Details

Time bar (total: 18.1s)

analyze5.9s (32.8%)

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)

sample106.0ms (0.6%)

Algorithm
1×intervals
Results
62.0ms249×body128valid
5.0ms4×body1024valid
2.0ms2×body512valid
1.0ms5×body128invalid
1.0ms1×body512invalid
1.0ms1×body256invalid
0.0ms1×body256valid
Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify110.0ms (0.6%)

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

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
16.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶16.1b
(*.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 128 to 80 computations (37.5% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (*.f64 K (+.f64 m n)) 2)
✓0.0b
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
✓0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓35.2b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite79.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
45×add-sqr-sqrt_binary64
42×*-un-lft-identity_binary64
42×prod-diff_binary64
38×add-cube-cbrt_binary64
25×times-frac_binary64
Counts
4 → 129
Calls

4 calls:

19.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
18.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
15.0ms
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
10.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)

series263.0ms (1.5%)

Counts
4 → 168
Calls

4 calls:

105.0ms
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
57.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
50.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
50.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify325.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
302×associate-*r*_binary64
289×fma-neg_binary64
265×associate-*l*_binary64
239×distribute-rgt-neg-in_binary64
212×*-commutative_binary64
Counts
297 → 559
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04367360
18935912
230525722
349375722

prune699.0ms (3.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New5545559
Fresh000
Picked101
Done000
Total5555560
Error
1.4b
Counts
560 → 5
Alt Table
StatusErrorProgram
16.1b
(*.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))))
16.1b
(*.f64 (log1p.f64 (expm1.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))))
▶1.6b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.1b
(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
36.3b
(*.f64 (cos.f64 (expm1.f64 (log1p.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 11200 to 5322 computations (52.5% saved)

localize30.0ms (0.2%)

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)

rewrite27.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
11×fma-def_binary64
8×add-sqr-sqrt_binary64
7×*-un-lft-identity_binary64
6×unpow-prod-down_binary64
3×add-log-exp_binary64
Counts
1 → 25
Calls

1 calls:

24.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series82.0ms (0.5%)

Counts
1 → 48
Calls

1 calls:

82.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

simplify98.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
737×distribute-rgt-in_binary64
733×fma-neg_binary64
455×fma-def_binary64
381×associate--l+_binary64
377×associate-+l+_binary64
Counts
73 → 130
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0881735
12931532
27421518
326101516
449541516
553591516

prune155.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2430243
Fresh044
Picked011
Done000
Total2435248
Error
1.4b
Counts
248 → 5
Alt Table
StatusErrorProgram
16.1b
(*.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))))
▶16.1b
(*.f64 (log1p.f64 (expm1.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))))
✓1.6b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.1b
(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
36.3b
(*.f64 (cos.f64 (expm1.f64 (log1p.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 3787 to 1897 computations (49.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓0.3b
(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
✓0.3b
(expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
35.2b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite2.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
3×log1p-expm1-u_binary64
2×*-un-lft-identity_binary64
2×add-sqr-sqrt_binary64
2×add-cube-cbrt_binary64
2×add-cbrt-cube_binary64
Counts
2 → 22
Calls

2 calls:

0.0ms
(expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.0ms
(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

series2.2s (12.1%)

Counts
2 → 96
Calls

2 calls:

2.1s
(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
89.0ms
(expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))

simplify111.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
899×associate-*r*_binary64
585×associate-*l*_binary64
415×fma-def_binary64
234×associate-+r+_binary64
191×*-commutative_binary64
Counts
118 → 223
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03795068
112144510
252064510

prune399.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New6091610
Fresh033
Picked101
Done011
Total6105615
Error
1.4b
Counts
615 → 5
Alt Table
StatusErrorProgram
✓1.6b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.1b
(*.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))))
16.1b
(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 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 (*.f64 (cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))) (cbrt.f64 (log1p.f64 (expm1.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))))
36.3b
(*.f64 (cos.f64 (expm1.f64 (log1p.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 14075 to 7197 computations (48.9% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.5b
(cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))
35.2b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
35.2b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
35.2b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite1.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
3×cbrt-prod_binary64
2×*-un-lft-identity_binary64
2×add-sqr-sqrt_binary64
2×add-cube-cbrt_binary64
1×add-cbrt-cube_binary64
Counts
1 → 13
Calls

1 calls:

1.0ms
(cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))

series4.2s (23.1%)

Counts
1 → 48
Calls

1 calls:

4.2s
(cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))

simplify102.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
852×associate-*r*_binary64
720×associate-*l*_binary64
311×fma-def_binary64
187×associate-+r+_binary64
177×*-commutative_binary64
Counts
61 → 119
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03653831
111563507
249803507

prune803.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New237122373
Fresh033
Picked101
Done011
Total237262378
Error
1.4b
Counts
2378 → 6
Alt Table
StatusErrorProgram
✓1.6b
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
16.1b
(*.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))))
16.1b
(*.f64 (*.f64 (*.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))) (cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))) (cbrt.f64 (log1p.f64 (expm1.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))))
16.2b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 M)) (cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))) (cbrt.f64 (log1p.f64 (expm1.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 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
36.3b
(*.f64 (cos.f64 (expm1.f64 (log1p.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 28713 to 15130 computations (47.3% saved)

regimes451.0ms (2.5%)

Accuracy

Total 0.2b remaining (15.6%)

Threshold costs 0.2b (15.6%)

Compiler

Compiled 12908 to 8724 computations (32.4% 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

end7.0ms (0%)

Remove

(sort m n)

Compiler

Compiled 75 to 54 computations (28% saved)

sample1.8s (10.2%)

Algorithm
1×intervals
Results
1.1s7817×body128valid
55.0ms88×body1024invalid
54.0ms76×body1024valid
41.0ms98×body512invalid
39.0ms308×body128invalid
24.0ms59×body512valid
17.0ms15×body2048invalid
14.0ms46×body256valid
12.0ms45×body256invalid
2.0ms2×body2048valid
Compiler

Compiled 322 to 223 computations (30.7% saved)

Profiling

Loading profile data...