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)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	32×	body	1280	valid
7.0ms	53×	body	640	valid
6.0ms	148×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify25.0ms (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: 17.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
2.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite69.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64` `times-frac_binary64`
64×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`
25×	`difference-of-squares_binary64`
13×	`associate-/r*_binary64` `distribute-lft-out--_binary64`
12×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-flip_binary64`
4×	`div-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 166

Calls

4 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))
4.0ms	(sqrt.f64 (+.f64 x 1))

series192.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
56.0ms	(/.f64 1 (sqrt.f64 x))
36.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
31.0ms	(sqrt.f64 (+.f64 x 1))

simplify109.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4956	3428
1	4956	3428

prune238.0ms (5.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	166	12	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	12	179

Merged error: 17.2b

Counts

179 → 12

Compiler

Compiled 3524 to 2601 computations (26.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.5b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite54.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
39×	`sqrt-prod_binary64`
36×	`*-un-lft-identity_binary64`
12×	`difference-of-squares_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/l*_binary64` `times-frac_binary64`
9×	`pow1_binary64` `distribute-lft-out--_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `sqrt-div_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
13.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 1 x))

series318.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
73.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
51.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
29.0ms	(sqrt.f64 (+.f64 1 x))

simplify120.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5230	2695

prune153.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	131	4	135

Merged error: 0.2b

Counts

135 → 4

Compiler

Compiled 2864 to 1866 computations (34.8% saved)

localize11.0ms (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 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

rewrite68.0ms (1.6%)

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:

25.0ms	(/.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)))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
10.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series316.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
55.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
53.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
39.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify96.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5090	4234

prune267.0ms (6.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	177	9	186

Merged error: 0.0b

Counts

186 → 9

Compiler

Compiled 4525 to 3094 computations (31.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite58.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64`
159×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
119×	`add-cube-cbrt_binary64`
87×	`sqrt-prod_binary64`
29×	`distribute-rgt-out_binary64`
21×	`associate-/l*_binary64`
20×	`distribute-lft-out_binary64` `associate-/r/_binary64`
19×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`associate-/r*_binary64`
10×	`div-inv_binary64`
9×	`pow1_binary64`
8×	`div-exp_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
4×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`pow-prod-down_binary64`
2×	`pow1/2_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `associate-*l/_binary64`
1×	`associate-/l/_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `inv-pow_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 256

Calls

4 calls:

16.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))
11.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
4.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series345.0ms (8%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))
83.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
55.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
42.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify184.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4955	9862
1	4955	9862

prune523.0ms (12.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	264	4	268
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	269	8	277

Merged error: 0b

Counts

277 → 8

Compiler

Compiled 7661 to 5475 computations (28.5% saved)

regimes24.0ms (0.6%)

Compiler: Compiled 205 to 160 computations (22% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	25
1	15	25

end0.0ms (0%)

sample1.1s (24.8%)

Algorithm

1×

intervals

Results

266.0ms	1842×	body	640	valid
212.0ms	1155×	body	1280	valid
160.0ms	4081×	body	80	valid
63.0ms	603×	body	320	valid
25.0ms	319×	body	160	valid

Compiler

Compiled 246 to 194 computations (21.1% saved)

Details

analyze1.0ms (0%)

sample30.0ms (0.7%)

simplify25.0ms (0.6%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite69.0ms (1.6%)

series192.0ms (4.5%)

simplify109.0ms (2.5%)

prune238.0ms (5.5%)

localize7.0ms (0.2%)

rewrite54.0ms (1.3%)

series318.0ms (7.4%)

simplify120.0ms (2.8%)

prune153.0ms (3.6%)

localize11.0ms (0.2%)

rewrite68.0ms (1.6%)

series316.0ms (7.3%)

simplify96.0ms (2.2%)

prune267.0ms (6.2%)

localize9.0ms (0.2%)

rewrite58.0ms (1.3%)

series345.0ms (8%)

simplify184.0ms (4.3%)

prune523.0ms (12.2%)

regimes24.0ms (0.6%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.1s (24.8%)

Profiling