Details

analyze1.8s (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample396.0ms (1.3%)

Algorithm

1×

intervals

Results

97.0ms	84×	body	1024	valid
73.0ms	51×	body	1024	nan
64.0ms	57×	body	2048	valid
37.0ms	92×	body	128	overflowed
28.0ms	43×	body	512	valid
21.0ms	13×	body	1024	invalid
16.0ms	20×	body	512	nan
9.0ms	23×	body	256	valid
8.0ms	49×	body	128	valid
8.0ms	8×	body	512	invalid
5.0ms	13×	body	256	nan
2.0ms	18×	body	128	nan
2.0ms	4×	body	256	invalid
2.0ms	8×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify209.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4831	19
1	4831	19

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

Error

34.6b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
16×	`unpow-prod-down_binary64`
13×	`pow-unpow_binary64`
12×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64` `times-frac_binary64`
8×	`sqr-pow_binary64`
7×	`cancel-sign-sub-inv_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
2×	`add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 57

Calls

2 calls:

13.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
4.0ms	(pow.f64 x (/.f64 1 n))

series278.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

229.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
48.0ms	(pow.f64 x (/.f64 1 n))

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4923	1285
1	4923	1285

prune164.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	5	64

Error

25.7b

Counts

64 → 5

Compiler

Compiled 1436 to 999 computations (30.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
0.0b	(pow.f64 x (/.f64 1 n))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.7b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64` `unpow-prod-down_binary64`
30×	`exp-prod_binary64`
27×	`difference-of-squares_binary64`
22×	`sqr-pow_binary64`
21×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
16×	`log-pow_binary64` `exp-sum_binary64`
13×	`pow-unpow_binary64`
11×	`log-prod_binary64`
9×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
6×	`pow1_binary64`
5×	`add-exp-log_binary64`
4×	`add-cbrt-cube_binary64`
3×	`sub-neg_binary64` `distribute-lft-out_binary64`
2×	`diff-log_binary64` `rem-exp-log_binary64` `exp-diff_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `div-inv_binary64` `log-div_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 126

Calls

4 calls:

13.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
13.0ms	(exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
4.0ms	(pow.f64 x (/.f64 1 n))

series895.0ms (3%)

Counts

4 → 12

Calls

4 calls:

358.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
280.0ms	(exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
173.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
84.0ms	(pow.f64 x (/.f64 1 n))

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5171	2919

prune253.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Error

25.7b

Counts

143 → 6

Compiler

Compiled 3308 to 2373 computations (28.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite55.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
36×	`unpow-prod-down_binary64`
30×	`log-prod_binary64`
27×	`difference-of-squares_binary64`
20×	`sqr-pow_binary64`
17×	`add-cube-cbrt_binary64`
15×	`exp-sum_binary64`
13×	`pow-unpow_binary64`
9×	`distribute-lft-out--_binary64` `times-frac_binary64`
7×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `log-div_binary64` `exp-prod_binary64`
3×	`flip3--_binary64` `distribute-lft-out_binary64` `flip--_binary64`
2×	`log-pow_binary64` `exp-diff_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `rem-exp-log_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 112

Calls

4 calls:

16.0ms	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
14.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
10.0ms	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
4.0ms	(pow.f64 x (/.f64 1 n))

series1.1s (3.6%)

Counts

4 → 12

Calls

4 calls:

473.0ms	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
365.0ms	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
197.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
54.0ms	(pow.f64 x (/.f64 1 n))

simplify130.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4953	3302
1	4953	3302

prune238.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	122	8	130

Error

25.5b

Counts

130 → 8

Compiler

Compiled 3209 to 2331 computations (27.4% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))) (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite77.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
42×	`unpow-prod-down_binary64`
34×	`*-un-lft-identity_binary64`
27×	`difference-of-squares_binary64`
22×	`sqr-pow_binary64`
21×	`cancel-sign-sub-inv_binary64`
13×	`add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
9×	`distribute-lft-out--_binary64`
7×	`pow-unpow_binary64`
6×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `log-pow_binary64` `exp-to-pow_binary64` `pow-exp_binary64` `exp-prod_binary64`

Counts

4 → 113

Calls

4 calls:

22.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
17.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
16.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
4.0ms	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))) (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

series12.7s (42.1%)

Counts

4 → 12

Calls

4 calls:

12.1s	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))) (cbrt.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
199.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
181.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
177.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5090	5858

prune650.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	126	7	133

Error

25.5b

Counts

133 → 7

Compiler

Compiled 7910 to 5817 computations (26.5% saved)

regimes395.0ms (1.3%)

Accuracy

Total 1.7b remaining (7.1%)

Threshold costs 0b (0%)

Compiler

Compiled 2664 to 2143 computations (19.6% saved)

bsearch172.0ms (0.6%)

Steps

Iters	Range		Point
8	13586.467377614885	8252833.8486652635	17640.450461715576
11	-348725.63373978116	-8.987864403474466e-25	-342438.035878186

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	101
1	108	101

end0.0ms (0%)

sample10.1s (33.6%)

Algorithm

1×

intervals

Results

2.3s	2706×	body	1024	valid
1.7s	1482×	body	1024	nan
1.6s	1747×	body	2048	valid
737.0ms	2670×	body	128	overflowed
647.0ms	1169×	body	512	valid
478.0ms	708×	body	512	nan
251.0ms	1774×	body	128	valid
221.0ms	176×	body	1024	invalid
209.0ms	604×	body	256	valid
160.0ms	231×	body	512	invalid
132.0ms	384×	body	256	nan
81.0ms	841×	body	128	nan
59.0ms	145×	body	256	invalid
47.0ms	258×	body	128	invalid
14.0ms	6×	body	2048	nan

Compiler

Compiled 653 to 512 computations (21.6% saved)

Details

analyze1.8s (6.1%)

sample396.0ms (1.3%)

simplify209.0ms (0.7%)

prune4.0ms (0%)

localize9.0ms (0%)

rewrite23.0ms (0.1%)

series278.0ms (0.9%)

simplify112.0ms (0.4%)

prune164.0ms (0.5%)

localize17.0ms (0.1%)

rewrite52.0ms (0.2%)

series895.0ms (3%)

simplify109.0ms (0.4%)

prune253.0ms (0.8%)

localize9.0ms (0%)

rewrite55.0ms (0.2%)

series1.1s (3.6%)

simplify130.0ms (0.4%)

prune238.0ms (0.8%)

localize15.0ms (0%)

rewrite77.0ms (0.3%)

series12.7s (42.1%)

simplify128.0ms (0.4%)

prune650.0ms (2.2%)

regimes395.0ms (1.3%)

bsearch172.0ms (0.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample10.1s (33.6%)

Profiling