Details

Time bar (total: 12.3s)

analyze3.3s (26.7%)

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)

sample118.0ms (1%)

Algorithm
1×intervals
Symmetry

(sort m n)

Results
39.0ms246×body128valid
3.0ms5×body1024invalid
2.0ms5×body512invalid
2.0ms12×body128invalid
1.0ms4×body512valid
1.0ms2×body1024valid
1.0ms1×body2048valid
1.0ms3×body256valid
1.0ms1×body2048invalid
0.0ms1×body256invalid
Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify61.0ms (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
14.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶14.6b
(*.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)

localize24.0ms (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)
✓0.0b
(*.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))))
✓35.8b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series430.0ms (3.5%)

Counts
4 → 180
Calls

4 calls:

375.0ms
(*.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))))
28.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
20.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms
(*.f64 K (+.f64 m n))

rewrite88.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
74×*-un-lft-identity_binary64
63×add-sqr-sqrt_binary64
57×prod-diff_binary64
48×associate-*r*_binary64
42×add-cube-cbrt_binary64
Counts
4 → 145
Calls

4 calls:

38.0ms
(*.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))))
11.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
5.0ms
(*.f64 K (+.f64 m n))

simplify358.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
921×fma-def_binary64
462×*-commutative_binary64
308×associate-*r*_binary64
167×+-commutative_binary64
153×cancel-sign-sub-inv_binary64
Counts
325 → 314
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
099019178
1263317041
2485717041
3499017041

prune839.0ms (6.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3068314
Fresh000
Picked101
Done000
Total3078315
Error
2.0b
Counts
315 → 8
Alt Table
StatusErrorProgram
14.6b
(*.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))))
47.2b
(+.f64 (fma.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4)))))) (*.f64 (sin.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))) (*.f64 m (*.f64 M M))) (fma.f64 n (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4)))))) (*.f64 (sin.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))) (*.f64 M M))) (fma.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4)))))) (*.f64 (cos.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))) (*.f64 M m)) (fma.f64 1/2 (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4)))))) (*.f64 (*.f64 m m) (*.f64 (cos.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))) (*.f64 M M)))) (fma.f64 (cos.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4)))))) (fma.f64 n (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4)))))) (*.f64 M (cos.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))))) (+.f64 (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4)))))) (+.f64 (*.f64 n (*.f64 (cos.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))) (*.f64 m (*.f64 M M)))) (*.f64 M (sin.f64 (*.f64 1/2 (*.f64 K (+.f64 n m))))))) (*.f64 1/2 (*.f64 (*.f64 n n) (*.f64 (*.f64 (cos.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))) (*.f64 M M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4)))))))))))))))) (*.f64 (*.f64 (*.f64 (cos.f64 (*.f64 1/2 (*.f64 K (+.f64 n m)))) (*.f64 M M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (+.f64 l (fma.f64 1/2 (*.f64 n m) (*.f64 (*.f64 n n) 1/4))))))) -3/2))
▶2.4b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
29.8b
(*.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))))
9.6b
(*.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))))
14.5b
(*.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 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1)))) (*.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 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
38.3b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 K) (*.f64 (sqrt.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))))
14.5b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (cbrt.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 26623 to 13134 computations (50.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓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
(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)

series352.0ms (2.9%)

Counts
3 → 144
Calls

3 calls:

214.0ms
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
77.0ms
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
59.0ms
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

rewrite109.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
158×*-un-lft-identity_binary64
115×add-sqr-sqrt_binary64
108×prod-diff_binary64
82×exp-sum_binary64
67×fabs-mul_binary64
Counts
3 → 197
Calls

3 calls:

32.0ms
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
22.0ms
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
19.0ms
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

simplify366.0ms (3%)

Algorithm
1×egg-herbie
Rules
769×fma-def_binary64
354×fma-neg_binary64
317×associate-+l+_binary64
277×*-commutative_binary64
229×associate--r+_binary64
Counts
341 → 335
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
066721753
1199117787
2497417785
3521717785

prune843.0ms (6.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3961397
Fresh167
Picked011
Done000
Total3978405
Error
2.0b
Counts
405 → 8
Alt Table
StatusErrorProgram
14.6b
(*.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))))
✓2.4b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
29.8b
(*.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))))
▶9.6b
(*.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))))
42.2b
(*.f64 (cos.f64 M) (-.f64 (fma.f64 n (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 m (*.f64 M M))) (+.f64 (fma.f64 1/2 (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 (*.f64 n M) (*.f64 n M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l)))))) (+.f64 (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 M (+.f64 n m))) (*.f64 1/2 (*.f64 (*.f64 (*.f64 M M) (*.f64 m m)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l)))))))))) (*.f64 (*.f64 M M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))))))
14.5b
(*.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 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1)))) (*.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 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
38.3b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 K) (*.f64 (sqrt.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))))
14.5b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (cbrt.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 26001 to 12981 computations (50.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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)
✓0.0b
(*.f64 1/2 (*.f64 K m))
✓23.6b
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))

series17.0ms (0.1%)

Counts
2 → 12
Calls

2 calls:

12.0ms
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))
5.0ms
(*.f64 1/2 (*.f64 K m))

rewrite12.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
7×add-cbrt-cube_binary64
7×add-exp-log_binary64
7×pow1_binary64
7×cos-sum_binary64
5×*-un-lft-identity_binary64
Counts
2 → 37
Calls

2 calls:

6.0ms
(cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M))
4.0ms
(*.f64 1/2 (*.f64 K m))

simplify72.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
742×fma-def_binary64
437×cancel-sign-sub-inv_binary64
433×unsub-neg_binary64
327×*-commutative_binary64
321×distribute-rgt-neg-in_binary64
Counts
49 → 57
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01501020
1267941
2858890
31810847
44414847
54996847

prune523.0ms (4.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2202222
Fresh156
Picked101
Done011
Total2228230
Error
2.0b
Counts
230 → 8
Alt Table
StatusErrorProgram
14.6b
(*.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))))
✓2.4b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
29.8b
(*.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))))
42.2b
(*.f64 (cos.f64 M) (-.f64 (fma.f64 n (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 m (*.f64 M M))) (+.f64 (fma.f64 1/2 (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 (*.f64 n M) (*.f64 n M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l)))))) (+.f64 (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 M (+.f64 n m))) (*.f64 1/2 (*.f64 (*.f64 (*.f64 M M) (*.f64 m m)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l)))))))))) (*.f64 (*.f64 M M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))))))
▶9.6b
(*.f64 (cos.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.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))))
42.7b
(*.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (*.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))) (exp.f64 (*.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) 0))))
14.5b
(*.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 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1)))) (*.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 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
38.3b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 K) (*.f64 (sqrt.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 14182 to 7345 computations (48.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (*.f64 1/2 (*.f64 K m))))
✓0.5b
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m))))
✓14.4b
(cbrt.f64 (*.f64 1/2 (*.f64 K m)))
✓23.8b
(cos.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) M))

series1.2s (9.6%)

Counts
4 → 108
Calls

4 calls:

683.0ms
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m))))
423.0ms
(cbrt.f64 (*.f64 1/2 (*.f64 K m)))
56.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (*.f64 1/2 (*.f64 K m))))
20.0ms
(cos.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) M))

rewrite34.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
30×pow1_binary64
16×pow1/3_binary64
14×add-sqr-sqrt_binary64
11×pow-prod-up_binary64
11×add-exp-log_binary64
Counts
4 → 96
Calls

4 calls:

10.0ms
(cos.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) M))
9.0ms
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m))))
7.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (*.f64 1/2 (*.f64 K m))))
2.0ms
(cbrt.f64 (*.f64 1/2 (*.f64 K m)))

simplify169.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
679×fma-neg_binary64
396×*-commutative_binary64
337×unswap-sqr_binary64
266×exp-prod_binary64
255×fma-def_binary64
Counts
204 → 157
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02473538
14583253
212422921
327792628
446052550
549642550
648702550

prune432.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1952197
Fresh156
Picked101
Done011
Total1978205
Error
2.0b
Counts
205 → 8
Alt Table
StatusErrorProgram
14.6b
(*.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))))
54.9b
(*.f64 (cos.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (cbrt.f64 (*.f64 1/2 (*.f64 K m)))) (*.f64 (exp.f64 (*.f64 1/3 (+.f64 (log.f64 K) (log.f64 m)))) (cbrt.f64 1/2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓2.4b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
42.2b
(*.f64 (cos.f64 M) (-.f64 (fma.f64 n (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 m (*.f64 M M))) (+.f64 (fma.f64 1/2 (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 (*.f64 n M) (*.f64 n M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l)))))) (+.f64 (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))) (*.f64 M (+.f64 n m))) (*.f64 1/2 (*.f64 (*.f64 (*.f64 M M) (*.f64 m m)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l)))))))))) (*.f64 (*.f64 M M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 1/4 (*.f64 m m) (fma.f64 1/2 (*.f64 n m) (fma.f64 1/4 (*.f64 n n) l))))))))
45.5b
(*.f64 (cos.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 K m))) (*.f64 (cbrt.f64 -1/2) (exp.f64 (*.f64 1/3 (-.f64 (log.f64 K) (log.f64 (/.f64 -1 m))))))) (cbrt.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))))
42.7b
(*.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K m)) M)) (*.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))) (exp.f64 (*.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) 0))))
14.5b
(*.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 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1)))) (*.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 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
38.3b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 K) (*.f64 (sqrt.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 9506 to 5317 computations (44.1% saved)

regimes1.1s (8.6%)

Accuracy

Total 0.2b remaining (13.9%)

Threshold costs 0.2b (13.9%)

Counts
119 → 1
Compiler

Compiled 36356 to 22326 computations (38.6% saved)

simplify3.0ms (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

end9.0ms (0.1%)

Remove

(sort m n)

Compiler

Compiled 75 to 54 computations (28% saved)

sample1.9s (15.1%)

Algorithm
1×intervals
Results
1000.0ms7834×body128valid
47.0ms78×body1024invalid
40.0ms298×body128invalid
38.0ms61×body1024valid
31.0ms64×body512valid
26.0ms71×body512invalid
20.0ms23×body2048invalid
13.0ms53×body256invalid
10.0ms40×body256valid
1.0ms1×body2048valid
Compiler

Compiled 597 to 364 computations (39% saved)

Profiling

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