Details

analyze3.2s (14.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5015	432
0	6	6
1	6	6

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

Symmetry

(sort M D)

Compiler

Compiled 19 to 19 computations (0% saved)

sample70.0ms (0.3%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
9.0ms	117×	body	128	nan
4.0ms	43×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (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

Error

13.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.1b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
8.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite473.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

7.9b

Rules

67×	`add-exp-log_binary64_1139`
38×	`add-sqr-sqrt_binary64_1123`
27×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
19×	`div-exp_binary64_1152` `associate-r_binary64_1041`
17×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
15×	`times-frac_binary64_1107`
13×	`associate-l_binary64_1042`
10×	`pow-exp_binary64_1169` `unswap-sqr_binary64_1069`
7×	`pow1_binary64_1162` `cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`unpow2_binary64_1166` `sqr-pow_binary64_1073` `associate-*r/_binary64_1043` `div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `*-commutative_binary64_1032` `flip3--_binary64_1105` `flip--_binary64_1076`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow-prod-down_binary64_1172`

Counts

4 → 116

Calls

4 calls:

16.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

Compiler

Compiled 3444 to 1962 computations (43% saved)

series2.1s (9.5%)

Error

7.8b

Counts

4 → 75

Calls

4 calls:

740.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
614.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
513.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
138.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4737 to 4130 computations (12.8% saved)

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5030	4354

prune265.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	179	12	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	12	192

Error

5.8b

Counts

192 → 12

Compiler

Compiled 4584 to 2413 computations (47.4% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.1b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
5.6b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)

rewrite204.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

Rules

67×	`add-exp-log_binary64_1139`
26×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
20×	`div-exp_binary64_1152` `add-sqr-sqrt_binary64_1123`
13×	`*-un-lft-identity_binary64_1101`
10×	`pow-exp_binary64_1169` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
6×	`cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `sqrt-prod_binary64_1117` `unpow-prod-down_binary64_1180`
5×	`pow1_binary64_1162` `times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045` `unswap-sqr_binary64_1069`
3×	`div-inv_binary64_1098` `associate-l_binary64_1042`
2×	`pow-to-exp_binary64_1170` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `sqrt-div_binary64_1118` `difference-of-squares_binary64_1070` `unpow2_binary64_1166` `sqr-pow_binary64_1073`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114` `*-commutative_binary64_1032`

Counts

4 → 99

Calls

4 calls:

12.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2731 to 1689 computations (38.2% saved)

series1.7s (8%)

Error

5.5b

Counts

4 → 62

Calls

4 calls:

618.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
498.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
429.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
128.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4060 to 3591 computations (11.6% saved)

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4963	3300
1	4963	3300

prune215.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	161	12	173

Error

5.1b

Counts

173 → 12

Compiler

Compiled 3760 to 2273 computations (39.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.1b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
5.6b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)

rewrite326.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

233×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
107×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
83×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
11×	`add-sqr-sqrt_binary64_1123`
10×	`*-un-lft-identity_binary64_1101`
7×	`add-cube-cbrt_binary64_1136`
6×	`sqrt-prod_binary64_1117`
5×	`pow1_binary64_1162` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-r/_binary64_1043` `associate-/l/_binary64_1048` `associate-/l_binary64_1046`
2×	`sqrt-div_binary64_1118` `difference-of-squares_binary64_1070`
1×	`frac-times_binary64_1111` `associate-*l/_binary64_1044` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114`

Counts

4 → 142

Calls

4 calls:

19.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
9.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 5730 to 2829 computations (50.6% saved)

series1.6s (7.2%)

Error

5.1b

Counts

4 → 59

Calls

4 calls:

681.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
515.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
168.0ms	(/.f64 (.f64 M D) (.f64 2 d))
150.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4078 to 3393 computations (16.8% saved)

simplify144.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5099	4994

prune327.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	201	12	213

Error

5.1b

Counts

213 → 12

Compiler

Compiled 5533 to 2990 computations (46% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.5b	(cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.5b	(cbrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))))
8.3b	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite446.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

102×	`add-exp-log_binary64_1139`
56×	`add-sqr-sqrt_binary64_1123`
44×	`prod-exp_binary64_1150`
30×	`div-exp_binary64_1152`
28×	`times-frac_binary64_1107`
24×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
23×	`associate-l_binary64_1042` `associate-r_binary64_1041`
20×	`pow-exp_binary64_1169`
16×	`unswap-sqr_binary64_1069`
14×	`add-cbrt-cube_binary64_1137` `unpow-prod-down_binary64_1180`
6×	`unpow2_binary64_1166` `sqr-pow_binary64_1073` `cbrt-prod_binary64_1132`
4×	`pow1_binary64_1162` `pow-to-exp_binary64_1170` `add-log-exp_binary64_1140` `cbrt-unprod_binary64_1134` `div-inv_binary64_1098` `cbrt-div_binary64_1133`
2×	`cbrt-undiv_binary64_1135` `*-commutative_binary64_1032` `pow1/3_binary64_1183` `flip3--_binary64_1105` `flip--_binary64_1076`
1×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`

Counts

4 → 138

Calls

4 calls:

12.0ms	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.0ms	(cbrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))))

Compiler

Compiled 6694 to 3913 computations (41.5% saved)

series3.0s (13.8%)

Error

5.1b

Counts

4 → 80

Calls

4 calls:

793.0ms	(cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
777.0ms	(cbrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))))
657.0ms	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
613.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

Compiler

Compiled 10514 to 8498 computations (19.2% saved)

simplify136.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5004	5603

prune584.0ms (2.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	217	13	230

Error

5.1b

Counts

230 → 13

Compiler

Compiled 9341 to 5432 computations (41.8% saved)

regimes2.8s (12.6%)

Accuracy

Total 4.9b remaining (55.6%)

Threshold costs 0b (0%)

Compiler

Compiled 29937 to 25817 computations (13.8% saved)

bsearch3.0ms (0%)

Compiler: Compiled 7 to 10 computations (-42.9% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	120	80
1	120	80

Compiler

Compiled 106 to 78 computations (26.4% saved)

end0.0ms (0%)

sample4.0s (18.2%)

Algorithm

1×

intervals

Results

744.0ms	8000×	body	128	valid
279.0ms	3057×	body	128	nan
127.0ms	1338×	body	128	invalid

Compiler

Compiled 1729 to 1494 computations (13.6% saved)

Details

analyze3.2s (14.5%)

sample70.0ms (0.3%)

simplify64.0ms (0.3%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite473.0ms (2.2%)

series2.1s (9.5%)

simplify91.0ms (0.4%)

prune265.0ms (1.2%)

localize28.0ms (0.1%)

rewrite204.0ms (0.9%)

series1.7s (8%)

simplify99.0ms (0.5%)

prune215.0ms (1%)

localize14.0ms (0.1%)

rewrite326.0ms (1.5%)

series1.6s (7.2%)

simplify144.0ms (0.7%)

prune327.0ms (1.5%)

localize29.0ms (0.1%)

rewrite446.0ms (2%)

series3.0s (13.8%)

simplify136.0ms (0.6%)

prune584.0ms (2.7%)

regimes2.8s (12.6%)

bsearch3.0ms (0%)

simplify13.0ms (0.1%)

end0.0ms (0%)

sample4.0s (18.2%)

Profiling