Details

analyze2.3s (23.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

sample56.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	80	valid
8.0ms	95×	body	80	nan
3.0ms	34×	body	80	invalid

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4904	18
1	4904	18

prune11.0ms (0.1%)

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: 12.1b

Counts

2 → 1

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.4b	(.f64 w0 (sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0) (/.f64 h l)))))
3.5b	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))
4.7b	(/.f64 (.f64 M D) (.f64 2.0 d))
9.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
35×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64` `div-exp_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`times-frac_binary64`
12×	`associate-l_binary64`
10×	`pow-exp_binary64`
8×	`unswap-sqr_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 113

Calls

4 calls:

11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))
9.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))

series678.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(.f64 w0 (sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0) (/.f64 h l)))))
237.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))
190.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))
8.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4977	1927
1	4977	1927

prune247.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	8	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Merged error: 6.7b

Counts

126 → 8

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))
3.8b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))
4.7b	(/.f64 (.f64 M D) (.f64 2.0 d))
6.4b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log_binary64`
91×	`prod-exp_binary64`
40×	`div-exp_binary64`
30×	`add-cbrt-cube_binary64`
25×	`pow-exp_binary64`
22×	`associate-r_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`cbrt-unprod_binary64` `times-frac_binary64`
8×	`1-exp_binary64` `rec-exp_binary64`
7×	`pow1_binary64`
6×	`cbrt-undiv_binary64` `unpow-prod-down_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
3×	`unswap-sqr_binary64` `div-inv_binary64` `sqrt-prod_binary64`
2×	`sqr-pow_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `un-div-inv_binary64` `flip--_binary64`

Counts

4 → 128

Calls

4 calls:

12.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
5.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))

series730.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

356.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))
203.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))
161.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))
9.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5085	1894

prune254.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 6.3b

Counts

148 → 8

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))))
3.8b	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
5.7b	(*.f64 (/.f64 M 2.0) (/.f64 D d))
6.4b	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log_binary64`
91×	`prod-exp_binary64`
44×	`add-sqr-sqrt_binary64`
40×	`div-exp_binary64`
31×	`associate-r_binary64` `times-frac_binary64`
30×	`add-cbrt-cube_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`pow-exp_binary64`
17×	`associate-l_binary64`
11×	`cbrt-unprod_binary64`
9×	`pow1_binary64`
8×	`1-exp_binary64` `rec-exp_binary64`
6×	`cbrt-undiv_binary64` `unswap-sqr_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64`
3×	`div-inv_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
2×	`pow-prod-down_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `un-div-inv_binary64` `flip--_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 152

Calls

4 calls:

11.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
11.0ms	(*.f64 (/.f64 M 2.0) (/.f64 D d))
8.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))))
6.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))

series730.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

349.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))
203.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
170.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))))
8.0ms	(*.f64 (/.f64 M 2.0) (/.f64 D d))

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4979	2107
1	4979	2107

prune282.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	164	8	172

Merged error: 6.3b

Counts

172 → 8

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2)) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))))))
4.7b	(/.f64 (.f64 M D) (.f64 2.0 d))
4.7b	(/.f64 (.f64 M D) (.f64 2.0 d))
10.4b	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64`
33×	`add-cbrt-cube_binary64`
30×	`prod-exp_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`div-exp_binary64`
15×	`times-frac_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`associate-l_binary64`
10×	`cbrt-unprod_binary64` `pow-exp_binary64`
9×	`associate-r_binary64` `cbrt-undiv_binary64`
7×	`unpow-prod-down_binary64`
6×	`unswap-sqr_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
3×	`sqr-pow_binary64` `sqrt-prod_binary64`
2×	`pow-to-exp_binary64` `associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 110

Calls

4 calls:

11.0ms	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))
9.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2)) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))))))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

series631.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

428.0ms	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))
188.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2)) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))))))
8.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
8.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4986	1788
1	4986	1788

prune218.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	122	8	130

Merged error: 6.3b

Counts

130 → 8

regimes1.7s (17.5%)

Accuracy

Total 1.5b remaining (16.3%)

Threshold costs 0b (0%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	169	68
1	169	68

end0.0ms (0%)

sample1.5s (14.8%)

Algorithm

1×

intervals

Results

632.0ms	8000×	body	80	valid
251.0ms	3134×	body	80	nan
114.0ms	1331×	body	80	invalid

Details

analyze2.3s (23.4%)

sample56.0ms (0.6%)

simplify60.0ms (0.6%)

prune11.0ms (0.1%)

localize15.0ms (0.1%)

rewrite38.0ms (0.4%)

series678.0ms (6.9%)

simplify74.0ms (0.7%)

prune247.0ms (2.5%)

localize16.0ms (0.2%)

rewrite38.0ms (0.4%)

series730.0ms (7.4%)

simplify43.0ms (0.4%)

prune254.0ms (2.6%)

localize15.0ms (0.2%)

rewrite44.0ms (0.4%)

series730.0ms (7.4%)

simplify69.0ms (0.7%)

prune282.0ms (2.9%)

localize17.0ms (0.2%)

rewrite39.0ms (0.4%)

series631.0ms (6.4%)

simplify62.0ms (0.6%)

prune218.0ms (2.2%)

regimes1.7s (17.5%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.5s (14.8%)

Profiling