Details

Time bar (total: 13.4s)

analyze2.9s (22%)

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)

sample108.0ms (0.8%)

Algorithm
1×intervals
Symmetry

(sort m n)

Results
33.0ms245×body128valid
3.0ms5×body1024valid
2.0ms4×body1024invalid
2.0ms13×body128invalid
1.0ms3×body512valid
1.0ms3×body256valid
0.0ms2×body256invalid
0.0ms1×body512invalid
Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify62.0ms (0.5%)

Algorithm
1×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
16.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶16.5b
(*.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 128 to 80 computations (37.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
✓0.0b
(exp.f64 (-.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)
✓36.7b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series176.0ms (1.3%)

Counts
4 → 180
Calls

4 calls:

78.0ms
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
52.0ms
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
28.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
17.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite91.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
129×*-un-lft-identity_binary64
103×add-sqr-sqrt_binary64
93×prod-diff_binary64
59×add-cube-cbrt_binary64
47×fabs-mul_binary64
Counts
4 → 193
Calls

4 calls:

24.0ms
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
21.0ms
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
9.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify260.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
791×associate-*r*_binary64
607×associate-*l*_binary64
607×fma-def_binary64
243×*-commutative_binary64
172×sub-neg_binary64
Counts
373 → 368
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
076319209
1187715239
2588215239

prune682.0ms (5.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3617368
Fresh000
Picked101
Done000
Total3627369
Error
2.3b
Counts
369 → 7
Alt Table
StatusErrorProgram
53.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (*.f64 (exp.f64 (fma.f64 1 (fabs.f64 (-.f64 m n)) (neg.f64 (*.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))) (exp.f64 (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))))
16.3b
(*.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶2.9b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))) (cbrt.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))))
16.1b
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (*.f64 1/2 (*.f64 n (*.f64 K (sin.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.4b
(*.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (*.f64 (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
11.0b
(*.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 23749 to 11688 computations (50.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series7.0ms (0.1%)

Counts
1 → 36
Calls

1 calls:

7.0ms
(-.f64 (/.f64 (+.f64 m n) 2) M)

rewrite17.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
76×*-un-lft-identity_binary64
55×add-sqr-sqrt_binary64
50×add-cube-cbrt_binary64
49×times-frac_binary64
48×prod-diff_binary64
Counts
1 → 83
Calls

1 calls:

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

simplify112.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
1011×fma-def_binary64
456×distribute-rgt-in_binary64
400×fma-neg_binary64
398×distribute-lft-in_binary64
288×times-frac_binary64
Counts
119 → 95
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01262560
12131627
25961258
318551257
443981257
549451257
648911257

prune795.0ms (5.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3822384
Fresh156
Picked011
Done000
Total3838391
Error
2.3b
Counts
391 → 8
Alt Table
StatusErrorProgram
16.1b
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (*.f64 1/2 (*.f64 n (*.f64 K (sin.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
42.8b
(*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (-.f64 m n) (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))) (*.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) 0))))
✓2.9b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))) (cbrt.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))))
52.9b
(*.f64 (cos.f64 M) (*.f64 (exp.f64 (fma.f64 1 (fabs.f64 (-.f64 m n)) (neg.f64 (*.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))) (exp.f64 (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))))
16.4b
(*.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (*.f64 (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.3b
(*.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶11.0b
(*.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 20081 to 9790 computations (51.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b
(exp.f64 (-.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)
✓27.1b
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))

series13.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

12.0ms
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))

rewrite6.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
7×cos-sum_binary64
3×cancel-sign-sub-inv_binary64
3×*-un-lft-identity_binary64
3×add-sqr-sqrt_binary64
3×prod-diff_binary64
Counts
1 → 17
Calls

1 calls:

5.0ms
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))

simplify90.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
690×fma-neg_binary64
649×distribute-rgt-neg-in_binary64
527×associate-*r*_binary64
509×associate-*l*_binary64
230×distribute-lft-neg-out_binary64
Counts
29 → 36
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0117810
1202773
2626723
32646701
44956701
54976701
64888701

prune624.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3241325
Fresh066
Picked101
Done011
Total3258333
Error
2.3b
Counts
333 → 8
Alt Table
StatusErrorProgram
16.1b
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (*.f64 1/2 (*.f64 n (*.f64 K (sin.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
42.8b
(*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (-.f64 m n) (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))) (*.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) 0))))
16.3b
(*.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶11.0b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓2.9b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))) (cbrt.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))))
52.9b
(*.f64 (cos.f64 M) (*.f64 (exp.f64 (fma.f64 1 (fabs.f64 (-.f64 m n)) (neg.f64 (*.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))) (exp.f64 (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))))
16.4b
(*.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (*.f64 (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 20017 to 10323 computations (48.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))))
✓0.4b
(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))))
✓0.5b
(cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))
27.1b
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))

series2.1s (15.7%)

Counts
3 → 108
Calls

3 calls:

1.2s
(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))))
920.0ms
(cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))
19.0ms
(*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))))

rewrite30.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

15.0ms
(*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))))
6.0ms
(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))))
2.0ms
(cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))

simplify184.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
663×cancel-sign-sub-inv_binary64
484×unswap-sqr_binary64
355×associate-*r*_binary64
296×associate-*l*_binary64
231×fma-neg_binary64
Counts
201 → 165
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02445482
16764981
224714827
347954766
449404766
549564766

prune1.1s (8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3352337
Fresh066
Picked101
Done011
Total3369345
Error
2.3b
Counts
345 → 9
Alt Table
StatusErrorProgram
16.1b
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (*.f64 1/2 (*.f64 n (*.f64 K (sin.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
42.8b
(*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (-.f64 m n) (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))) (*.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) 0))))
16.3b
(*.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
11.0b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))) (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓2.9b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))) (cbrt.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))))
52.9b
(*.f64 (cos.f64 M) (*.f64 (exp.f64 (fma.f64 1 (fabs.f64 (-.f64 m n)) (neg.f64 (*.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))) (exp.f64 (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))))
16.4b
(*.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (*.f64 (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2)) (neg.f64 (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 M) (*.f64 (cbrt.f64 M) (cbrt.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
22.7b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)))) (pow.f64 (cos.f64 (neg.f64 M)) 1/3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
Compiler

Compiled 21460 to 12107 computations (43.6% saved)

regimes2.1s (15.4%)

Accuracy

Total 0.2b remaining (14.5%)

Threshold costs 0.2b (14.5%)

Counts
251 → 1
Compiler

Compiled 59624 to 39702 computations (33.4% saved)

simplify4.0ms (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

end6.0ms (0%)

Remove

(sort m n)

Compiler

Compiled 75 to 54 computations (28% saved)

sample1.9s (14.1%)

Algorithm
1×intervals
Results
991.0ms7792×body128valid
73.0ms103×body1024invalid
57.0ms94×body1024valid
39.0ms316×body128invalid
34.0ms96×body512invalid
24.0ms66×body512valid
17.0ms20×body2048invalid
13.0ms54×body256invalid
12.0ms45×body256valid
3.0ms3×body2048valid
Compiler

Compiled 672 to 393 computations (41.5% saved)

Profiling

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