Details

Time bar (total: 8.6s)

analyze3.5s (40.3%)

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)

sample62.0ms (0.7%)

Algorithm
1×intervals
Results
34.0ms252×body128valid
2.0ms4×body1024valid
1.0ms2×body1024invalid
1.0ms6×body128invalid
1.0ms2×body512invalid
Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify54.0ms (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
15.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶15.5b
(*.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)

localize22.0ms (0.3%)

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)
0.0b
(*.f64 K (+.f64 m n))
34.1b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite141.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Error
15.4b
Rules
19×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
7×add-exp-log_binary64
7×pow1_binary64
Counts
4 → 72
Calls

4 calls:

14.0ms
(-.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))
5.0ms
(*.f64 K (+.f64 m n))
Compiler

Compiled 2469 to 1205 computations (51.2% saved)

series210.0ms (2.4%)

Error
0.8b
Counts
4 → 75
Calls

4 calls:

64.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
56.0ms
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
35.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
25.0ms
(*.f64 K (+.f64 m n))
Compiler

Compiled 5327 to 3563 computations (33.1% saved)

simplify148.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
349×distribute-rgt-in_binary64
341×distribute-lft-in_binary64
309×cancel-sign-sub-inv_binary64
305×unswap-sqr_binary64
258×exp-prod_binary64
Counts
147 → 115
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02082455
14932272
212362212
331972209
446712209
548982209
649562209

prune84.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1096115
Fresh000
Picked101
Done000
Total1106116
Error
0.9b
Counts
116 → 6
Alt Table
StatusErrorProgram
15.5b
(*.f64 (cos.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
41.5b
(*.f64 (cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 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))))
39.6b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 K (+.f64 n m))) (sqrt.f64 (*.f64 K (+.f64 n m)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.5b
(*.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 2551 to 1314 computations (48.5% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite40.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Error
0.9b
Rules
8×add-sqr-sqrt_binary64
6×unpow-prod-down_binary64
5×*-un-lft-identity_binary64
3×pow-unpow_binary64
3×add-cube-cbrt_binary64
Counts
1 → 21
Calls

1 calls:

9.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
Compiler

Compiled 553 to 296 computations (46.5% saved)

series83.0ms (1%)

Error
0.9b
Counts
1 → 27
Calls

1 calls:

63.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
Compiler

Compiled 1665 to 1109 computations (33.4% saved)

simplify134.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
510×cancel-sign-sub-inv_binary64
416×unswap-sqr_binary64
402×distribute-rgt-in_binary64
402×exp-prod_binary64
380×distribute-lft-in_binary64
Counts
48 → 43
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0841031
1212933
2506885
31651873
44172873
54255873
64565873
74949873
84939873

prune39.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New43043
Fresh055
Picked011
Done000
Total43649
Error
0.9b
Counts
49 → 6
Alt Table
StatusErrorProgram
15.5b
(*.f64 (cos.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
41.5b
(*.f64 (cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 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))))
39.6b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 K (+.f64 n m))) (sqrt.f64 (*.f64 K (+.f64 n m)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶15.5b
(*.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 1034 to 581 computations (43.8% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 K (+.f64 n m))
0.5b
(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
0.5b
(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))
34.1b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))

rewrite131.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Error
0.9b
Rules
15×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
12×cbrt-prod_binary64
7×add-cbrt-cube_binary64
Counts
4 → 79
Calls

4 calls:

8.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
6.0ms
(*.f64 K (+.f64 n m))
3.0ms
(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
2.0ms
(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))
Compiler

Compiled 2755 to 1468 computations (46.7% saved)

series242.0ms (2.8%)

Error
0.8b
Counts
4 → 51
Calls

4 calls:

112.0ms
(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
43.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
37.0ms
(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))
28.0ms
(*.f64 K (+.f64 n m))
Compiler

Compiled 4462 to 3083 computations (30.9% saved)

simplify139.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
367×sqr-pow_binary64
261×*-commutative_binary64
253×distribute-rgt-in_binary64
251×distribute-lft-in_binary64
240×exp-prod_binary64
Counts
130 → 92
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01562425
13462210
29222191
320702191
436172188
547252188
648792188

prune71.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New90292
Fresh134
Picked101
Done011
Total92698
Error
0.9b
Counts
98 → 6
Alt Table
StatusErrorProgram
41.5b
(*.f64 (cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶15.5b
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.5b
(*.f64 (cos.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.5b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M))) 2) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.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))))
39.6b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 K (+.f64 n m))) (sqrt.f64 (*.f64 K (+.f64 n m)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 1837 to 1040 computations (43.4% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3)) 3)
0.5b
(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3))
0.5b
(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3)) 3))
34.1b
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M))

rewrite188.0ms (2.2%)

Algorithm
1×rewrite-expression-head
Error
0.9b
Rules
96×cbrt-prod_binary64
45×cube-prod_binary64
45×unpow-prod-down_binary64
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
Counts
4 → 130
Calls

4 calls:

8.0ms
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M))
8.0ms
(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3)) 3))
6.0ms
(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3)) 3)
3.0ms
(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3))
Compiler

Compiled 4275 to 2492 computations (41.7% saved)

series218.0ms (2.5%)

Error
0.8b
Counts
4 → 52
Calls

4 calls:

80.0ms
(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3)) 3)
39.0ms
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M))
38.0ms
(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3))
36.0ms
(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)) 3)) 3))
Compiler

Compiled 4908 to 3414 computations (30.4% saved)

simplify217.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
607×sqr-pow_binary64
516×associate-*l*_binary64
461×associate-*r*_binary64
448×log-prod_binary64
427×exp-prod_binary64
Counts
182 → 158
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01894848
12714299
25674248
320904248
438884245
542474245
652974245

prune68.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1571158
Fresh224
Picked101
Done011
Total1604164
Error
0.9b
Counts
164 → 4
Alt Table
StatusErrorProgram
15.5b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M))) 2) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.4b
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (cos.f64 (*.f64 1/2 (*.f64 n K)))) (*.f64 (sin.f64 (*.f64 1/2 (*.f64 n K))) (sin.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))) 3)) 3)) (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))))
39.6b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 K (+.f64 n m))) (sqrt.f64 (*.f64 K (+.f64 n m)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 1756 to 977 computations (44.4% saved)

regimes908.0ms (10.6%)

Accuracy

Total 0.2b remaining (12.8%)

Threshold costs 0.2b (12.8%)

Compiler

Compiled 24602 to 16842 computations (31.5% saved)

simplify4.0ms (0.1%)

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

end8.0ms (0.1%)

Remove

(sort m n)

Compiler

Compiled 75 to 54 computations (28% saved)

sample1.9s (21.6%)

Algorithm
1×intervals
Results
1.1s7840×body128valid
50.0ms308×body128invalid
49.0ms76×body1024valid
47.0ms73×body1024invalid
29.0ms73×body512invalid
21.0ms52×body512valid
20.0ms17×body2048invalid
10.0ms39×body256invalid
8.0ms30×body256valid
2.0ms2×body2048valid
Compiler

Compiled 239 to 164 computations (31.4% saved)

Profiling

Loading profile data...