Details

analyze2.3s (25.7%)

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)

sample47.0ms (0.5%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
5.0ms	79×	body	128	nan
3.0ms	44×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify130.0ms (1.4%)

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

Merged error: 12.6b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.9b	(/.f64 (.f64 M D) (.f64 2 d))
7.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite39.0ms (0.4%)

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:

11.0ms	(.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))))

series564.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

288.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
164.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
86.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
26.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5147	2845

prune179.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	7	129

Merged error: 8.4b

Counts

129 → 7

Compiler

Compiled 3260 to 1890 computations (42% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) l))))
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.4b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
4.9b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64_1139`
23×	`add-cbrt-cube_binary64_1137`
21×	`add-sqr-sqrt_binary64_1123`
16×	`*-un-lft-identity_binary64_1101` `prod-exp_binary64_1150` `div-exp_binary64_1152`
13×	`sqrt-prod_binary64_1117`
10×	`add-cube-cbrt_binary64_1136`
9×	`associate-r_binary64_1041`
7×	`pow1_binary64_1162`
6×	`cbrt-unprod_binary64_1134` `cbrt-undiv_binary64_1135`
5×	`pow-exp_binary64_1169`
4×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140` `times-frac_binary64_1107` `sqrt-div_binary64_1118` `associate-/r*_binary64_1045`
3×	`associate-l_binary64_1042`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-r/_binary64_1043` `div-inv_binary64_1098` `associate-/l_binary64_1046` `unswap-sqr_binary64_1069`
1×	`*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `pow-prod-down_binary64_1172` `pow-to-exp_binary64_1170` `pow1/2_binary64_1181`

Counts

4 → 93

Calls

4 calls:

11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) l))))
7.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
6.0ms	(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))

series874.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

418.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) l))))
324.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
110.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5200	2325

prune123.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	105	7	112

Merged error: 8.4b

Counts

112 → 7

Compiler

Compiled 2648 to 1700 computations (35.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))
4.1b	(*.f64 (/.f64 M 2) (/.f64 D d))
7.1b	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1139`
58×	`add-sqr-sqrt_binary64_1123`
34×	`times-frac_binary64_1107`
32×	`associate-r_binary64_1041`
30×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
27×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
22×	`associate-l_binary64_1042`
19×	`div-exp_binary64_1152`
12×	`unswap-sqr_binary64_1069`
10×	`pow-exp_binary64_1169`
9×	`pow1_binary64_1162`
7×	`cbrt-unprod_binary64_1134` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
3×	`*-commutative_binary64_1032` `div-inv_binary64_1098` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172` `pow-to-exp_binary64_1170`
1×	`rem-sqrt-square_binary64_1114` `unpow-prod-down_binary64_1180` `frac-times_binary64_1111` `sqrt-pow1_binary64_1119` `associate-*l/_binary64_1044` `pow1/2_binary64_1181`

Counts

4 → 139

Calls

4 calls:

14.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
10.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))

series546.0ms (6%)

Counts

4 → 12

Calls

4 calls:

272.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
164.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))
88.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))
21.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4999	3140
1	4999	3140

prune188.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	150	8	158

Merged error: 8.2b

Counts

158 → 8

Compiler

Compiled 3838 to 2213 computations (42.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (/.f64 h l)))))
4.1b	(*.f64 (/.f64 M 2) (/.f64 D d))
4.1b	(*.f64 (/.f64 M 2) (/.f64 D d))
7.5b	(.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (/.f64 h l))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
65×	`add-sqr-sqrt_binary64_1123`
53×	`times-frac_binary64_1107`
40×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
39×	`associate-r_binary64_1041`
27×	`associate-l_binary64_1042`
26×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
21×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
14×	`pow1_binary64_1162`
8×	`unswap-sqr_binary64_1069`
7×	`frac-times_binary64_1111` `associate-*l/_binary64_1044`
5×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `pow-prod-down_binary64_1172`
4×	`add-log-exp_binary64_1140`
3×	`*-commutative_binary64_1032` `sqrt-prod_binary64_1117`
2×	`sqrt-div_binary64_1118`
1×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `pow1/2_binary64_1181`

Counts

4 → 166

Calls

4 calls:

12.0ms	(.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (/.f64 h l))
12.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (/.f64 h l)))))

series275.0ms (3%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (/.f64 h l)))))
60.0ms	(.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (/.f64 h l))
24.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
22.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5049	2949

prune219.0ms (2.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	177	9	186

Merged error: 8.0b

Counts

186 → 9

Compiler

Compiled 5175 to 2574 computations (50.3% saved)

regimes1.1s (11.9%)

Compiler: Compiled 12495 to 10970 computations (12.2% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	150	106
1	150	106

end0.0ms (0%)

sample2.0s (21.8%)

Algorithm

1×

intervals

Results

595.0ms	8000×	body	128	valid
218.0ms	3068×	body	128	nan
94.0ms	1294×	body	128	invalid

Compiler

Compiled 739 to 632 computations (14.5% saved)

Details

analyze2.3s (25.7%)

sample47.0ms (0.5%)

simplify130.0ms (1.4%)

prune4.0ms (0%)

localize19.0ms (0.2%)

rewrite39.0ms (0.4%)

series564.0ms (6.2%)

simplify77.0ms (0.8%)

prune179.0ms (2%)

localize13.0ms (0.1%)

rewrite39.0ms (0.4%)

series874.0ms (9.6%)

simplify64.0ms (0.7%)

prune123.0ms (1.3%)

localize13.0ms (0.1%)

rewrite49.0ms (0.5%)

series546.0ms (6%)

simplify77.0ms (0.8%)

prune188.0ms (2.1%)

localize13.0ms (0.1%)

rewrite63.0ms (0.7%)

series275.0ms (3%)

simplify78.0ms (0.9%)

prune219.0ms (2.4%)

regimes1.1s (11.9%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.0s (21.8%)

Profiling