Details

analyze359.0ms (6.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5790	44
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample25.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify177.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (172.0ms)

Iter	Nodes	Cost
0	4979	22
1	4979	22

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

Error

17.6b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
17.3b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite62.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

17.3b

Rules

8×	`associate-/l/_binary64_2753`
7×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
5×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
4×	`add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `frac-times_binary64_2816`
3×	`times-frac_binary64_2812` `flip3--_binary64_2810` `flip--_binary64_2781` `associate-/r*_binary64_2750`
2×	`pow1_binary64_2867` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `associate-l/_binary64_2749` `associate-r/_binary64_2748` `associate-/r/_binary64_2752`
1×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `associate-/l*_binary64_2751` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

2 → 42

Calls

2 calls:

12.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
8.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 1154 to 190 computations (83.5% saved)

series248.0ms (4.4%)

Error

0.3b

Counts

2 → 27

Calls

2 calls:

140.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
90.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 828 to 629 computations (24% saved)

simplify39.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5436	1206

prune51.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	5	70

Error

0.3b

Counts

70 → 5

Compiler

Compiled 1312 to 272 computations (79.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
17.3b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

rewrite118.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

24×	`times-frac_binary64_2812`
22×	`add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
19×	`log-pow_binary64_2895`
18×	`exp-prod_binary64_2858`
8×	`add-log-exp_binary64_2845` `difference-of-squares_binary64_2775`
6×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
5×	`pow1_binary64_2867`
4×	`associate-/r/_binary64_2752` `associate-/l*_binary64_2751`
3×	`flip3-+_binary64_2809` `flip-+_binary64_2780` `associate-/r*_binary64_2750` `log-prod_binary64_2892`
2×	`div-sub_binary64_2811` `div-inv_binary64_2803` `flip3--_binary64_2810` `associate-/l/_binary64_2753` `flip--_binary64_2781`
1×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `diff-log_binary64_2898` `sub-neg_binary64_2799` `cancel-sign-sub-inv_binary64_2772` `exp-diff_binary64_2854` `log-div_binary64_2893` `rem-log-exp_binary64_2847` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 91

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
10.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 2755 to 430 computations (84.4% saved)

series575.0ms (10.2%)

Error

0.3b

Counts

4 → 54

Calls

4 calls:

213.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
144.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
94.0ms	(-.f64 (.f64 x x) (.f64 y y))
85.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 1890 to 1488 computations (21.3% saved)

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4992	2833
1	4992	2833

prune101.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	145	5	150

Error

0.3b

Counts

150 → 5

Compiler

Compiled 3117 to 533 computations (82.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
16.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
16.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite240.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

99×	`add-sqr-sqrt_binary64_2828`
93×	`*-un-lft-identity_binary64_2806`
90×	`times-frac_binary64_2812`
55×	`add-cube-cbrt_binary64_2841`
54×	`sqrt-prod_binary64_2822`
36×	`associate-l_binary64_2747`
30×	`associate-r_binary64_2746`
18×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
13×	`distribute-lft-out_binary64_2757`
10×	`sqrt-div_binary64_2823`
9×	`unswap-sqr_binary64_2774`
8×	`pow1_binary64_2867`
6×	`flip3-+_binary64_2809` `flip-+_binary64_2780` `difference-of-squares_binary64_2775` `distribute-lft-out--_binary64_2758` `associate-/r/_binary64_2752` `associate-/r*_binary64_2750`
5×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
4×	`add-log-exp_binary64_2845` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `associate-/l*_binary64_2751`
3×	`div-inv_binary64_2803`
2×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `associate-/l/_binary64_2753`
1×	`pow-prod-down_binary64_2877` `frac-times_binary64_2816` `associate-l/_binary64_2749` `associate-r/_binary64_2748` `*-commutative_binary64_2737` `frac-2neg_binary64_2817` `clear-num_binary64_2805`

Counts

4 → 175

Calls

4 calls:

40.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
10.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 7103 to 642 computations (91% saved)

series552.0ms (9.8%)

Error

0.3b

Counts

4 → 72

Calls

4 calls:

151.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
132.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
124.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
86.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Compiler

Compiled 3951 to 2314 computations (41.4% saved)

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5058	6727

prune204.0ms (3.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	247	5	252

Error

0.3b

Counts

252 → 5

Compiler

Compiled 7918 to 1011 computations (87.2% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

16.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
16.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
16.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
16.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite104.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

12×	`add-sqr-sqrt_binary64_2828` `sqrt-prod_binary64_2822`
8×	`pow1_binary64_2867` `add-cube-cbrt_binary64_2841` `sqrt-div_binary64_2823` `*-un-lft-identity_binary64_2806`
4×	`pow1/2_binary64_2886` `add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `sqrt-pow1_binary64_2824` `flip3-+_binary64_2809` `flip-+_binary64_2780` `rem-sqrt-square_binary64_2819`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 3996 to 317 computations (92.1% saved)

series675.0ms (12%)

Error

0.3b

Counts

4 → 72

Calls

4 calls:

153.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
149.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
140.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
132.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 10368 to 3492 computations (66.3% saved)

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5050	2004

prune180.0ms (3.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	132	5	137

Error

0.3b

Counts

137 → 5

Compiler

Compiled 8036 to 937 computations (88.3% saved)

regimes252.0ms (4.5%)

Accuracy

Total 4.7b remaining (91%)

Threshold costs 0b (0%)

Compiler

Compiled 2722 to 1133 computations (58.4% saved)

bsearch72.0ms (1.3%)

Steps

Iters	Range	Point
8	2.3397017508897708e-166	9.670065903316018e-163	9.53965689937808e-163
10	-4.2200504254316455e-141	-1.441110177398771e-154	-1.4573801156715909e-154
8	-1.8920838548270488e+155	-3.4817310480786594e+151	-1.3405462746826308e+154

Iters

Range

Point

2.3397017508897708e-166

9.670065903316018e-163

9.53965689937808e-163

-4.2200504254316455e-141

-1.441110177398771e-154

-1.4573801156715909e-154

-1.8920838548270488e+155

-3.4817310480786594e+151

-1.3405462746826308e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	177
1	62	177

end0.0ms (0%)

sample1.3s (22.8%)

Algorithm

1×

intervals

Results

312.0ms	8000×	body	128	valid
147.0ms	8000×	pre	128	true

Compiler

Compiled 1072 to 443 computations (58.7% saved)

Details

analyze359.0ms (6.4%)

sample25.0ms (0.4%)

simplify177.0ms (3.2%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite62.0ms (1.1%)

series248.0ms (4.4%)

simplify39.0ms (0.7%)

prune51.0ms (0.9%)

localize10.0ms (0.2%)

rewrite118.0ms (2.1%)

series575.0ms (10.2%)

simplify91.0ms (1.6%)

prune101.0ms (1.8%)

localize11.0ms (0.2%)

rewrite240.0ms (4.3%)

series552.0ms (9.8%)

simplify90.0ms (1.6%)

prune204.0ms (3.6%)

localize21.0ms (0.4%)

rewrite104.0ms (1.8%)

series675.0ms (12%)

simplify65.0ms (1.2%)

prune180.0ms (3.2%)

regimes252.0ms (4.5%)

bsearch72.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (22.8%)

Profiling