Details

Time bar (total: 8.9s)

analyze3.3s (37%)

Algorithm
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)

sample66.0ms (0.7%)

Algorithm
intervals
Results
35.0ms250×body128valid
3.0msbody1024invalid
2.0msbody512valid
1.0msbody1024valid
1.0msbody128invalid
1.0msbody512invalid
1.0msbody2048invalid
1.0msbody256invalid
Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify67.0ms (0.8%)

Algorithm
egg-herbie
Rules
691×exp-prod_binary64
507×exp-sum_binary64
446×fma-neg_binary64
375×associate-*l*_binary64
251×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02245
15845
212943
338443
4126643
5402343
6494543
7501943

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
13.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
13.8b
(*.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 128 to 80 computations (37.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 K (+.f64 m n))
0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.2b
(/.f64 (*.f64 K (+.f64 m n)) 2)
34.9b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite86.0ms (1%)

Algorithm
rewrite-expression-head
Rules
42×add-cube-cbrt_binary64
22×pow1_binary64
19×add-exp-log_binary64
19×add-sqr-sqrt_binary64
18×add-cbrt-cube_binary64
Counts
4 → 174
Calls

4 calls:

21.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
18.0ms
(*.f64 K (+.f64 m n))
18.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series175.0ms (2%)

Counts
4 → 156
Calls

4 calls:

94.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
36.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
25.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
20.0ms
(*.f64 K (+.f64 m n))

simplify187.0ms (2.1%)

Algorithm
egg-herbie
Rules
400×associate-*r*_binary64
383×fma-neg_binary64
369×associate-*l*_binary64
293×fma-def_binary64
260×unswap-sqr_binary64
Counts
330 → 567
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03566127
110435156
237355058
352195058

prune508.0ms (5.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New5598567
Fresh000
Picked101
Done000
Total5608568
Error
1.6b
Counts
568 → 8
Alt Table
StatusErrorProgram
13.8b
(*.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))))
1.7b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
13.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
28.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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))))
28.9b
(*.f64 (cos.f64 (-.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (*.f64 K (+.f64 n m)) 2) 2) 2)) (cbrt.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))))
28.9b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 K (+.f64 n m)) 2)) (cbrt.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))))
13.7b
(*.f64 (cos.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) 3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
13.7b
(*.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (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 12974 to 6133 computations (52.7% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
add-cube-cbrt_binary64
add-log-exp_binary64
*-un-lft-identity_binary64
flip3-+_binary64
pow1_binary64
Counts
1 → 41
Calls

1 calls:

20.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series79.0ms (0.9%)

Counts
1 → 48
Calls

1 calls:

78.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

simplify128.0ms (1.4%)

Algorithm
egg-herbie
Rules
772×fma-neg_binary64
554×fma-def_binary64
381×associate--l+_binary64
377×associate-+l+_binary64
303×unswap-sqr_binary64
Counts
89 → 160
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01122291
13442014
29551974
333561974
447101974
549571974

prune253.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2920292
Fresh077
Picked011
Done000
Total2928300
Error
1.6b
Counts
300 → 8
Alt Table
StatusErrorProgram
13.8b
(*.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))))
1.7b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
13.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
28.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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))))
28.9b
(*.f64 (cos.f64 (-.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (*.f64 K (+.f64 n m)) 2) 2) 2)) (cbrt.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))))
28.9b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 K (+.f64 n m)) 2)) (cbrt.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))))
13.7b
(*.f64 (cos.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) 3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
13.7b
(*.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (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 5028 to 2615 computations (48% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 K (+.f64 m n)) 2)
0.4b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
34.9b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
34.9b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
16×pow1_binary64
add-cube-cbrt_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
add-cbrt-cube_binary64
Counts
1 → 55
Calls

1 calls:

20.0ms
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))

series95.0ms (1.1%)

Counts
1 → 48
Calls

1 calls:

95.0ms
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))

simplify127.0ms (1.4%)

Algorithm
egg-herbie
Rules
708×cancel-sign-sub-inv_binary64
397×associate-*r*_binary64
313×unswap-sqr_binary64
296×associate-*l*_binary64
277×fma-neg_binary64
Counts
103 → 185
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02433550
17243157
226583106
350483106

prune619.0ms (6.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New7944798
Fresh516
Picked101
Done011
Total8006806
Error
1.5b
Counts
806 → 6
Alt Table
StatusErrorProgram
13.8b
(*.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))))
1.7b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
30.9b
(*.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (*.f64 K (+.f64 n m)) 2) 2) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 n m)) 2))) M)) (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))))
25.6b
(*.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2))) M)) (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))))
8.2b
(*.f64 (sqrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
47.1b
(*.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) (/.f64 (*.f64 K (+.f64 m n)) 2)) (/.f64 (*.f64 K (+.f64 m n)) 2)) 1/3) M)) (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 22275 to 10568 computations (52.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.1b
(sqrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) 2))
0.4b
(pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) 2)
25.6b
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))

rewrite60.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
26×add-cube-cbrt_binary64
11×add-sqr-sqrt_binary64
10×pow1_binary64
add-cbrt-cube_binary64
log1p-expm1-u_binary64
Counts
3 → 117
Calls

3 calls:

20.0ms
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))
19.0ms
(pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) 2)
15.0ms
(sqrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) 2))

series62.0ms (0.7%)

Counts
3 → 60
Calls

3 calls:

40.0ms
(pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) 2)
11.0ms
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))
11.0ms
(sqrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) 2))

simplify160.0ms (1.8%)

Algorithm
egg-herbie
Rules
709×fma-neg_binary64
696×cancel-sign-sub-inv_binary64
406×neg-mul-1_binary64
268×distribute-rgt-neg-in_binary64
244×distribute-lft-neg-in_binary64
Counts
177 → 264
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02103746
15733422
220303088
342092888
448652888
548722888

prune393.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New5271528
Fresh044
Picked101
Done011
Total5286534
Error
1.5b
Counts
534 → 6
Alt Table
StatusErrorProgram
1.7b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
8.2b
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) 2)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
13.8b
(*.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))))
30.9b
(*.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (*.f64 K (+.f64 n m)) 2) 2) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 n m)) 2))) M)) (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))))
25.6b
(*.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2))) M)) (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))))
47.1b
(*.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) (/.f64 (*.f64 K (+.f64 m n)) 2)) (/.f64 (*.f64 K (+.f64 m n)) 2)) 1/3) M)) (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 10255 to 5420 computations (47.1% saved)

regimes579.0ms (6.5%)

Accuracy

Total 0.1b remaining (8.3%)

Threshold costs 0.1b (8.3%)

Compiler

Compiled 18734 to 11928 computations (36.3% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
12×+-commutative_binary64
10×sub-neg_binary64
*-commutative_binary64
neg-sub0_binary64
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 (20.7%)

Algorithm
intervals
Results
1.1s7813×body128valid
54.0ms89×body1024invalid
46.0ms75×body1024valid
39.0ms297×body128invalid
30.0ms79×body512invalid
29.0ms72×body512valid
20.0ms23×body2048invalid
19.0ms69×body256invalid
11.0ms39×body256valid
1.0msbody2048valid
Compiler

Compiled 337 to 231 computations (31.5% saved)

Profiling

Loading profile data...