Details

analyze2.0ms (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)

sample32.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	33×	body	1280	valid
8.0ms	57×	body	640	valid
5.0ms	137×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	76	17
1	76	17

prune3.0ms (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)

localize8.0ms (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))))

rewrite71.0ms (1.7%)

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:

44.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(/.f64 1 (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series190.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
57.0ms	(/.f64 1 (sqrt.f64 x))
33.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
24.0ms	(sqrt.f64 (+.f64 x 1))

simplify111.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4956	3428
1	4956	3428

prune232.0ms (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: 18.7b

Counts

179 → 12

Compiler

Compiled 3517 to 2598 computations (26.1% saved)

localize8.0ms (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 (1.2%)

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:

23.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))

series324.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
80.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
56.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
23.0ms	(sqrt.f64 (+.f64 1 x))

simplify121.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5230	2695

prune154.0ms (3.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	132	3	135

Merged error: 0.2b

Counts

135 → 3

Compiler

Compiled 2838 to 1839 computations (35.2% saved)

localize11.0ms (0.3%)

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))))

rewrite63.0ms (1.5%)

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` `insert-posit16`
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 → 172

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

series290.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
53.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
48.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
25.0ms	(sqrt.f64 (+.f64 1 x))

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5166	4173

prune279.0ms (6.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	176	8	184
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	178	9	187

Merged error: 0.0b

Counts

187 → 9

Compiler

Compiled 4580 to 3139 computations (31.5% 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)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite57.0ms (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))
6.0ms	(/.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)))

series330.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))
77.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
54.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
43.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify185.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4955	9862
1	4955	9862

prune529.0ms (12.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	265	3	268
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	269	8	277

Merged error: 0.0b

Counts

277 → 8

Compiler

Compiled 7661 to 5478 computations (28.5% saved)

regimes21.0ms (0.5%)

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

sample1.0s (24.5%)

Algorithm

1×

intervals

Results

268.0ms	1892×	body	640	valid
203.0ms	1091×	body	1280	valid
154.0ms	4065×	body	80	valid
68.0ms	641×	body	320	valid
22.0ms	311×	body	160	valid

Compiler

Compiled 221 to 178 computations (19.5% saved)

Details

analyze2.0ms (0%)

sample32.0ms (0.8%)

simplify27.0ms (0.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite71.0ms (1.7%)

series190.0ms (4.5%)

simplify111.0ms (2.6%)

prune232.0ms (5.5%)

localize8.0ms (0.2%)

rewrite53.0ms (1.2%)

series324.0ms (7.6%)

simplify121.0ms (2.9%)

prune154.0ms (3.6%)

localize11.0ms (0.3%)

rewrite63.0ms (1.5%)

series290.0ms (6.8%)

simplify93.0ms (2.2%)

prune279.0ms (6.6%)

localize9.0ms (0.2%)

rewrite57.0ms (1.3%)

series330.0ms (7.8%)

simplify185.0ms (4.3%)

prune529.0ms (12.5%)

regimes21.0ms (0.5%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.0s (24.5%)

Profiling