Details

Time bar (total: 9.0s)

analyze2.7s (30.6%)

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)

sample53.0ms (0.6%)

Algorithm
intervals
Results
23.0ms249×body128valid
3.0msbody1024invalid
1.0msbody2048invalid
1.0ms10×body128invalid
1.0msbody1024valid
1.0msbody256valid
1.0msbody512valid
1.0msbody512invalid
Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify52.0ms (0.6%)

Algorithm
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

prune10.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
15.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
15.1b
(*.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)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b
(*.f64 K (+.f64 m n))
0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
33.4b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite186.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
14.9b
Rules
19×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
add-exp-log_binary64
pow1_binary64
Counts
4 → 72
Calls

4 calls:

12.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
6.0ms
(*.f64 K (+.f64 m n))
Compiler

Compiled 2469 to 1205 computations (51.2% saved)

series300.0ms (3.3%)

Error
1.4b
Counts
4 → 82
Calls

4 calls:

79.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
66.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
65.0ms
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
34.0ms
(*.f64 K (+.f64 m n))
Compiler

Compiled 6226 to 4087 computations (34.4% saved)

simplify120.0ms (1.3%)

Algorithm
egg-herbie
Rules
360×distribute-rgt-in_binary64
342×distribute-lft-in_binary64
217×cancel-sign-sub-inv_binary64
213×associate-+l+_binary64
161×associate-*r*_binary64
Counts
154 → 127
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02542741
16232519
217072430
346752427
450482427

prune106.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1216127
Fresh000
Picked101
Done000
Total1226128
Error
1.4b
Counts
128 → 6
Alt Table
StatusErrorProgram
35.8b
(*.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))))
38.5b
(*.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))))
15.1b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.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))))
15.1b
(*.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))))
39.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 K) (*.f64 (+.f64 n m) (sqrt.f64 K))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
1.5b
(*.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 2781 to 1415 computations (49.1% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.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)

rewrite201.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
1.4b
Rules
22×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
add-cube-cbrt_binary64
associate-*r*_binary64
cancel-sign-sub-inv_binary64
Counts
3 → 71
Calls

3 calls:

31.0ms
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
24.0ms
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
18.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
Compiler

Compiled 2363 to 1183 computations (49.9% saved)

series412.0ms (4.6%)

Error
1.4b
Counts
3 → 74
Calls

3 calls:

139.0ms
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
130.0ms
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
74.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
Compiler

Compiled 5465 to 3598 computations (34.2% saved)

simplify169.0ms (1.9%)

Algorithm
egg-herbie
Rules
425×distribute-rgt-in_binary64
366×cancel-sign-sub-inv_binary64
305×sub-neg_binary64
206×exp-sum_binary64
177×exp-prod_binary64
Counts
145 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02605195
17524722
222484456
346224456
449664456

prune142.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1290129
Fresh055
Picked011
Done000
Total1296135
Error
1.4b
Counts
135 → 6
Alt Table
StatusErrorProgram
35.8b
(*.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))))
38.5b
(*.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))))
15.1b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.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))))
15.1b
(*.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))))
39.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 K) (*.f64 (+.f64 n m) (sqrt.f64 K))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
1.5b
(*.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 2686 to 1355 computations (49.6% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))
33.4b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
33.4b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
33.4b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))

rewrite160.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
1.4b
Rules
12×cos-sum_binary64
cancel-sign-sub-inv_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
4 → 47
Calls

4 calls:

10.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
10.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
9.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
4.0ms
(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))
Compiler

Compiled 3040 to 1495 computations (50.8% saved)

series624.0ms (7%)

Error
1.4b
Counts
4 → 67
Calls

4 calls:

245.0ms
(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)))
84.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
84.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
81.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
Compiler

Compiled 11883 to 7434 computations (37.4% saved)

simplify133.0ms (1.5%)

Algorithm
egg-herbie
Rules
451×neg-mul-1_binary64
324×cancel-sign-sub-inv_binary64
284×associate-+l+_binary64
273×distribute-rgt-neg-in_binary64
270×associate-*r*_binary64
Counts
114 → 84
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02043352
15093038
216822995
346342995
449802995

prune123.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New84084
Fresh044
Picked011
Done011
Total84690
Error
1.4b
Counts
90 → 6
Alt Table
StatusErrorProgram
35.8b
(*.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))))
38.5b
(*.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))))
15.1b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.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))))
15.1b
(*.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))))
39.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 K) (*.f64 (+.f64 n m) (sqrt.f64 K))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
1.5b
(*.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 3265 to 1679 computations (48.6% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (+.f64 m n))
0.5b
(cbrt.f64 (+.f64 n m))
0.5b
(cbrt.f64 (+.f64 n m))
33.6b
(cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.f64 m n))) 2) M))

rewrite177.0ms (2%)

Algorithm
rewrite-expression-head
Error
1.4b
Rules
14×*-un-lft-identity_binary64
12×cbrt-prod_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
cbrt-div_binary64
Counts
4 → 54
Calls

4 calls:

20.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.f64 m n))) 2) M))
3.0ms
(cbrt.f64 (+.f64 n m))
3.0ms
(cbrt.f64 (+.f64 n m))
3.0ms
(cbrt.f64 (+.f64 m n))
Compiler

Compiled 2536 to 956 computations (62.3% saved)

series199.0ms (2.2%)

Error
1.4b
Counts
4 → 39
Calls

4 calls:

70.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.f64 m n))) 2) M))
32.0ms
(cbrt.f64 (+.f64 n m))
30.0ms
(cbrt.f64 (+.f64 n m))
26.0ms
(cbrt.f64 (+.f64 m n))
Compiler

Compiled 4543 to 2992 computations (34.1% saved)

simplify174.0ms (1.9%)

Algorithm
egg-herbie
Rules
616×distribute-rgt-neg-in_binary64
589×distribute-lft-neg-in_binary64
458×associate-*l*_binary64
456×associate-*r*_binary64
225×*-commutative_binary64
Counts
93 → 66
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01811409
13741345
28881325
329671321
449401321
549991321
650001321
749461321

prune93.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New64266
Fresh033
Picked011
Done112
Total65772
Error
1.4b
Counts
72 → 7
Alt Table
StatusErrorProgram
15.1b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 n m))) (cbrt.f64 (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (cbrt.f64 (+.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))))
13.1b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
35.8b
(*.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))))
38.5b
(*.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))))
15.1b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.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))))
39.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 K) (*.f64 (+.f64 n m) (sqrt.f64 K))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
1.5b
(*.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 1851 to 880 computations (52.5% saved)

regimes1.1s (11.9%)

Accuracy

Total 0.2b remaining (15.5%)

Threshold costs 0.2b (15.5%)

Compiler

Compiled 23456 to 15168 computations (35.3% 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)

sample1.6s (18.1%)

Algorithm
intervals
Results
796.0ms7843×body128valid
38.0ms91×body1024invalid
29.0ms66×body1024valid
27.0ms264×body128invalid
25.0ms82×body512invalid
23.0ms55×body512valid
19.0ms17×body2048invalid
9.0ms47×body256invalid
8.0ms35×body256valid
1.0msbody2048valid
Compiler

Compiled 346 to 223 computations (35.5% saved)

Profiling

Loading profile data...