Details

analyze1.9s (9.9%)

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%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample155.0ms (0.8%)

Algorithm

1×

intervals

Results

48.0ms	256×	body	128	valid
46.0ms	292×	body	128	nan
29.0ms	150×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify192.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5139	41

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 27.2b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
10.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
10.9b	(sqrt.f64 (/.f64 d h))
12.3b	(sqrt.f64 (/.f64 d l))

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_1123`
41×	`prod-exp_binary64_1134`
32×	`add-sqr-sqrt_binary64_1109`
29×	`times-frac_binary64_1094`
26×	`sqrt-prod_binary64_1103` `*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
21×	`add-cbrt-cube_binary64_1121`
16×	`associate-r_binary64_1030` `div-exp_binary64_1136`
14×	`sqrt-div_binary64_1104`
13×	`pow1_binary64_1146`
10×	`pow-exp_binary64_1153`
9×	`cbrt-unprod_binary64_1118` `frac-times_binary64_1098`
6×	`associate-l/_binary64_1033` `associate-r/_binary64_1032`
4×	`rem-sqrt-square_binary64_1101` `flip3--_binary64_1092` `flip--_binary64_1063` `pow-prod-down_binary64_1156` `add-log-exp_binary64_1124`
3×	`div-inv_binary64_1085`
2×	`-commutative_binary64_1021` `sub-neg_binary64_1081` `associate-l*_binary64_1031` `cbrt-undiv_binary64_1119` `pow-to-exp_binary64_1154` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`distribute-rgt-in_binary64_1040` `distribute-lft-in_binary64_1039`

Counts

4 → 125

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

series890.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

561.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
172.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
81.0ms	(sqrt.f64 (/.f64 d l))
76.0ms	(sqrt.f64 (/.f64 d h))

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5038	3491

prune265.0ms (1.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	118	19	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	19	138

Merged error: 10.4b

Counts

138 → 19

Compiler

Compiled 5225 to 2599 computations (50.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(/.f64 (.f64 M D) (.f64 d 2))
5.9b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
10.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.3b	(sqrt.f64 (/.f64 d l))

rewrite62.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64_1123`
48×	`prod-exp_binary64_1134`
37×	`add-cbrt-cube_binary64_1121`
22×	`add-sqr-sqrt_binary64_1109`
20×	`times-frac_binary64_1094` `div-exp_binary64_1136`
19×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
16×	`associate-r_binary64_1030` `cbrt-unprod_binary64_1118` `pow1_binary64_1146`
13×	`sqrt-prod_binary64_1103` `sqrt-div_binary64_1104`
12×	`associate-*r/_binary64_1032`
10×	`pow-exp_binary64_1153`
9×	`frac-times_binary64_1098`
7×	`pow-prod-down_binary64_1156`
6×	`associate-*l/_binary64_1033` `cbrt-undiv_binary64_1119`
4×	`flip3--_binary64_1092` `flip--_binary64_1063` `add-log-exp_binary64_1124`
3×	`div-inv_binary64_1085`
2×	`-commutative_binary64_1021` `rem-sqrt-square_binary64_1101` `sub-neg_binary64_1081` `associate-l*_binary64_1031` `pow-to-exp_binary64_1154`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `distribute-rgt-in_binary64_1040` `associate-/r_binary64_1034` `sqrt-pow1_binary64_1105` `associate-/l_binary64_1035` `distribute-lft-in_binary64_1039` `pow1/2_binary64_1165`

Counts

4 → 124

Calls

4 calls:

21.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

series2.2s (11.2%)

Counts

4 → 12

Calls

4 calls:

1.9s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
165.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
73.0ms	(sqrt.f64 (/.f64 d l))
44.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify93.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4967	4317
1	4967	4317

prune250.0ms (1.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	133	22	155

Merged error: 9.0b

Counts

155 → 22

Compiler

Compiled 6631 to 2684 computations (59.5% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
5.6b	(/.f64 (.f64 M D) (.f64 d 2))
5.9b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
10.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite80.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1123`
55×	`prod-exp_binary64_1134`
46×	`add-cbrt-cube_binary64_1121`
30×	`add-sqr-sqrt_binary64_1109` `times-frac_binary64_1094`
25×	`pow1_binary64_1146` `*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
23×	`cbrt-unprod_binary64_1118`
22×	`sqrt-prod_binary64_1103`
20×	`div-exp_binary64_1136`
18×	`associate-*r/_binary64_1032`
16×	`associate-r_binary64_1030`
14×	`pow-prod-down_binary64_1156`
13×	`sqrt-div_binary64_1104`
10×	`pow-exp_binary64_1153` `cbrt-prod_binary64_1116`
9×	`frac-times_binary64_1098`
6×	`associate-*l/_binary64_1033` `cbrt-undiv_binary64_1119`
4×	`flip3--_binary64_1092` `flip--_binary64_1063` `add-log-exp_binary64_1124`
3×	`rem-sqrt-square_binary64_1101` `div-inv_binary64_1085`
2×	`-commutative_binary64_1021` `sub-neg_binary64_1081` `associate-l*_binary64_1031` `pow-to-exp_binary64_1154`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `distribute-rgt-in_binary64_1040` `associate-/r_binary64_1034` `sqrt-pow1_binary64_1105` `associate-/l_binary64_1035` `distribute-lft-in_binary64_1039` `pow1/2_binary64_1165`

Counts

4 → 140

Calls

4 calls:

26.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
5.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

series2.9s (14.9%)

Counts

4 → 12

Calls

4 calls:

2.5s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
191.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
171.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
43.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify103.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4951	5501
1	4951	5501

prune321.0ms (1.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	146	6	152
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	149	25	174

Merged error: 8.7b

Counts

174 → 25

Compiler

Compiled 8403 to 3194 computations (62% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
3.1b	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))
5.6b	(/.f64 (.f64 M D) (.f64 d 2))
10.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite74.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-exp-log_binary64_1123`
57×	`prod-exp_binary64_1134`
49×	`add-cbrt-cube_binary64_1121`
30×	`times-frac_binary64_1094`
29×	`add-sqr-sqrt_binary64_1109`
28×	`pow1_binary64_1146`
25×	`cbrt-unprod_binary64_1118`
24×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
22×	`sqrt-prod_binary64_1103` `associate-*r/_binary64_1032`
20×	`div-exp_binary64_1136`
16×	`pow-prod-down_binary64_1156`
14×	`associate-r_binary64_1030`
13×	`sqrt-div_binary64_1104`
10×	`pow-exp_binary64_1153` `cbrt-prod_binary64_1116`
9×	`frac-times_binary64_1098`
6×	`cbrt-undiv_binary64_1119`
4×	`distribute-rgt-in_binary64_1040` `flip3--_binary64_1092` `sub-neg_binary64_1081` `flip--_binary64_1063` `add-log-exp_binary64_1124` `distribute-lft-in_binary64_1039`
3×	`rem-sqrt-square_binary64_1101` `associate-*l/_binary64_1033` `div-inv_binary64_1085`
2×	`-commutative_binary64_1021` `associate-l*_binary64_1031` `pow-to-exp_binary64_1154`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `associate-/r_binary64_1034` `sqrt-pow1_binary64_1105` `associate-/l_binary64_1035` `pow1/2_binary64_1165`

Counts

4 → 143

Calls

4 calls:

25.0ms	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
5.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

series2.9s (14.9%)

Counts

4 → 12

Calls

4 calls:

2.5s	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))
200.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
158.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
40.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify100.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4965	5678
1	4965	5678

prune264.0ms (1.4%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	24	24
Picked	1	0	1
Done	0	0	0
Total	155	25	180

Merged error: 8.6b

Counts

180 → 25

Compiler

Compiled 7598 to 2615 computations (65.6% saved)

regimes588.0ms (3.1%)

Compiler: Compiled 6511 to 4918 computations (24.5% saved)

bsearch487.0ms (2.5%)

Steps

Iters	Range		Point
3	4.060873817385953e+47	5.253783697313529e+47	4.8809993598361614e+47
10	6.607294170196105e-102	2.017736470574129e-91	1.1325155143509525e-91
5	-9.436724157699417e-35	-4.076006795624688e-35	-4.314269898258209e-35
7	-3.980045932243328e+40	-1.717355057370576e+38	-7.37093766928314e+39

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	172	135
1	172	135

end0.0ms (0%)

sample5.3s (27.4%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.3s	8519×	body	128	nan
920.0ms	4791×	body	128	invalid

Compiler

Compiled 1060 to 798 computations (24.7% saved)

Details

analyze1.9s (9.9%)

sample155.0ms (0.8%)

simplify192.0ms (1%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite50.0ms (0.3%)

series890.0ms (4.6%)

simplify79.0ms (0.4%)

prune265.0ms (1.4%)

localize27.0ms (0.1%)

rewrite62.0ms (0.3%)

series2.2s (11.2%)

simplify93.0ms (0.5%)

prune250.0ms (1.3%)

localize30.0ms (0.2%)

rewrite80.0ms (0.4%)

series2.9s (14.9%)

simplify103.0ms (0.5%)

prune321.0ms (1.7%)

localize29.0ms (0.2%)

rewrite74.0ms (0.4%)

series2.9s (14.9%)

simplify100.0ms (0.5%)

prune264.0ms (1.4%)

regimes588.0ms (3.1%)

bsearch487.0ms (2.5%)

simplify8.0ms (0%)

end0.0ms (0%)

sample5.3s (27.4%)

Profiling