Details

analyze1.6s (9.6%)

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%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample109.0ms (0.7%)

Algorithm

1×

intervals

Results

38.0ms	256×	body	128	valid
26.0ms	214×	body	128	nan
18.0ms	129×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify121.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5205	41

prune9.0ms (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: 30.1b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.1b	(sqrt.f64 (/.f64 d l))
12.4b	(sqrt.f64 (/.f64 d h))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_1139`
41×	`prod-exp_binary64_1150`
32×	`add-sqr-sqrt_binary64_1123`
29×	`times-frac_binary64_1107`
26×	`*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
21×	`add-cbrt-cube_binary64_1137`
16×	`associate-r_binary64_1041` `div-exp_binary64_1152`
14×	`sqrt-div_binary64_1118`
13×	`pow1_binary64_1162`
10×	`pow-exp_binary64_1169`
9×	`cbrt-unprod_binary64_1134` `frac-times_binary64_1111`
6×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
4×	`rem-sqrt-square_binary64_1114` `add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172`
3×	`div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `distribute-lft-in_binary64_1050` `cbrt-undiv_binary64_1135` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051` `pow1/2_binary64_1181`

Counts

4 → 127

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d h))
3.0ms	(sqrt.f64 (/.f64 d l))

series480.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

308.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
91.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
41.0ms	(sqrt.f64 (/.f64 d l))
40.0ms	(sqrt.f64 (/.f64 d h))

simplify84.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5007	3595

prune278.0ms (1.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	119	20	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	20	140

Merged error: 14.8b

Counts

140 → 20

Compiler

Compiled 5406 to 2681 computations (50.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.3b	(/.f64 (.f64 M D) (.f64 d 2))
7.5b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
12.1b	(sqrt.f64 (/.f64 d l))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite62.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64_1139`
48×	`prod-exp_binary64_1150`
37×	`add-cbrt-cube_binary64_1137`
22×	`add-sqr-sqrt_binary64_1123`
20×	`times-frac_binary64_1107` `div-exp_binary64_1152`
19×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`cbrt-unprod_binary64_1134` `pow1_binary64_1162` `associate-r_binary64_1041`
13×	`sqrt-prod_binary64_1117` `sqrt-div_binary64_1118`
12×	`associate-*r/_binary64_1043`
10×	`pow-exp_binary64_1169`
9×	`frac-times_binary64_1111`
7×	`pow-prod-down_binary64_1172`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105`
3×	`div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`
1×	`frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 126

Calls

4 calls:

22.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
14.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

series1.2s (7.5%)

Counts

4 → 12

Calls

4 calls:

1.1s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
91.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
39.0ms	(sqrt.f64 (/.f64 d l))
24.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5089	4485

prune250.0ms (1.5%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	134	24	158

Merged error: 12.8b

Counts

158 → 24

Compiler

Compiled 6893 to 2781 computations (59.7% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
4.3b	(/.f64 (.f64 M D) (.f64 d 2))
7.5b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite88.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
37×	`sqrt-div_binary64_1118`
30×	`add-sqr-sqrt_binary64_1123` `associate-*r/_binary64_1043` `times-frac_binary64_1107`
29×	`frac-times_binary64_1111`
25×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
23×	`cbrt-unprod_binary64_1134`
22×	`sqrt-prod_binary64_1117`
20×	`div-exp_binary64_1152`
16×	`associate-r_binary64_1041` `associate-*l/_binary64_1044`
14×	`pow-prod-down_binary64_1172`
10×	`pow-exp_binary64_1169` `cbrt-prod_binary64_1132`
8×	`flip--_binary64_1076` `flip3--_binary64_1105`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
3×	`rem-sqrt-square_binary64_1114` `div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`
1×	`frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 154

Calls

4 calls:

39.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
5.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

series1.7s (10.4%)

Counts

4 → 12

Calls

4 calls:

1.5s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
98.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
93.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
22.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify115.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4974	7171
1	4974	7171

prune357.0ms (2.1%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	2	21	23
Picked	1	0	1
Done	0	0	0
Total	167	23	190

Merged error: 12.3b

Counts

190 → 23

Compiler

Compiled 10009 to 4157 computations (58.5% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
4.3b	(/.f64 (.f64 M D) (.f64 d 2))
7.5b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite70.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
30×	`add-sqr-sqrt_binary64_1123` `times-frac_binary64_1107`
25×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
23×	`cbrt-unprod_binary64_1134`
22×	`sqrt-prod_binary64_1117`
20×	`div-exp_binary64_1152`
18×	`associate-*r/_binary64_1043`
16×	`associate-r_binary64_1041`
14×	`pow-prod-down_binary64_1172`
13×	`sqrt-div_binary64_1118`
10×	`pow-exp_binary64_1169` `cbrt-prod_binary64_1132`
9×	`frac-times_binary64_1111`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105`
3×	`rem-sqrt-square_binary64_1114` `div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`
1×	`frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 142

Calls

4 calls:

25.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
5.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

series1.7s (10%)

Counts

4 → 12

Calls

4 calls:

1.4s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
101.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
97.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
23.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4959	5759
1	4959	5759

prune256.0ms (1.5%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	1	21	22
Picked	1	0	1
Done	0	0	0
Total	152	25	177

Merged error: 11.8b

Counts

177 → 25

Compiler

Compiled 7627 to 2560 computations (66.4% saved)

regimes1.6s (9.8%)

Compiler: Compiled 22739 to 16463 computations (27.6% saved)

bsearch7.0ms (0%)

Compiler: Compiled 35 to 31 computations (11.4% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	205	298
1	205	298

end0.0ms (0%)

sample6.1s (36.8%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.0s	8243×	body	128	nan
678.0ms	4859×	body	128	invalid

Compiler

Compiled 3446 to 2456 computations (28.7% saved)

Details

analyze1.6s (9.6%)

sample109.0ms (0.7%)

simplify121.0ms (0.7%)

prune9.0ms (0.1%)

localize18.0ms (0.1%)

rewrite48.0ms (0.3%)

series480.0ms (2.9%)

simplify84.0ms (0.5%)

prune278.0ms (1.7%)

localize25.0ms (0.1%)

rewrite62.0ms (0.4%)

series1.2s (7.5%)

simplify100.0ms (0.6%)

prune250.0ms (1.5%)

localize31.0ms (0.2%)

rewrite88.0ms (0.5%)

series1.7s (10.4%)

simplify115.0ms (0.7%)

prune357.0ms (2.1%)

localize31.0ms (0.2%)

rewrite70.0ms (0.4%)

series1.7s (10%)

simplify113.0ms (0.7%)

prune256.0ms (1.5%)

regimes1.6s (9.8%)

bsearch7.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample6.1s (36.8%)

Profiling