Details

analyze100.0ms (2.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Symmetry

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite98.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

3 → 71

Calls

3 calls:

8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 1133 to 876 computations (22.7% saved)

series87.0ms (2.5%)

Error

0.1b

Counts

3 → 18

Calls

3 calls:

36.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
17.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 446 to 364 computations (18.4% saved)

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4923	1202
1	4923	1202

prune79.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Error

Counts

90 → 3

Compiler

Compiled 1157 to 870 computations (24.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
0.2b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

rewrite280.0ms (8.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

166×	`*-un-lft-identity_binary64_2806`
156×	`times-frac_binary64_2812`
114×	`add-sqr-sqrt_binary64_2828`
79×	`add-cube-cbrt_binary64_2841`
69×	`distribute-lft-out_binary64_2757`
38×	`sqrt-prod_binary64_2822`
25×	`associate-/r*_binary64_2750`
17×	`add-exp-log_binary64_2844`
11×	`add-cbrt-cube_binary64_2842`
9×	`associate-/l*_binary64_2751`
8×	`div-exp_binary64_2857`
6×	`pow1_binary64_2867` `add-log-exp_binary64_2845` `div-inv_binary64_2803`
4×	`cbrt-undiv_binary64_2840`
3×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
2×	`1-exp_binary64_2850` `rec-exp_binary64_2856` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `associate-/l/_binary64_2753` `sqrt-div_binary64_2823`
1×	`inv-pow_binary64_2891` `pow-flip_binary64_2880` `associate-/r/_binary64_2752` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 183

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
9.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 3743 to 2963 computations (20.8% saved)

series120.0ms (3.5%)

Error

Counts

4 → 24

Calls

4 calls:

38.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
29.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
18.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
16.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 668 to 562 computations (15.9% saved)

simplify113.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5168	3834

prune199.0ms (5.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	207	3	210

Error

Counts

210 → 3

Compiler

Compiled 3352 to 2550 computations (23.9% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 x (+.f64 (.f64 x 1/16) -1/8))
0.1b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))
4.1b	(/.f64 x (+.f64 2 (.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))))

rewrite119.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-sqr-sqrt_binary64_2828`
15×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `times-frac_binary64_2812`
7×	`pow1_binary64_2867`
6×	`associate-l_binary64_2747` `associate-r_binary64_2746`
4×	`associate-*r/_binary64_2748`
3×	`add-log-exp_binary64_2845` `flip3-+_binary64_2809` `flip-+_binary64_2780` `associate-/l_binary64_2751` `associate-/r_binary64_2750`
2×	`associate-/r/_binary64_2752` `pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `*-commutative_binary64_2737`
1×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803`

Counts

3 → 73

Calls

3 calls:

8.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))
7.0ms	(.f64 x (+.f64 (.f64 x 1/16) -1/8))
5.0ms	(/.f64 x (+.f64 2 (.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))))

Compiler

Compiled 1945 to 1446 computations (25.7% saved)

series138.0ms (4%)

Error

Counts

3 → 19

Calls

3 calls:

45.0ms	(/.f64 x (+.f64 2 (.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))))
43.0ms	(.f64 x (+.f64 (.f64 x 1/16) -1/8))
34.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))

Compiler

Compiled 612 to 512 computations (16.3% saved)

simplify46.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4964	1882
1	4964	1882

prune102.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Error

Counts

95 → 3

Compiler

Compiled 1998 to 1471 computations (26.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite231.0ms (6.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

119×	`*-un-lft-identity_binary64_2806`
92×	`add-sqr-sqrt_binary64_2828`
79×	`sqrt-prod_binary64_2822`
76×	`times-frac_binary64_2812`
57×	`distribute-lft-out_binary64_2757`
47×	`add-cube-cbrt_binary64_2841`
42×	`associate-r_binary64_2746`
11×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
7×	`pow1_binary64_2867`
6×	`add-log-exp_binary64_2845` `unswap-sqr_binary64_2774` `associate-l_binary64_2747` `associate-/l_binary64_2751` `associate-/r_binary64_2750`
4×	`flip3-+_binary64_2809` `associate-/r/_binary64_2752` `flip-+_binary64_2780`
2×	`div-exp_binary64_2857` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `cbrt-undiv_binary64_2840` `div-inv_binary64_2803` `sqrt-div_binary64_2823`
1×	`pow-prod-down_binary64_2877` `associate-r/_binary64_2748` `-commutative_binary64_2737` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 160

Calls

4 calls:

23.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 3521 to 2199 computations (37.5% saved)

series134.0ms (3.9%)

Error

Counts

4 → 21

Calls

4 calls:

45.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
39.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
19.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 740 to 546 computations (26.2% saved)

simplify88.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5028	3000

prune165.0ms (4.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	181	3	184

Error

Counts

184 → 3

Compiler

Compiled 3197 to 1999 computations (37.5% saved)

regimes131.0ms (3.8%)

Accuracy

Total 0.2b remaining (99.9%)

Threshold costs 0.2b (99.9%)

Compiler

Compiled 1212 to 1012 computations (16.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

Removed

()

end0.0ms (0%)

sample1.1s (31.2%)

Algorithm

1×

intervals

Results

235.0ms	7999×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 614 to 514 computations (16.3% saved)

Details

analyze100.0ms (2.9%)

sample15.0ms (0.4%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite98.0ms (2.9%)

series87.0ms (2.5%)

simplify64.0ms (1.9%)

prune79.0ms (2.3%)

localize9.0ms (0.3%)

rewrite280.0ms (8.2%)

series120.0ms (3.5%)

simplify113.0ms (3.3%)

prune199.0ms (5.8%)

localize9.0ms (0.3%)

rewrite119.0ms (3.5%)

series138.0ms (4%)

simplify46.0ms (1.3%)

prune102.0ms (3%)

localize8.0ms (0.2%)

rewrite231.0ms (6.8%)

series134.0ms (3.9%)

simplify88.0ms (2.6%)

prune165.0ms (4.8%)

regimes131.0ms (3.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (31.2%)

Profiling