Details

analyze2.9s (8.9%)

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)

sample86.0ms (0.3%)

Algorithm

1×

intervals

Results

52.0ms	253×	body	128	valid
2.0ms	3×	body	1024	invalid
2.0ms	4×	body	512	invalid
2.0ms	12×	body	128	invalid
1.0ms	3×	body	256	invalid
1.0ms	1×	body	2048	invalid
1.0ms	1×	body	512	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify155.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5097	43

prune8.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 12.9b

Counts

2 → 2

Compiler

Compiled 85 to 67 computations (21.2% saved)

localize47.0ms (0.1%)

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))
0.0b	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
32.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite117.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_760`
22×	`add-sqr-sqrt_binary64_782`
15×	`add-log-exp_binary64_799`
11×	`add-cube-cbrt_binary64_795`
8×	`exp-prod_binary64_812` `cancel-sign-sub-inv_binary64_726` `distribute-lft-out--_binary64_712`
7×	`add-exp-log_binary64_798` `exp-sum_binary64_806` `pow1_binary64_821`
6×	`diff-log_binary64_852` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
5×	`rem-exp-log_binary64_800`
4×	`cos-sum_binary64_894` `difference-of-squares_binary64_729` `associate-r_binary64_700`
3×	`associate-l_binary64_701` `pow-unpow_binary64_837`
2×	`neg-log_binary64_853` `associate-*r/_binary64_702` `distribute-rgt-neg-in_binary64_718` `sub-neg_binary64_753`
1×	`unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `unpow2_binary64_825` `prod-exp_binary64_809` `flip3-+_binary64_763` `distribute-lft-in_binary64_709` `exp-diff_binary64_808` `pow-exp_binary64_828` `distribute-rgt-in_binary64_710` `flip-+_binary64_734` `pow-to-exp_binary64_829` `associate--r-_binary64_699` `sqr-pow_binary64_732` `cos-diff_binary64_897` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `times-frac_binary64_766` `*-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 84

Calls

4 calls:

47.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
21.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
18.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
12.0ms	(*.f64 K (+.f64 m n))

series404.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
111.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
72.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
25.0ms	(*.f64 K (+.f64 m n))

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5200	1713

prune768.0ms (2.3%)

Pruning

35 alts after pruning (34 fresh and 1 done)

	Pruned	Kept	Total
New	63	33	96
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	63	35	98

Merged error: 0.6b

Counts

98 → 35

Compiler

Compiled 4666 to 2520 computations (46% saved)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))

rewrite65.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_760`
15×	`add-sqr-sqrt_binary64_782`
13×	`add-log-exp_binary64_799`
8×	`exp-prod_binary64_812` `distribute-lft-out--_binary64_712`
7×	`exp-sum_binary64_806`
6×	`diff-log_binary64_852` `add-cube-cbrt_binary64_795` `unpow-prod-down_binary64_839`
5×	`cancel-sign-sub-inv_binary64_726` `rem-exp-log_binary64_800`
4×	`difference-of-squares_binary64_729`
3×	`add-exp-log_binary64_798` `pow1_binary64_821` `pow-unpow_binary64_837`
2×	`add-cbrt-cube_binary64_796` `neg-log_binary64_853` `distribute-rgt-neg-in_binary64_718`
1×	`unpow2_binary64_825` `exp-diff_binary64_808` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `associate--r-_binary64_699` `sqr-pow_binary64_732` `sub-neg_binary64_753` `times-frac_binary64_766` `pow-pow_binary64_832`

Counts

2 → 49

Calls

2 calls:

35.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
24.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series252.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

194.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
58.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify71.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5016	1126

prune577.0ms (1.7%)

Pruning

56 alts after pruning (54 fresh and 2 done)

	Pruned	Kept	Total
New	34	21	55
Fresh	0	33	33
Picked	0	1	1
Done	0	1	1
Total	34	56	90

Merged error: 0.6b

Counts

90 → 56

Compiler

Compiled 3383 to 2214 computations (34.6% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) 3)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
0.2b	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) 3))

rewrite109.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_760`
28×	`add-sqr-sqrt_binary64_782`
25×	`exp-sum_binary64_806`
22×	`cbrt-prod_binary64_791` `unpow-prod-down_binary64_839`
20×	`cancel-sign-sub-inv_binary64_726`
19×	`add-cube-cbrt_binary64_795`
16×	`cube-prod_binary64_788`
12×	`exp-prod_binary64_812`
10×	`add-log-exp_binary64_799`
8×	`pow-pow_binary64_832`
7×	`distribute-lft-out_binary64_711`
6×	`pow1_binary64_821` `pow-unpow_binary64_837`
5×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712` `sub-neg_binary64_753`
4×	`difference-of-squares_binary64_729`
3×	`exp-diff_binary64_808` `rem-exp-log_binary64_800` `sqr-pow_binary64_732`
2×	`cube-mult_binary64_790` `diff-log_binary64_852` `unpow3_binary64_826` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `cube-div_binary64_789`
1×	`pow1/3_binary64_842` `rem-cbrt-cube_binary64_784` `unpow2_binary64_825` `rem-cube-cbrt_binary64_783` `sum-log_binary64_851` `cbrt-div_binary64_792` `times-frac_binary64_766`

Counts

4 → 115

Calls

4 calls:

30.0ms	(pow.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) 3)
26.0ms	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) 3))
22.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series1.2s (3.6%)

Counts

4 → 12

Calls

4 calls:

667.0ms	(pow.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) 3)
235.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
231.0ms	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) 3))
62.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify115.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4983	3709
1	4983	3709

prune1.5s (4.5%)

Pruning

73 alts after pruning (71 fresh and 2 done)

	Pruned	Kept	Total
New	105	22	127
Fresh	4	49	53
Picked	1	0	1
Done	0	2	2
Total	110	73	183

Merged error: 0.6b

Counts

183 → 73

Compiler

Compiled 6245 to 4054 computations (35.1% saved)

localize31.0ms (0.1%)

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	(exp.f64 (-.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)))
0.2b	(cbrt.f64 (.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))

rewrite195.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_760`
22×	`add-log-exp_binary64_799`
18×	`exp-prod_binary64_812`
16×	`add-sqr-sqrt_binary64_782`
15×	`exp-diff_binary64_808` `exp-sum_binary64_806`
12×	`cancel-sign-sub-inv_binary64_726`
10×	`add-cube-cbrt_binary64_795`
9×	`rem-exp-log_binary64_800`
7×	`cbrt-div_binary64_792`
6×	`diff-log_binary64_852` `distribute-lft-out_binary64_711` `distribute-lft-out--_binary64_712`
5×	`associate-*l/_binary64_703` `frac-times_binary64_770`
4×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`difference-of-squares_binary64_729` `sum-log_binary64_851` `associate-*r/_binary64_702` `sub-neg_binary64_753`
1×	`pow1/3_binary64_842` `rem-cbrt-cube_binary64_784` `pow3_binary64_843` `cbrt-prod_binary64_791`

Counts

4 → 83

Calls

4 calls:

118.0ms	(cbrt.f64 (.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (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)))
20.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
19.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

series808.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(cbrt.f64 (.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
218.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
207.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
164.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

simplify143.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4970	2679
1	4970	2679

prune1.8s (5.4%)

Pruning

82 alts after pruning (79 fresh and 3 done)

	Pruned	Kept	Total
New	83	12	95
Fresh	3	67	70
Picked	0	1	1
Done	0	2	2
Total	86	82	168

Merged error: 0.6b

Counts

168 → 82

Compiler

Compiled 5519 to 2848 computations (48.4% saved)

regimes4.8s (14.6%)

Compiler: Compiled 49484 to 36936 computations (25.4% saved)

bsearch5.0s (15.3%)

simplify80.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	67	84
1	67	84

end0.0ms (0%)

sample11.6s (35%)

Algorithm

1×

intervals

Results

1.2s	7836×	body	128	valid
61.0ms	99×	body	1024	invalid
51.0ms	301×	body	128	invalid
42.0ms	59×	body	1024	valid
39.0ms	83×	body	512	invalid
34.0ms	73×	body	512	valid
15.0ms	49×	body	256	invalid
15.0ms	32×	body	256	valid
14.0ms	15×	body	2048	invalid

Compiler

Compiled 8614 to 6431 computations (25.3% saved)

Pareto

0.32080197964943885

Details

analyze2.9s (8.9%)

sample86.0ms (0.3%)

simplify155.0ms (0.5%)

prune8.0ms (0%)

localize47.0ms (0.1%)

rewrite117.0ms (0.4%)

series404.0ms (1.2%)

simplify92.0ms (0.3%)

prune768.0ms (2.3%)

localize17.0ms (0.1%)

rewrite65.0ms (0.2%)

series252.0ms (0.8%)

simplify71.0ms (0.2%)

prune577.0ms (1.7%)

localize35.0ms (0.1%)

rewrite109.0ms (0.3%)

series1.2s (3.6%)

simplify115.0ms (0.3%)

prune1.5s (4.5%)

localize31.0ms (0.1%)

rewrite195.0ms (0.6%)

series808.0ms (2.4%)

simplify143.0ms (0.4%)

prune1.8s (5.4%)

regimes4.8s (14.6%)

bsearch5.0s (15.3%)

simplify80.0ms (0.2%)

end0.0ms (0%)

sample11.6s (35%)

Profiling