Details

analyze2.1s (24.9%)

Algorithm

1×

Search

True	Other	False	Iter
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 30 to 24 computations (20% saved)

sample50.0ms (0.6%)

Algorithm

1×

intervals

Results

24.0ms	252×	body	128	valid
2.0ms	7×	body	512	invalid
1.0ms	10×	body	128	invalid
1.0ms	2×	body	2048	invalid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	1024	invalid
0.0ms	2×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify141.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5097	43

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.8b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.2b	(/.f64 (*.f64 K (+.f64 m n)) 2)
33.8b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
12×	`add-exp-log_binary64_798`
11×	`add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796`
7×	`pow1_binary64_821`
6×	`unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799` `associate-r_binary64_700` `associate-*r/_binary64_702` `times-frac_binary64_766`
3×	`cancel-sign-sub-inv_binary64_726` `associate-/r_binary64_704` `associate-l*_binary64_701` `pow-unpow_binary64_837`
2×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `flip3-+_binary64_763` `associate-/l/_binary64_707` `difference-of-squares_binary64_729` `flip-+_binary64_734` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `distribute-lft-out_binary64_711` `unpow2_binary64_825` `distribute-lft-in_binary64_709` `pow-exp_binary64_828` `div-inv_binary64_757` `distribute-rgt-in_binary64_710` `associate-/l_binary64_705` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `sqr-pow_binary64_732` `cos-diff_binary64_897` `clear-num_binary64_759` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 79

Calls

4 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
6.0ms	(*.f64 K (+.f64 m n))

series188.0ms (2.2%)

Counts

4 → 39

Calls

4 calls:

85.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
39.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
37.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
27.0ms	(*.f64 K (+.f64 m n))

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5022	1738

prune178.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	5	119

Merged error: 13.1b

Counts

119 → 5

Compiler

Compiled 4016 to 1979 computations (50.7% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))))
7.2b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
24.3b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
24.4b	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

rewrite66.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cancel-sign-sub-inv_binary64_726`
20×	`sin-sum_binary64_893`
16×	`*-un-lft-identity_binary64_760` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `add-sqr-sqrt_binary64_782`
14×	`add-cube-cbrt_binary64_795`
11×	`add-cbrt-cube_binary64_796` `pow1_binary64_821`
10×	`add-exp-log_binary64_798`
9×	`associate-r_binary64_700`
7×	`sub-neg_binary64_753`
6×	`associate-l_binary64_701`
5×	`exp-sum_binary64_806`
4×	`prod-exp_binary64_809` `cos-sum_binary64_894` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
3×	`exp-diff_binary64_808`
2×	`associate-l/_binary64_703` `frac-times_binary64_770` `-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`
1×	`unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `cos-diff_binary64_897` `sin-diff_binary64_896`

Counts

4 → 86

Calls

4 calls:

27.0ms	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
12.0ms	(.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))))
7.0ms	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
7.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

series1.2s (14%)

Counts

4 → 45

Calls

4 calls:

870.0ms	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
237.0ms	(.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))))
41.0ms	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
37.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

simplify108.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4990	6380
1	4990	6380

prune348.0ms (4.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	131	5	136

Merged error: 9.3b

Counts

136 → 5

Compiler

Compiled 7753 to 3979 computations (48.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
0.0b	(*.f64 K (/.f64 (+.f64 m n) 2))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
33.8b	(cos.f64 (-.f64 (*.f64 K (/.f64 (+.f64 m n) 2)) M))

rewrite61.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_760`
30×	`add-sqr-sqrt_binary64_782`
18×	`add-cube-cbrt_binary64_795`
16×	`associate-r_binary64_700`
14×	`times-frac_binary64_766`
10×	`add-exp-log_binary64_798` `add-log-exp_binary64_799`
9×	`add-cbrt-cube_binary64_796`
7×	`cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
6×	`exp-prod_binary64_812` `unpow-prod-down_binary64_839`
5×	`distribute-lft-out_binary64_711` `exp-sum_binary64_806`
4×	`cos-sum_binary64_894`
3×	`rem-exp-log_binary64_800` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `associate-l_binary64_701` `pow-unpow_binary64_837`
2×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `sub-neg_binary64_753`
1×	`cbrt-undiv_binary64_794` `unpow2_binary64_825` `exp-diff_binary64_808` `pow-exp_binary64_828` `div-inv_binary64_757` `pow-to-exp_binary64_829` `sum-log_binary64_851` `associate-r/_binary64_702` `sqr-pow_binary64_732` `cos-diff_binary64_897` `div-exp_binary64_811` `pow-prod-down_binary64_831` `-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 90

Calls

4 calls:

22.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(*.f64 K (/.f64 (+.f64 m n) 2))
9.0ms	(cos.f64 (-.f64 (*.f64 K (/.f64 (+.f64 m n) 2)) M))

series329.0ms (3.9%)

Counts

4 → 42

Calls

4 calls:

170.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
81.0ms	(cos.f64 (-.f64 (*.f64 K (/.f64 (+.f64 m n) 2)) M))
41.0ms	(*.f64 K (/.f64 (+.f64 m n) 2))
37.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5411	2755

prune194.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	132	5	137

Merged error: 9.3b

Counts

137 → 5

Compiler

Compiled 4802 to 2425 computations (49.5% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

13.8b	(cbrt.f64 (*.f64 K (+.f64 m n)))
13.8b	(cbrt.f64 (*.f64 K (+.f64 m n)))
13.8b	(cbrt.f64 (*.f64 K (+.f64 m n)))
33.6b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.f64 (*.f64 K (+.f64 m n)))) 2) M))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-div_binary64_792` `associate-*r/_binary64_702`
5×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
4×	`cos-sum_binary64_894` `add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`pow1/3_binary64_842` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `flip-+_binary64_734` `cbrt-prod_binary64_791`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753`

Counts

4 → 45

Calls

4 calls:

15.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.f64 (*.f64 K (+.f64 m n)))) 2) M))
5.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
5.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
5.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))

series610.0ms (7.2%)

Counts

4 → 39

Calls

4 calls:

170.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
167.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
154.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
119.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.f64 (*.f64 K (+.f64 m n)))) 2) M))

simplify86.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4904	1510
1	4904	1510

prune125.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	83	6	89

Merged error: 9.3b

Counts

89 → 6

Compiler

Compiled 3792 to 1414 computations (62.7% saved)

regimes404.0ms (4.8%)

Compiler: Compiled 4802 to 3258 computations (32.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 29 to 23 computations (20.7% saved)

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	1113	299
1	1113	299

end0.0ms (0%)

sample1.9s (22.5%)

Algorithm

1×

intervals

Results

771.0ms	7849×	body	128	valid
35.0ms	80×	body	1024	invalid
33.0ms	85×	body	512	invalid
31.0ms	314×	body	128	invalid
27.0ms	62×	body	1024	valid
18.0ms	45×	body	512	valid
11.0ms	57×	body	256	invalid
9.0ms	43×	body	256	valid
7.0ms	14×	body	2048	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 1013 to 644 computations (36.4% saved)

Details

analyze2.1s (24.9%)

sample50.0ms (0.6%)

simplify141.0ms (1.7%)

prune5.0ms (0.1%)

localize22.0ms (0.3%)

rewrite42.0ms (0.5%)

series188.0ms (2.2%)

simplify62.0ms (0.7%)

prune178.0ms (2.1%)

localize28.0ms (0.3%)

rewrite66.0ms (0.8%)

series1.2s (14%)

simplify108.0ms (1.3%)

prune348.0ms (4.1%)

localize17.0ms (0.2%)

rewrite61.0ms (0.7%)

series329.0ms (3.9%)

simplify75.0ms (0.9%)

prune194.0ms (2.3%)

localize23.0ms (0.3%)

rewrite35.0ms (0.4%)

series610.0ms (7.2%)

simplify86.0ms (1%)

prune125.0ms (1.5%)

regimes404.0ms (4.8%)

bsearch2.0ms (0%)

simplify48.0ms (0.6%)

end0.0ms (0%)

sample1.9s (22.5%)

Profiling