Details

Time bar (total: 8.8s)

analyze2.6s (29.4%)

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)

sample58.0ms (0.7%)

Algorithm
1×intervals
Results
31.0ms251×body128valid
1.0ms3×body512invalid
1.0ms2×body1024valid
1.0ms5×body128invalid
0.0ms1×body1024invalid
0.0ms2×body256valid
0.0ms2×body256invalid
0.0ms1×body512valid
Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify52.0ms (0.6%)

Algorithm
1×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

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
13.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶13.4b
(*.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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b
(*.f64 K (+.f64 m n))
0.2b
(/.f64 (*.f64 K (+.f64 m n)) 2)
32.1b
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite209.0ms (2.4%)

Algorithm
1×rewrite-expression-head
Error
13.0b
Rules
18×add-sqr-sqrt_binary64
15×*-un-lft-identity_binary64
12×add-exp-log_binary64
11×add-cube-cbrt_binary64 add-cbrt-cube_binary64
7×pow1_binary64
Counts
4 → 79
Calls

4 calls:

12.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
11.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
6.0ms
(*.f64 K (+.f64 m n))
Compiler

Compiled 2692 to 1327 computations (50.7% saved)

series240.0ms (2.7%)

Error
1.3b
Counts
4 → 63
Calls

4 calls:

83.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
43.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
35.0ms
(/.f64 (*.f64 K (+.f64 m n)) 2)
29.0ms
(*.f64 K (+.f64 m n))
Compiler

Compiled 4901 to 3218 computations (34.3% saved)

simplify135.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
360×distribute-rgt-in_binary64
345×distribute-lft-in_binary64
303×unswap-sqr_binary64
287×associate-/l*_binary64
238×*-commutative_binary64
Counts
142 → 100
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02282351
15212099
213992042
339272039
448802039
549362039

prune105.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New946100
Fresh000
Picked101
Done000
Total956101
Error
1.2b
Counts
101 → 6
Alt Table
StatusErrorProgram
13.4b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
36.0b
(*.f64 (cos.f64 (-.f64 (exp.f64 (log.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))))) 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 (*.f64 m 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))))
13.5b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2))) (sqrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
13.4b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (*.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))))
Compiler

Compiled 1993 to 1057 computations (47% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

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)

rewrite95.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Error
1.2b
Rules
9×add-sqr-sqrt_binary64
8×*-un-lft-identity_binary64
6×unpow-prod-down_binary64
4×add-cube-cbrt_binary64 add-log-exp_binary64
3×pow-unpow_binary64 pow1_binary64 add-exp-log_binary64
Counts
2 → 33
Calls

2 calls:

14.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
10.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
Compiler

Compiled 914 to 485 computations (46.9% saved)

series282.0ms (3.2%)

Error
1.2b
Counts
2 → 60
Calls

2 calls:

141.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
79.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
Compiler

Compiled 3800 to 2520 computations (33.7% saved)

simplify141.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
477×unswap-sqr_binary64
375×associate-+l+_binary64
369×associate--l+_binary64
286×sub-neg_binary64
258×log-prod_binary64
Counts
93 → 83
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01382319
13762062
28791927
329361927
443791927
548951927
649661927

prune97.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New83083
Fresh055
Picked011
Done000
Total83689
Error
1.2b
Counts
89 → 6
Alt Table
StatusErrorProgram
13.4b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
36.0b
(*.f64 (cos.f64 (-.f64 (exp.f64 (log.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))))) 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 (*.f64 m 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))))
13.5b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2))) (sqrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
13.4b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (*.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))))
Compiler

Compiled 1543 to 814 computations (47.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)
0.2b
(/.f64 (*.f64 m K) 2)
22.1b
(cos.f64 (-.f64 (/.f64 (*.f64 m K) 2) M))

rewrite206.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Error
1.2b
Rules
14×add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
10×add-exp-log_binary64
9×add-cube-cbrt_binary64 add-cbrt-cube_binary64
6×add-log-exp_binary64 unpow-prod-down_binary64
Counts
4 → 66
Calls

4 calls:

17.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 m K) 2) M))
4.0ms
(/.f64 (*.f64 m K) 2)
Compiler

Compiled 2209 to 1211 computations (45.2% saved)

series349.0ms (4%)

Error
1.2b
Counts
4 → 75
Calls

4 calls:

146.0ms
(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
80.0ms
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
25.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 m K) 2) M))
20.0ms
(/.f64 (*.f64 m K) 2)
Compiler

Compiled 5510 to 3686 computations (33.1% saved)

simplify121.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
383×associate-+l+_binary64
373×associate--l+_binary64
326×sub-neg_binary64
320×associate-*l*_binary64
279×associate-*r*_binary64
Counts
141 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02322973
15372646
212692511
342452511
449452511

prune147.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1132115
Fresh224
Picked011
Done011
Total1156121
Error
1.2b
Counts
121 → 6
Alt Table
StatusErrorProgram
13.4b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) 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 (*.f64 K (/.f64 m (sqrt.f64 2))) (sqrt.f64 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 (*.f64 m 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))))
36.1b
(*.f64 (cos.f64 (-.f64 (exp.f64 (log.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))))
13.4b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (*.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))))
Compiler

Compiled 2271 to 1234 computations (45.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 K (/.f64 m (sqrt.f64 2)))
0.4b
(/.f64 m (sqrt.f64 2))
0.5b
(/.f64 (*.f64 K (/.f64 m (sqrt.f64 2))) (sqrt.f64 2))
22.2b
(cos.f64 (-.f64 (/.f64 (*.f64 K (/.f64 m (sqrt.f64 2))) (sqrt.f64 2)) M))

rewrite305.0ms (3.5%)

Algorithm
1×rewrite-expression-head
Error
1.2b
Rules
46×add-sqr-sqrt_binary64
44×times-frac_binary64
38×add-cube-cbrt_binary64 *-un-lft-identity_binary64
28×sqrt-prod_binary64
22×associate-*r*_binary64
Counts
4 → 123
Calls

4 calls:

12.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (/.f64 m (sqrt.f64 2))) (sqrt.f64 2)) M))
10.0ms
(/.f64 (*.f64 K (/.f64 m (sqrt.f64 2))) (sqrt.f64 2))
10.0ms
(*.f64 K (/.f64 m (sqrt.f64 2)))
4.0ms
(/.f64 m (sqrt.f64 2))
Compiler

Compiled 4226 to 2680 computations (36.6% saved)

series123.0ms (1.4%)

Error
1.2b
Counts
4 → 24
Calls

4 calls:

36.0ms
(/.f64 (*.f64 K (/.f64 m (sqrt.f64 2))) (sqrt.f64 2))
31.0ms
(cos.f64 (-.f64 (/.f64 (*.f64 K (/.f64 m (sqrt.f64 2))) (sqrt.f64 2)) M))
29.0ms
(*.f64 K (/.f64 m (sqrt.f64 2)))
12.0ms
(/.f64 m (sqrt.f64 2))
Compiler

Compiled 1853 to 1338 computations (27.8% saved)

simplify173.0ms (2%)

Algorithm
1×egg-herbie
Rules
397×associate-*l*_binary64
358×associate-/r/_binary64
341×associate-*r*_binary64
322×associate-/r*_binary64
262×distribute-rgt-in_binary64
Counts
147 → 97
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01832313
13631837
211711836
327431820
434161820
546441820
649291820
748981820

prune117.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh033
Picked101
Done112
Total985103
Error
1.2b
Counts
103 → 5
Alt Table
StatusErrorProgram
13.4b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 K (+.f64 m n))) 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))))
36.1b
(*.f64 (cos.f64 (-.f64 (exp.f64 (log.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))))
9.3b
(*.f64 (cos.f64 (-.f64 (*.f64 (/.f64 K (fabs.f64 (cbrt.f64 2))) (/.f64 (/.f64 m (sqrt.f64 2)) (sqrt.f64 (cbrt.f64 2)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
13.4b
(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (*.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))))
Compiler

Compiled 1881 to 1133 computations (39.8% saved)

regimes1.3s (15.1%)

Accuracy

Total 0.2b remaining (16.2%)

Threshold costs 0.2b (16.2%)

Compiler

Compiled 26336 to 18390 computations (30.2% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
12×+-commutative_binary64
10×sub-neg_binary64
7×*-commutative_binary64
6×neg-mul-1_binary64 neg-sub0_binary64
2×unsub-neg_binary64 distribute-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01833
13233
24733
36133
46933
57233
67233

end8.0ms (0.1%)

Remove

(sort m n)

Compiler

Compiled 78 to 57 computations (26.9% saved)

sample1.8s (20.8%)

Algorithm
1×intervals
Results
1.0s7830×body128valid
37.0ms80×body1024invalid
33.0ms64×body1024valid
31.0ms73×body512invalid
30.0ms297×body128invalid
23.0ms72×body512valid
12.0ms58×body256invalid
9.0ms16×body2048invalid
7.0ms33×body256valid
1.0ms1×body2048valid
Compiler

Compiled 262 to 185 computations (29.4% saved)

Profiling

Loading profile data...