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)

sample25.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	67×	body	1024	valid
6.0ms	144×	body	128	valid
4.0ms	32×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	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: 19.3b

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)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite72.0ms (1.8%)

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` `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 → 162

Calls

4 calls:

41.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series181.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
56.0ms	(/.f64 1 (sqrt.f64 x))
33.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4950	3382
1	4950	3382

prune231.0ms (5.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	162	12	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	12	175

Merged error: 18.7b

Counts

175 → 12

Compiler

Compiled 3465 to 2558 computations (26.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.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)))
2.7b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite53.0ms (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`
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 → 107

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))

series314.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.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))
47.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
26.0ms	(sqrt.f64 (+.f64 1 x))

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5224	2642

prune152.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	128	3	131

Merged error: 0.2b

Counts

131 → 3

Compiler

Compiled 2774 to 1796 computations (35.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite68.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
55×	`sqrt-prod_binary64`
49×	`add-sqr-sqrt_binary64`
42×	`distribute-lft-out_binary64`
40×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`
27×	`associate-/l*_binary64`
20×	`add-cbrt-cube_binary64`
14×	`div-exp_binary64`
10×	`pow1_binary64`
8×	`associate-/r/_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64` `cbrt-undiv_binary64`
6×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64` `sqrt-div_binary64`
5×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `div-inv_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `rec-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 168

Calls

4 calls:

22.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))

series297.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
63.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
52.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
24.0ms	(sqrt.f64 (+.f64 1 x))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5160	4111

prune271.0ms (6.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	172	8	180
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	174	9	183

Merged error: 0.0b

Counts

183 → 9

Compiler

Compiled 4506 to 3088 computations (31.5% saved)

localize8.0ms (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)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite67.0ms (1.7%)

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` `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 → 252

Calls

4 calls:

14.0ms	(/.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))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series323.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))
86.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
45.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
43.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify127.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4949	9789
1	4949	9789

prune509.0ms (12.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	261	3	264
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	265	8	273

Merged error: 0.0b

Counts

273 → 8

Compiler

Compiled 7590 to 5427 computations (28.5% saved)

regimes20.0ms (0.5%)

Compiler: Compiled 180 to 144 computations (20% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample994.0ms (25.1%)

Algorithm

1×

intervals

Results

334.0ms	2220×	body	1024	valid
182.0ms	4256×	body	128	valid
111.0ms	1013×	body	512	valid
38.0ms	511×	body	256	valid

Compiler

Compiled 221 to 178 computations (19.5% saved)

Details

analyze1.0ms (0%)

sample25.0ms (0.6%)

simplify11.0ms (0.3%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite72.0ms (1.8%)

series181.0ms (4.6%)

simplify68.0ms (1.7%)

prune231.0ms (5.8%)

localize7.0ms (0.2%)

rewrite53.0ms (1.3%)

series314.0ms (7.9%)

simplify70.0ms (1.8%)

prune152.0ms (3.8%)

localize9.0ms (0.2%)

rewrite68.0ms (1.7%)

series297.0ms (7.5%)

simplify67.0ms (1.7%)

prune271.0ms (6.9%)

localize8.0ms (0.2%)

rewrite67.0ms (1.7%)

series323.0ms (8.2%)

simplify127.0ms (3.2%)

prune509.0ms (12.9%)

regimes20.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample994.0ms (25.1%)

Profiling