Details

analyze1.1s (11.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	52
1	67	52
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample47.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	192×	body	128	valid
7.0ms	25×	body	2048	valid
5.0ms	256×	pre	128	true
4.0ms	17×	body	1024	valid
2.0ms	7×	body	4096	valid
1.0ms	6×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.6b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.9b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.5b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite220.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

13.3b

Rules

22×	`*-un-lft-identity_binary64_2806`
21×	`add-sqr-sqrt_binary64_2828`
20×	`add-cube-cbrt_binary64_2841`
18×	`times-frac_binary64_2812`
16×	`sqrt-prod_binary64_2822`
8×	`pow1_binary64_2867`
6×	`add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `sqrt-div_binary64_2823` `associate-/r*_binary64_2750`
4×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
3×	`sqrt-pow1_binary64_2824` `associate-/l*_binary64_2751`
2×	`pow1/2_binary64_2886` `associate-/r/_binary64_2752` `associate-*r/_binary64_2748`
1×	`rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `distribute-lft-out_binary64_2757` `+-commutative_binary64_2736` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `pow-prod-down_binary64_2877`

Counts

4 → 81

Calls

4 calls:

18.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2495 to 1576 computations (36.8% saved)

series751.0ms (7.2%)

Error

3.8b

Counts

4 → 54

Calls

4 calls:

204.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
167.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
161.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
160.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2319 to 2045 computations (11.8% saved)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5024	3051

prune212.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	129	6	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	6	136

Error

2.7b

Counts

136 → 6

Compiler

Compiled 3092 to 2045 computations (33.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))
0.9b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
0.9b	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
14.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

rewrite214.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

26×	`*-un-lft-identity_binary64_2806`
23×	`add-sqr-sqrt_binary64_2828`
22×	`add-cube-cbrt_binary64_2841`
18×	`times-frac_binary64_2812`
15×	`sqrt-prod_binary64_2822`
6×	`pow1_binary64_2867` `add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `associate-/r*_binary64_2750`
5×	`log-pow_binary64_2895`
4×	`sqrt-div_binary64_2823` `exp-prod_binary64_2858` `log-prod_binary64_2892`
3×	`flip3-+_binary64_2809` `flip-+_binary64_2780` `associate-/l*_binary64_2751`
2×	`distribute-lft-out_binary64_2757` `associate-/r/_binary64_2752`
1×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `exp-sum_binary64_2852` `rem-log-exp_binary64_2847` `sum-log_binary64_2897` `+-commutative_binary64_2736` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803`

Counts

4 → 85

Calls

4 calls:

18.0ms	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
12.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 2753 to 1804 computations (34.5% saved)

series678.0ms (6.5%)

Error

2.6b

Counts

4 → 51

Calls

4 calls:

240.0ms	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
155.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
117.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))
115.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))

Compiler

Compiled 2178 to 1939 computations (11% saved)

simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4926	2917
1	4926	2917

prune456.0ms (4.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	137	5	142

Error

2.7b

Counts

142 → 5

Compiler

Compiled 3312 to 2260 computations (31.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
0.9b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
14.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
14.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

rewrite214.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

10×	`*-un-lft-identity_binary64_2806`
8×	`add-log-exp_binary64_2845` `add-sqr-sqrt_binary64_2828`
6×	`pow1_binary64_2867` `add-cube-cbrt_binary64_2841` `sqrt-prod_binary64_2822`
4×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `flip3-+_binary64_2809` `sqrt-div_binary64_2823` `flip-+_binary64_2780`
2×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `distribute-lft-out_binary64_2757` `+-commutative_binary64_2736`

Counts

4 → 54

Calls

4 calls:

19.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
15.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
9.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 2738 to 1840 computations (32.8% saved)

series694.0ms (6.7%)

Error

2.7b

Counts

4 → 56

Calls

4 calls:

150.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
150.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))
146.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
131.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))

Compiler

Compiled 5034 to 4003 computations (20.5% saved)

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5028	1986

prune263.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	110	5	115

Error

2.7b

Counts

115 → 5

Compiler

Compiled 4539 to 3147 computations (30.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (/.f64 p (/.f64 (.f64 x x) p)))
0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
0.2b	(/.f64 (*.f64 x x) p)
23.4b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

rewrite201.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

69×	`times-frac_binary64_2812`
45×	`add-sqr-sqrt_binary64_2828`
37×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
32×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
26×	`associate-r_binary64_2746`
12×	`pow1_binary64_2867` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
10×	`div-inv_binary64_2803` `associate-/r*_binary64_2750`
7×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
4×	`add-log-exp_binary64_2845` `pow-prod-down_binary64_2877` `associate-/l*_binary64_2751`
3×	`sqrt-pow1_binary64_2824` `associate-r/_binary64_2748` `unswap-sqr_binary64_2774` `associate-l*_binary64_2747`
2×	`frac-2neg_binary64_2817` `clear-num_binary64_2805` `associate-/r/_binary64_2752`
1×	`pow1/2_binary64_2886` `sqrt-div_binary64_2823` `sqrt-prod_binary64_2822` `*-commutative_binary64_2737`

Counts

4 → 132

Calls

4 calls:

16.0ms	(.f64 2 (/.f64 p (/.f64 (.f64 x x) p)))
8.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
6.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
5.0ms	(/.f64 (*.f64 x x) p)

Compiler

Compiled 2638 to 1100 computations (58.3% saved)

series365.0ms (3.5%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

108.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
106.0ms	(.f64 2 (/.f64 p (/.f64 (.f64 x x) p)))
80.0ms	(/.f64 (*.f64 x x) p)
53.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

Compiler

Compiled 714 to 645 computations (9.7% saved)

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4940	1917
1	4940	1917

prune138.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	157	4	161

Error

0.1b

Counts

161 → 4

Compiler

Compiled 2412 to 1076 computations (55.4% saved)

regimes1.3s (12.2%)

Accuracy

Total 5.8b remaining (99.5%)

Threshold costs 0b (0%)

Compiler

Compiled 13607 to 10384 computations (23.7% saved)

bsearch5.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	102
1	38	102

end0.0ms (0%)

sample3.1s (29.6%)

Algorithm

1×

intervals

Results

390.0ms	6071×	body	128	valid
259.0ms	776×	body	2048	valid
178.0ms	8000×	pre	128	true
125.0ms	503×	body	1024	valid
121.0ms	285×	body	4096	valid
51.0ms	246×	body	512	valid
17.0ms	119×	body	256	valid

Compiler

Compiled 1815 to 1379 computations (24% saved)

Details

analyze1.1s (11.1%)

sample47.0ms (0.5%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite220.0ms (2.1%)

series751.0ms (7.2%)

simplify70.0ms (0.7%)

prune212.0ms (2%)

localize18.0ms (0.2%)

rewrite214.0ms (2.1%)

series678.0ms (6.5%)

simplify103.0ms (1%)

prune456.0ms (4.4%)

localize17.0ms (0.2%)

rewrite214.0ms (2.1%)

series694.0ms (6.7%)

simplify86.0ms (0.8%)

prune263.0ms (2.5%)

localize8.0ms (0.1%)

rewrite201.0ms (1.9%)

series365.0ms (3.5%)

simplify110.0ms (1.1%)

prune138.0ms (1.3%)

regimes1.3s (12.2%)

bsearch5.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (29.6%)

Profiling