Details

analyze2.1s (21.6%)

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

Compiler

Compiled 19 to 19 computations (0% saved)

sample53.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
13.0ms	108×	body	128	nan
3.0ms	37×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify127.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	6100	27

prune4.0ms (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

14.7b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
11.9b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

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

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)))))
7.0ms	(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))

series559.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

290.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
158.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
89.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5147	2845

prune198.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Error

7.9b

Counts

129 → 10

Compiler

Compiled 3372 to 1965 computations (41.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
7.1b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`add-exp-log_binary64_1139`
121×	`prod-exp_binary64_1150`
43×	`div-exp_binary64_1152`
33×	`add-cbrt-cube_binary64_1137`
30×	`pow-exp_binary64_1169`
23×	`add-sqr-sqrt_binary64_1123` `associate-r_binary64_1041`
20×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `times-frac_binary64_1107`
19×	`cbrt-unprod_binary64_1134`
11×	`associate-l_binary64_1042`
9×	`cbrt-prod_binary64_1132`
7×	`pow1_binary64_1162` `cbrt-undiv_binary64_1135`
6×	`unpow-prod-down_binary64_1180` `pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140` `unswap-sqr_binary64_1069`
3×	`sqrt-prod_binary64_1117` `div-inv_binary64_1098`
2×	`*-commutative_binary64_1032` `pow-prod-down_binary64_1172` `sqrt-div_binary64_1118` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-r/_binary64_1043` `associate-/l_binary64_1046` `pow2_binary64_1182` `associate-/r*_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 145

Calls

4 calls:

18.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

series553.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
169.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
145.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4989	3414
1	4989	3414

prune357.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	157	10	167

Error

7.8b

Counts

167 → 10

Compiler

Compiled 4341 to 2300 computations (47% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
7.1b	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`add-exp-log_binary64_1139`
47×	`prod-exp_binary64_1150`
45×	`add-sqr-sqrt_binary64_1123`
33×	`add-cbrt-cube_binary64_1137`
28×	`associate-r_binary64_1041`
26×	`times-frac_binary64_1107`
24×	`div-exp_binary64_1152`
22×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`cbrt-prod_binary64_1132`
15×	`cbrt-unprod_binary64_1134`
12×	`pow-exp_binary64_1169`
11×	`associate-l_binary64_1042` `unswap-sqr_binary64_1069`
9×	`cbrt-undiv_binary64_1135`
7×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
3×	`sqrt-prod_binary64_1117` `div-inv_binary64_1098`
2×	`*-commutative_binary64_1032` `sqrt-div_binary64_1118` `pow-to-exp_binary64_1170`
1×	`rem-sqrt-square_binary64_1114` `unpow-prod-down_binary64_1180` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-r/_binary64_1043` `associate-/l_binary64_1046` `pow-prod-down_binary64_1172` `associate-l/_binary64_1044` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 133

Calls

4 calls:

16.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
10.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))

series475.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
141.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
102.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5165	3525

prune197.0ms (2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	142	13	155

Error

7.5b

Counts

155 → 13

Compiler

Compiled 4360 to 2173 computations (50.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.1b	(.f64 (pow.f64 (.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
18.9b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
18.9b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
18.9b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-exp-log_binary64_1139`
39×	`add-sqr-sqrt_binary64_1123`
27×	`times-frac_binary64_1107` `cbrt-prod_binary64_1132`
24×	`prod-exp_binary64_1150`
22×	`associate-r_binary64_1041`
21×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`unswap-sqr_binary64_1069`
8×	`pow-exp_binary64_1169` `add-cbrt-cube_binary64_1137`
6×	`div-exp_binary64_1152` `associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `div-inv_binary64_1098` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
3×	`pow1/3_binary64_1183` `cbrt-div_binary64_1133`
2×	`cbrt-unprod_binary64_1134` `pow-to-exp_binary64_1170`
1×	`-commutative_binary64_1032` `unpow-prod-down_binary64_1180` `associate-r/_binary64_1043` `cbrt-undiv_binary64_1135`

Counts

4 → 102

Calls

4 calls:

18.0ms	(.f64 (pow.f64 (.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
5.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
4.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
4.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

series622.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(.f64 (pow.f64 (.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
107.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
101.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
99.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4953	2868
1	4953	2868

prune188.0ms (1.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	114	13	127

Error

7.5b

Counts

127 → 13

Compiler

Compiled 4427 to 2330 computations (47.4% saved)

regimes1.5s (15.2%)

Accuracy

Total 1.9b remaining (20.3%)

Threshold costs 0b (0%)

Compiler

Compiled 15491 to 13336 computations (13.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 13 to 14 computations (-7.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	98	61
1	98	61

end0.0ms (0%)

sample2.3s (23.4%)

Algorithm

1×

intervals

Results

623.0ms	8000×	body	128	valid
232.0ms	3108×	body	128	nan
97.0ms	1306×	body	128	invalid

Compiler

Compiled 947 to 806 computations (14.9% saved)

Details

analyze2.1s (21.6%)

sample53.0ms (0.5%)

simplify127.0ms (1.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

rewrite45.0ms (0.5%)

series559.0ms (5.6%)

simplify73.0ms (0.7%)

prune198.0ms (2%)

localize18.0ms (0.2%)

rewrite63.0ms (0.6%)

series553.0ms (5.6%)

simplify93.0ms (0.9%)

prune357.0ms (3.6%)

localize17.0ms (0.2%)

rewrite51.0ms (0.5%)

series475.0ms (4.8%)

simplify92.0ms (0.9%)

prune197.0ms (2%)

localize22.0ms (0.2%)

rewrite46.0ms (0.5%)

series622.0ms (6.3%)

simplify77.0ms (0.8%)

prune188.0ms (1.9%)

regimes1.5s (15.2%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.3s (23.4%)

Profiling