Details

analyze2.4s (15.9%)

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

Compiler

Compiled 19 to 19 computations (0% saved)

sample60.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
6.0ms	90×	body	128	nan
3.0ms	37×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

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

15.3b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.8b	(/.f64 (.f64 M D) (.f64 2 d))
5.2b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
11.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite221.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

8.4b

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:

12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.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)

series1.4s (9.3%)

Error

6.7b

Counts

4 → 57

Calls

4 calls:

539.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
458.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
238.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
121.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3306 to 2982 computations (9.8% saved)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5385	3695

prune198.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	162	11	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Error

4.5b

Counts

174 → 11

Compiler

Compiled 4053 to 2202 computations (45.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(/.f64 (.f64 M D) (.f64 2 d))
4.2b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
4.2b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
5.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))

rewrite167.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

67×	`add-exp-log_binary64_1139`
26×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
20×	`add-sqr-sqrt_binary64_1123` `div-exp_binary64_1152`
13×	`*-un-lft-identity_binary64_1101`
10×	`add-cube-cbrt_binary64_1136` `pow-exp_binary64_1169` `associate-r_binary64_1041`
6×	`sqrt-prod_binary64_1117` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `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×	`sqrt-div_binary64_1118` `difference-of-squares_binary64_1070` `pow-to-exp_binary64_1170` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `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:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
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)

series1.3s (8.5%)

Error

4.3b

Counts

4 → 51

Calls

4 calls:

534.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
340.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
235.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
131.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3091 to 2803 computations (9.3% saved)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4987	2858
1	4987	2858

prune184.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	148	13	161

Error

3.2b

Counts

161 → 13

Compiler

Compiled 3465 to 2127 computations (38.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(/.f64 (.f64 M D) (.f64 2 d))
4.2b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
5.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
6.6b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite306.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

239×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
112×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
83×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
15×	`add-sqr-sqrt_binary64_1123`
12×	`*-un-lft-identity_binary64_1101`
9×	`add-cube-cbrt_binary64_1136`
7×	`pow1_binary64_1162`
6×	`sqrt-prod_binary64_1117`
5×	`associate-r_binary64_1041` `times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `associate-r/_binary64_1043` `associate-/r_binary64_1045`
3×	`associate-l_binary64_1042` `div-inv_binary64_1098` `associate-/l/_binary64_1048`
2×	`sqrt-div_binary64_1118` `difference-of-squares_binary64_1070` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046`
1×	`pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114` `frac-times_binary64_1111` `associate-l/_binary64_1044`

Counts

4 → 150

Calls

4 calls:

18.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
9.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
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)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 6032 to 2978 computations (50.6% saved)

series1.2s (7.9%)

Error

3.2b

Counts

4 → 51

Calls

4 calls:

546.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
236.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
233.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
123.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3325 to 2776 computations (16.5% saved)

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5072	4786

prune270.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	196	5	201
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	200	14	214

Error

2.9b

Counts

214 → 14

Compiler

Compiled 5602 to 3108 computations (44.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(/.f64 (.f64 M D) (.f64 d 2))
5.2b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l))))
6.6b	(.f64 h (/.f64 (.f64 M D) (*.f64 d 2)))
6.7b	(/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l)

rewrite184.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

2.9b

Rules

52×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
21×	`times-frac_binary64_1107`
20×	`add-sqr-sqrt_binary64_1123`
17×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `add-cube-cbrt_binary64_1136` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `*-un-lft-identity_binary64_1101`
7×	`pow1_binary64_1162` `div-inv_binary64_1098`
6×	`associate-/l*_binary64_1046`
5×	`associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045`
3×	`associate-l_binary64_1042` `sqrt-prod_binary64_1117`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-div_binary64_1118`
1×	`associate-/l/_binary64_1048` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `associate-r/_binary64_1043` `-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 109

Calls

4 calls:

8.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 d 2)))
8.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l)
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l))))

Compiler

Compiled 3748 to 2031 computations (45.8% saved)

series869.0ms (5.7%)

Error

2.9b

Counts

4 → 48

Calls

4 calls:

239.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l)
225.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l))))
222.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 d 2)))
138.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 3199 to 2490 computations (22.2% saved)

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5034	2686

prune183.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	6	7	13
Picked	0	1	1
Done	0	0	0
Total	160	11	171

Error

2.7b

Counts

171 → 11

Compiler

Compiled 4211 to 2169 computations (48.5% saved)

regimes2.2s (14.6%)

Accuracy

Total 5.8b remaining (63.9%)

Threshold costs 0b (0%)

Compiler

Compiled 26402 to 23279 computations (11.8% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	36
1	89	36

Compiler

Compiled 48 to 40 computations (16.7% saved)

end0.0ms (0%)

sample3.6s (23.6%)

Algorithm

1×

intervals

Results

627.0ms	8000×	body	128	valid
234.0ms	3058×	body	128	nan
95.0ms	1275×	body	128	invalid

Compiler

Compiled 1588 to 1399 computations (11.9% saved)

Details

analyze2.4s (15.9%)

sample60.0ms (0.4%)

simplify44.0ms (0.3%)

prune3.0ms (0%)

localize21.0ms (0.1%)

rewrite221.0ms (1.5%)

series1.4s (9.3%)

simplify68.0ms (0.5%)

prune198.0ms (1.3%)

localize18.0ms (0.1%)

rewrite167.0ms (1.1%)

series1.3s (8.5%)

simplify58.0ms (0.4%)

prune184.0ms (1.2%)

localize18.0ms (0.1%)

rewrite306.0ms (2%)

series1.2s (7.9%)

simplify88.0ms (0.6%)

prune270.0ms (1.8%)

localize15.0ms (0.1%)

rewrite184.0ms (1.2%)

series869.0ms (5.7%)

simplify62.0ms (0.4%)

prune183.0ms (1.2%)

regimes2.2s (14.6%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample3.6s (23.6%)

Profiling