Details

analyze464.0ms (11.7%)

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%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 9 to 9 computations (0% saved)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	85×	body	128	nan
1.0ms	24×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify164.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

prune2.0ms (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: 20.3b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.9b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.4b	(/.f64 A (*.f64 V l))
17.7b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1109`
15×	`sqrt-prod_binary64_1103`
11×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
10×	`associate-r_binary64_1030` `add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
9×	`times-frac_binary64_1094`
6×	`pow1_binary64_1146`
3×	`associate-l_binary64_1031` `add-log-exp_binary64_1124` `associate-/l*_binary64_1035` `div-inv_binary64_1085`
2×	`unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `div-exp_binary64_1136` `sqrt-div_binary64_1104` `cbrt-undiv_binary64_1119` `prod-exp_binary64_1134`
1×	`-commutative_binary64_1021` `clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-sqrt-square_binary64_1101` `associate-/r_binary64_1034` `pow-prod-down_binary64_1156` `sqrt-pow1_binary64_1105` `associate-*r/_binary64_1032` `pow1/2_binary64_1165`

Counts

3 → 66

Calls

3 calls:

9.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

series201.0ms (5.1%)

Counts

3 → 9

Calls

3 calls:

101.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
65.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
35.0ms	(/.f64 A (*.f64 V l))

simplify88.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4940	857
1	4940	857

prune83.0ms (2.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	58	17	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	17	76

Merged error: 6.6b

Counts

76 → 17

Compiler

Compiled 1129 to 398 computations (64.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
0.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
4.1b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
17.7b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

rewrite52.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_1109`
28×	`times-frac_binary64_1094`
27×	`add-exp-log_binary64_1123`
26×	`associate-r_binary64_1030`
22×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
20×	`add-cbrt-cube_binary64_1121`
14×	`cbrt-prod_binary64_1116`
11×	`pow1_binary64_1146`
10×	`associate-l_binary64_1031`
9×	`cbrt-unprod_binary64_1118` `prod-exp_binary64_1134`
7×	`unswap-sqr_binary64_1056` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119`
6×	`sqrt-div_binary64_1104` `associate-*r/_binary64_1032`
4×	`add-log-exp_binary64_1124`
3×	`associate-*l/_binary64_1033` `frac-times_binary64_1098` `pow-prod-down_binary64_1156`
2×	`*-commutative_binary64_1021` `sqrt-prod_binary64_1103` `sqrt-pow1_binary64_1105` `div-inv_binary64_1085`
1×	`pow1/3_binary64_1167` `pow1/2_binary64_1165`

Counts

4 → 106

Calls

4 calls:

15.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
15.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
9.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms	(cbrt.f64 A)

series454.0ms (11.4%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt.f64 A)
139.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
84.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
69.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4941	1503
1	4941	1503

prune102.0ms (2.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	119	16	135

Merged error: 3.5b

Counts

135 → 16

Compiler

Compiled 2041 to 731 computations (64.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
5.1b	(*.f64 (/.f64 A V) (/.f64 1 l))
17.7b	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))

rewrite37.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_1109`
27×	`add-exp-log_binary64_1123`
25×	`times-frac_binary64_1094`
21×	`*-un-lft-identity_binary64_1088`
19×	`add-cube-cbrt_binary64_1120`
17×	`associate-r_binary64_1030` `add-cbrt-cube_binary64_1121`
16×	`associate-l_binary64_1031`
10×	`pow1_binary64_1146`
9×	`prod-exp_binary64_1134`
8×	`div-exp_binary64_1136` `sqrt-div_binary64_1104`
7×	`unswap-sqr_binary64_1056` `associate-*r/_binary64_1032`
5×	`cbrt-unprod_binary64_1118`
4×	`cbrt-undiv_binary64_1119`
3×	`associate-*l/_binary64_1033` `frac-times_binary64_1098` `un-div-inv_binary64_1086` `pow-prod-down_binary64_1156` `add-log-exp_binary64_1124`
2×	`*-commutative_binary64_1021` `rec-exp_binary64_1135` `sqrt-prod_binary64_1103` `1-exp_binary64_1129` `sqrt-pow1_binary64_1105` `div-inv_binary64_1085`
1×	`pow1/2_binary64_1165`

Counts

3 → 95

Calls

3 calls:

12.0ms	(*.f64 (/.f64 A V) (/.f64 1 l))
10.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
6.0ms	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))

series200.0ms (5%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
61.0ms	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))
36.0ms	(*.f64 (/.f64 A V) (/.f64 1 l))

simplify98.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4875	1146
1	4875	1146

prune80.0ms (2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	104	16	120

Merged error: 3.5b

Counts

120 → 16

Compiler

Compiled 1507 to 595 computations (60.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.9b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
4.6b	(/.f64 (/.f64 A l) V)
17.7b	(sqrt.f64 (/.f64 (/.f64 A l) V))

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

213×	`times-frac_binary64_1094`
134×	`add-sqr-sqrt_binary64_1109`
117×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
89×	`sqrt-prod_binary64_1103`
46×	`associate-r_binary64_1030`
13×	`associate-/l*_binary64_1035` `div-inv_binary64_1085`
10×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
6×	`pow1_binary64_1146`
4×	`unswap-sqr_binary64_1056`
3×	`rem-sqrt-square_binary64_1101` `associate-/r_binary64_1034` `div-exp_binary64_1136` `associate-l*_binary64_1031` `cbrt-undiv_binary64_1119` `add-log-exp_binary64_1124`
2×	`sqrt-div_binary64_1104`
1×	`-commutative_binary64_1021` `clear-num_binary64_1087` `frac-2neg_binary64_1099` `cbrt-unprod_binary64_1118` `associate-/l/_binary64_1037` `pow-prod-down_binary64_1156` `prod-exp_binary64_1134` `sqrt-pow1_binary64_1105` `associate-r/_binary64_1032` `pow1/2_binary64_1165`

Counts

3 → 191

Calls

3 calls:

17.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
8.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
7.0ms	(/.f64 (/.f64 A l) V)

series199.0ms (5%)

Counts

3 → 9

Calls

3 calls:

100.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
61.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
38.0ms	(/.f64 (/.f64 A l) V)

simplify108.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4900	3477
1	4900	3477

prune146.0ms (3.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	191	9	200
Fresh	6	8	14
Picked	0	1	1
Done	1	0	1
Total	198	18	216

Merged error: 0.0b

Counts

216 → 18

Compiler

Compiled 3242 to 765 computations (76.4% saved)

regimes258.0ms (6.5%)

Compiler: Compiled 2257 to 1653 computations (26.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	35
1	16	35

end0.0ms (0%)

sample1.0s (25.9%)

Algorithm

1×

intervals

Results

288.0ms	8000×	body	128	valid
110.0ms	3059×	body	128	nan
30.0ms	874×	body	128	invalid

Compiler

Compiled 319 to 232 computations (27.3% saved)

Details

analyze464.0ms (11.7%)

sample24.0ms (0.6%)

simplify164.0ms (4.1%)

prune2.0ms (0%)

localize6.0ms (0.2%)

rewrite22.0ms (0.6%)

series201.0ms (5.1%)

simplify88.0ms (2.2%)

prune83.0ms (2.1%)

localize11.0ms (0.3%)

rewrite52.0ms (1.3%)

series454.0ms (11.4%)

simplify76.0ms (1.9%)

prune102.0ms (2.6%)

localize8.0ms (0.2%)

rewrite37.0ms (0.9%)

series200.0ms (5%)

simplify98.0ms (2.5%)

prune80.0ms (2%)

localize7.0ms (0.2%)

rewrite53.0ms (1.3%)

series199.0ms (5%)

simplify108.0ms (2.7%)

prune146.0ms (3.7%)

regimes258.0ms (6.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (25.9%)

Profiling