0.1%)

Remove

(sort m n)

Compiler

Compiled 75 to 54 computations (28% saved)

sample1.9s (19.6%)

Algorithm
1×intervals
Results
1.1s7827×body128valid
58.0ms84×body1024invalid
42.0ms68×body1024valid
33.0ms256×body128invalid
27.0ms71×body512invalid
27.0ms64×body512valid
22.0ms25×body2048invalid
14.0ms53×body256invalid
11.0ms41×body256valid
Compiler

Compiled 224 to 164 computations (26.8% saved)

Profiling

Loading profile data...