Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample28.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	53×	body	640	valid
6.0ms	32×	body	1280	valid
5.0ms	130×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	19×	body	160	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify24.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	76	17
1	76	17

prune2.0ms (0.1%)

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

Merged error: 21.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
4.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite64.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`add-sqr-sqrt_binary64`
97×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64`
60×	`sqrt-prod_binary64`
40×	`add-cube-cbrt_binary64`
25×	`difference-of-squares_binary64`
13×	`associate-/r*_binary64` `distribute-lft-out--_binary64`
11×	`add-exp-log_binary64`
7×	`pow1_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64` `pow-flip_binary64`
5×	`add-log-exp_binary64`
4×	`div-exp_binary64`
3×	`insert-posit16`
2×	`pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64`

Counts

3 → 149

Calls

3 calls:

42.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series162.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

73.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
55.0ms	(/.f64 1 (sqrt.f64 x))
34.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify136.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4957	3168
1	4957	3168

prune216.0ms (5.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	141	17	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	17	159

Merged error: 21.1b

Counts

159 → 17

Compiler

Compiled 3284 to 2442 computations (25.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.6b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite48.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
35×	`sqrt-prod_binary64`
32×	`*-un-lft-identity_binary64`
12×	`difference-of-squares_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64` `times-frac_binary64`
9×	`add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
7×	`pow1_binary64` `associate-r_binary64`
6×	`associate-l_binary64`
5×	`add-log-exp_binary64`
4×	`distribute-lft-out_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `insert-posit16`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

3 → 94

Calls

3 calls:

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

series301.0ms (7.3%)

Counts

3 → 9

Calls

3 calls:

176.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
67.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
57.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

simplify119.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5319	2429

prune138.0ms (3.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	14	2	16
Picked	1	0	1
Done	0	0	0
Total	116	4	120

Merged error: 0.2b

Counts

120 → 4

Compiler

Compiled 2432 to 1586 computations (34.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite69.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
55×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
45×	`distribute-lft-out_binary64`
39×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`
27×	`associate-/l*_binary64`
20×	`add-cbrt-cube_binary64`
14×	`div-exp_binary64`
9×	`pow1_binary64`
8×	`associate-/r/_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64` `cbrt-undiv_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `associate-l_binary64` `flip-+_binary64`
5×	`prod-exp_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `rec-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sqrt-unprod_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 170

Calls

4 calls:

24.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
10.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series318.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
61.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
51.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
39.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify97.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5090	4234

prune283.0ms (6.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	173	9	182
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	175	11	186

Merged error: 0b

Counts

186 → 11

Compiler

Compiled 4592 to 3144 computations (31.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.1b	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite66.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64`
82×	`times-frac_binary64`
66×	`*-un-lft-identity_binary64`
54×	`add-exp-log_binary64`
53×	`add-cube-cbrt_binary64`
38×	`sqrt-prod_binary64`
29×	`associate-r_binary64`
28×	`associate-l_binary64`
22×	`add-cbrt-cube_binary64`
20×	`div-exp_binary64`
19×	`unswap-sqr_binary64`
17×	`prod-exp_binary64`
15×	`pow1_binary64`
12×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
10×	`associate-/r*_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
8×	`frac-add_binary64`
7×	`distribute-rgt-out_binary64`
6×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `pow-flip_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `inv-pow_binary64` `div-inv_binary64` `insert-posit16`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64` `sqrt-unprod_binary64` `un-div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 217

Calls

4 calls:

28.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
10.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
5.0ms	(/.f64 1 (sqrt.f64 x))

series277.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
59.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
57.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
48.0ms	(/.f64 1 (sqrt.f64 x))

simplify188.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	4937	5535
1	4937	5535

prune355.0ms (8.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	232	8	240

Merged error: 0b

Counts

240 → 8

Compiler

Compiled 5938 to 3969 computations (33.2% saved)

regimes23.0ms (0.6%)

Compiler: Compiled 218 to 171 computations (21.6% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	26
1	18	26

end0.0ms (0%)

sample1.2s (28.2%)

Algorithm

1×

intervals

Results

281.0ms	1846×	body	640	valid
224.0ms	1159×	body	1280	valid
180.0ms	4089×	body	80	valid
72.0ms	618×	body	320	valid
22.0ms	288×	body	160	valid

Compiler

Compiled 260 to 207 computations (20.4% saved)

Details

analyze1.0ms (0%)

sample28.0ms (0.7%)

simplify24.0ms (0.6%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite64.0ms (1.6%)

series162.0ms (3.9%)

simplify136.0ms (3.3%)

prune216.0ms (5.3%)

localize7.0ms (0.2%)

rewrite48.0ms (1.2%)

series301.0ms (7.3%)

simplify119.0ms (2.9%)

prune138.0ms (3.4%)

localize9.0ms (0.2%)

rewrite69.0ms (1.7%)

series318.0ms (7.7%)

simplify97.0ms (2.4%)

prune283.0ms (6.9%)

localize10.0ms (0.2%)

rewrite66.0ms (1.6%)

series277.0ms (6.7%)

simplify188.0ms (4.6%)

prune355.0ms (8.6%)

regimes23.0ms (0.6%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.2s (28.2%)

Profiling