Details

Time bar (total: 24.8s)

analyze3.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.8%0.2%0
99.8%0%0.2%1
Compiler

Compiled 35 to 24 computations (31.4% saved)

sample2.0s (8.2%)

Symmetry

(sort m n)

Results
1.7s7857×body128valid
110.0ms140×body1024valid
89.0ms157×body512valid
37.0ms79×body256valid
29.0ms23×body2048valid
Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify106.0ms (0.4%)

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

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
15.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶15.9b
(*.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)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (*.f64 K (+.f64 m n)) 2)
✓0.0b
(*.f64 K (+.f64 m n))
✓0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓32.8b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series86.0ms (0.3%)

Counts
4 → 156
Calls

4 calls:

40.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
25.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
9.0ms
(*.f64 K (+.f64 m n))

rewrite68.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
31×add-sqr-sqrt_binary64
28×*-un-lft-identity_binary64
25×cos-sum_binary64
24×add-cube-cbrt_binary64
21×prod-diff_binary64
Counts
4 → 108
Calls

4 calls:

27.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
13.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
7.0ms
(*.f64 K (+.f64 m n))

simplify321.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
429×fma-neg_binary64
332×associate-*r*_binary64
300×associate-*l*_binary64
225×*-commutative_binary64
213×fma-def_binary64
Counts
264 → 231
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
04386329
19035067
231364940
347794856
449394856

prune723.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2256231
Fresh000
Picked101
Done000
Total2266232
Error
1.0b
Counts
232 → 6
Alt Table
StatusErrorProgram
▶2.1b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (*.f64 K (+.f64 m n)) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.6b
(*.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
28.2b
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)) (fma.f64 1/2 (*.f64 K (*.f64 m (sin.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))) (*.f64 1/8 (*.f64 (*.f64 K K) (*.f64 (*.f64 m m) (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.9b
(*.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 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (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))))
Compiler

Compiled 10274 to 4944 computations (51.9% saved)

localize32.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune225.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New61061
Fresh055
Picked011
Done000
Total61667
Error
1.0b
Counts
67 → 6
Alt Table
StatusErrorProgram
✓2.1b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (*.f64 K (+.f64 m n)) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶15.6b
(*.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
28.2b
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)) (fma.f64 1/2 (*.f64 K (*.f64 m (sin.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))) (*.f64 1/8 (*.f64 (*.f64 K K) (*.f64 (*.f64 m m) (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.9b
(*.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 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (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))))
Compiler

Compiled 2117 to 1117 computations (47.2% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)))
✓0.4b
(/.f64 (+.f64 m n) (sqrt.f64 2))
✓0.4b
(/.f64 K (sqrt.f64 2))
✓32.6b
(cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))

series277.0ms (1.1%)

Counts
4 → 108
Calls

4 calls:

126.0ms
(*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)))
117.0ms
(cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))
21.0ms
(/.f64 (+.f64 m n) (sqrt.f64 2))
12.0ms
(/.f64 K (sqrt.f64 2))

rewrite76.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
96×times-frac_binary64
96×add-sqr-sqrt_binary64
92×*-un-lft-identity_binary64
66×add-cube-cbrt_binary64
54×sqrt-prod_binary64
Counts
4 → 189
Calls

4 calls:

31.0ms
(*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)))
14.0ms
(cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))
6.0ms
(/.f64 (+.f64 m n) (sqrt.f64 2))
5.0ms
(/.f64 K (sqrt.f64 2))

simplify371.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
650×fma-def_binary64
258×associate-*r*_binary64
226×associate-*l*_binary64
219×*-commutative_binary64
199×associate-/l*_binary64
Counts
297 → 264
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03746442
19135829
232505639
347105587
449875587
549205587

prune1.0s (4.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2631264
Fresh044
Picked101
Done011
Total2646270
Error
1.0b
Counts
270 → 6
Alt Table
StatusErrorProgram
▶15.6b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 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 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (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))))
✓2.1b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (*.f64 K (+.f64 m n)) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
28.2b
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)) (fma.f64 1/2 (*.f64 K (*.f64 m (sin.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))) (*.f64 1/8 (*.f64 (*.f64 K K) (*.f64 (*.f64 m m) (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.9b
(*.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))))
Compiler

Compiled 12041 to 6936 computations (42.4% saved)

localize51.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))))
0.4b
(/.f64 K (sqrt.f64 2))
✓0.5b
(cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)))
32.6b
(cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))

series12.9s (52%)

Counts
2 → 96
Calls

2 calls:

7.1s
(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))))
5.8s
(cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)))

rewrite25.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64
19×cbrt-prod_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
9×pow1_binary64
Counts
2 → 55
Calls

2 calls:

12.0ms
(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))))
3.0ms
(cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)))

simplify288.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
582×associate-*l*_binary64
432×fma-def_binary64
234×associate-*r/_binary64
203×associate-/l*_binary64
180×*-commutative_binary64
Counts
151 → 153
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
048310783
115708703
249648703

prune3.8s (15.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New5802582
Fresh044
Picked101
Done011
Total5817588
Error
1.0b
Counts
588 → 7
Alt Table
StatusErrorProgram
15.1b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)))) (cbrt.f64 (cos.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.8b
(*.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (*.f64 K (+.f64 m n)) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓2.1b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.6b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M)) 2)) (cbrt.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
28.2b
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)) (fma.f64 1/2 (*.f64 K (*.f64 m (sin.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))) (*.f64 1/8 (*.f64 (*.f64 K K) (*.f64 (*.f64 m m) (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.9b
(*.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 (cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (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))))
Compiler

Compiled 56999 to 36368 computations (36.2% saved)

regimes1.9s (7.6%)

Accuracy

Total 1.0b remaining (43.9%)

Threshold costs 1.0b (43.9%)

Counts
123 → 1
Compiler

Compiled 30836 to 20904 computations (32.2% 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

end415.0ms (1.7%)

Remove

(sort m n)

Compiler

Compiled 439 to 297 computations (32.3% saved)

Profiling

Loading profile data...