Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample26.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	63×	body	1024	valid
5.0ms	146×	body	128	valid
2.0ms	22×	body	512	valid
1.0ms	18×	body	256	valid
1.0ms	7×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify223.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

prune2.0ms (0.1%)

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: 27.7b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
3.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite69.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64_2773`
60×	`times-frac_binary64_2779`
57×	`add-sqr-sqrt_binary64_2794`
25×	`add-cube-cbrt_binary64_2805`
20×	`distribute-lft-out_binary64_2726`
18×	`distribute-lft-out--_binary64_2727`
14×	`difference-of-squares_binary64_2742`
11×	`associate-/r*_binary64_2719`
7×	`add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806` `associate-/l*_binary64_2720`
5×	`difference-of-sqr-1_binary64_2743` `add-log-exp_binary64_2809`
4×	`associate-/r/_binary64_2721`
3×	`pow1_binary64_2831`
2×	`cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `associate-/l/_binary64_2722` `div-inv_binary64_2770` `flip3-+_binary64_2776` `flip3--_binary64_2777` `div-exp_binary64_2821` `flip--_binary64_2748` `clear-num_binary64_2772` `flip-+_binary64_2747`
1×	`diff-log_binary64_2862` `sub-neg_binary64_2766` `frac-sub_binary64_2782`

Counts

3 → 113

Calls

3 calls:

45.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series123.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

75.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
24.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
24.0ms	(/.f64 x (+.f64 x 1))

simplify77.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5940	2299

prune169.0ms (5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	5	123

Merged error: 0.0b

Counts

123 → 5

Compiler

Compiled 2577 to 1841 computations (28.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
0.0b	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
3.8b	(-.f64 (/.f64 x (+.f64 x 1)) (log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite98.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`*-un-lft-identity_binary64_2773`
76×	`add-sqr-sqrt_binary64_2794`
69×	`times-frac_binary64_2779`
68×	`exp-prod_binary64_2822`
39×	`add-cube-cbrt_binary64_2805`
36×	`log-pow_binary64_2859`
18×	`difference-of-squares_binary64_2742` `distribute-lft-out_binary64_2726`
10×	`distribute-lft-out--_binary64_2727`
8×	`difference-of-sqr-1_binary64_2743`
6×	`associate-/r/_binary64_2721` `add-exp-log_binary64_2808` `pow1_binary64_2831` `log-prod_binary64_2856` `add-cbrt-cube_binary64_2806` `add-log-exp_binary64_2809`
4×	`associate-/r*_binary64_2719`
3×	`associate--r+_binary64_2711` `div-inv_binary64_2770` `flip3--_binary64_2777` `flip--_binary64_2748` `associate-/l*_binary64_2720`
1×	`rem-log-exp_binary64_2811` `cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `diff-log_binary64_2862` `sub-neg_binary64_2766` `flip3-+_binary64_2776` `div-exp_binary64_2821` `clear-num_binary64_2772` `rem-exp-log_binary64_2810` `flip-+_binary64_2747`

Counts

4 → 139

Calls

4 calls:

52.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
13.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
12.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
5.0ms	(/.f64 x (+.f64 x 1))

series180.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
34.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
31.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
25.0ms	(/.f64 x (+.f64 x 1))

simplify75.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5250	2330

prune186.0ms (5.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	151	5	156

Merged error: 0.0b

Counts

156 → 5

Compiler

Compiled 3440 to 2514 computations (26.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.1b	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
7.7b	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
13.8b	(/.f64 x (+.f64 (*.f64 x x) -1))

rewrite73.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_2773`
64×	`add-sqr-sqrt_binary64_2794`
53×	`times-frac_binary64_2779`
35×	`add-cube-cbrt_binary64_2805`
18×	`associate-l_binary64_2716`
13×	`add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806`
12×	`difference-of-squares_binary64_2742`
11×	`associate-/r*_binary64_2719`
8×	`distribute-lft-out_binary64_2726`
7×	`associate-r_binary64_2715` `associate-/l*_binary64_2720` `difference-of-sqr--1_binary64_2744`
6×	`difference-of-sqr-1_binary64_2743` `associate-/r/_binary64_2721` `pow1_binary64_2831` `flip3--_binary64_2777` `flip--_binary64_2748` `add-log-exp_binary64_2809` `distribute-lft-out--_binary64_2727`
5×	`sub-neg_binary64_2766` `frac-sub_binary64_2782`
4×	`associate-*r/_binary64_2717` `frac-times_binary64_2783`
3×	`cbrt-undiv_binary64_2804` `div-inv_binary64_2770` `flip3-+_binary64_2776` `div-exp_binary64_2821` `flip-+_binary64_2747`
2×	`cbrt-unprod_binary64_2803` `frac-2neg_binary64_2784` `distribute-rgt-in_binary64_2725` `associate-/l/_binary64_2722` `unswap-sqr_binary64_2741` `distribute-lft-in_binary64_2724` `clear-num_binary64_2772` `prod-exp_binary64_2819` `associate--l+_binary64_2712` `associate-*l/_binary64_2718`
1×	`pow-prod-down_binary64_2841` `diff-log_binary64_2862` `*-commutative_binary64_2706`

Counts

4 → 153

Calls

4 calls:

24.0ms	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
17.0ms	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
7.0ms	(/.f64 x (+.f64 (*.f64 x x) -1))

series231.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
55.0ms	(/.f64 x (+.f64 (*.f64 x x) -1))
43.0ms	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
27.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify84.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4988	3017
1	4988	3017

prune405.0ms (11.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	165	5	170

Merged error: 0.0b

Counts

170 → 5

Compiler

Compiled 4238 to 2776 computations (34.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (-.f64 x 1))
0.0b	(*.f64 (+.f64 x 1) (+.f64 x 1))
0.0b	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 (*.f64 x x) -1))
18.4b	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))

rewrite68.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`associate-*r/_binary64_2717`
36×	`*-un-lft-identity_binary64_2773`
32×	`frac-sub_binary64_2782`
31×	`flip3-+_binary64_2776` `flip-+_binary64_2747`
27×	`add-sqr-sqrt_binary64_2794`
20×	`frac-times_binary64_2783`
19×	`flip3--_binary64_2777` `add-cube-cbrt_binary64_2805` `flip--_binary64_2748`
18×	`associate-/l/_binary64_2722`
13×	`pow1_binary64_2831`
12×	`times-frac_binary64_2779`
11×	`associate-r_binary64_2715`
10×	`add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806` `associate-*l/_binary64_2718`
7×	`associate-l_binary64_2716`
6×	`swap-sqr_binary64_2740` `distribute-lft-out_binary64_2726` `add-log-exp_binary64_2809`
5×	`sub-neg_binary64_2766`
4×	`distribute-rgt-in_binary64_2725` `associate-/r*_binary64_2719` `distribute-lft-in_binary64_2724` `difference-of-sqr--1_binary64_2744`
3×	`associate-/l*_binary64_2720`
2×	`cbrt-unprod_binary64_2803` `associate-/r/_binary64_2721` `associate--r+_binary64_2711` `difference-of-squares_binary64_2742` `pow-prod-down_binary64_2841` `unswap-sqr_binary64_2741` `*-commutative_binary64_2706` `prod-exp_binary64_2819` `associate--l+_binary64_2712`
1×	`div-sub_binary64_2778` `cbrt-undiv_binary64_2804` `pow-sqr_binary64_2746` `frac-2neg_binary64_2784` `difference-of-sqr-1_binary64_2743` `diff-log_binary64_2862` `div-inv_binary64_2770` `div-exp_binary64_2821` `distribute-lft-out--_binary64_2727` `pow2_binary64_2851` `clear-num_binary64_2772` `pow-plus_binary64_2833` `pow-prod-up_binary64_2840`

Counts

4 → 149

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 (*.f64 x x) -1))
13.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))
10.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))
7.0ms	(*.f64 x (-.f64 x 1))

series156.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))
51.0ms	(*.f64 x (-.f64 x 1))
37.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 (*.f64 x x) -1))
15.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))

simplify89.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4929	3890
1	4929	3890

prune276.0ms (8.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	163	3	166

Merged error: 0b

Counts

166 → 3

Compiler

Compiled 4968 to 3384 computations (31.9% saved)

regimes20.0ms (0.6%)

Compiler: Compiled 43 to 35 computations (18.6% saved)

bsearch23.0ms (0.7%)

Steps

Iters	Range		Point
8	4414.421257120372	1214676.4328457448	115681.34454920547
3	-22491933.214658808	-15699985.11392875	-21016462.154633567

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	52
1	79	52

end0.0ms (0%)

sample722.0ms (21.1%)

Algorithm

1×

intervals

Results

232.0ms	1972×	body	1024	valid
138.0ms	4378×	body	128	valid
88.0ms	924×	body	512	valid
35.0ms	239×	body	2048	valid
29.0ms	487×	body	256	valid

Compiler

Compiled 90 to 71 computations (21.1% saved)

Details

analyze4.0ms (0.1%)

sample26.0ms (0.8%)

simplify223.0ms (6.5%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite69.0ms (2%)

series123.0ms (3.6%)

simplify77.0ms (2.3%)

prune169.0ms (5%)

localize10.0ms (0.3%)

rewrite98.0ms (2.9%)

series180.0ms (5.3%)

simplify75.0ms (2.2%)

prune186.0ms (5.4%)

localize10.0ms (0.3%)

rewrite73.0ms (2.1%)

series231.0ms (6.7%)

simplify84.0ms (2.4%)

prune405.0ms (11.9%)

localize10.0ms (0.3%)

rewrite68.0ms (2%)

series156.0ms (4.6%)

simplify89.0ms (2.6%)

prune276.0ms (8.1%)

regimes20.0ms (0.6%)

bsearch23.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample722.0ms (21.1%)

Profiling