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)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	65×	body	1024	valid
6.0ms	140×	body	128	valid
4.0ms	37×	body	512	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify170.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune3.0ms (0%)

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: 19.4b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

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))
2.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite72.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64_2120`
97×	`times-frac_binary64_2105` `*-un-lft-identity_binary64_2099`
64×	`sqrt-prod_binary64_2114`
42×	`add-cube-cbrt_binary64_2131`
25×	`difference-of-squares_binary64_2068`
13×	`associate-/r*_binary64_2045` `distribute-lft-out--_binary64_2053`
12×	`add-exp-log_binary64_2134`
9×	`pow1_binary64_2157`
8×	`distribute-lft-out_binary64_2052` `add-cbrt-cube_binary64_2132`
6×	`pow-flip_binary64_2170` `add-log-exp_binary64_2135` `associate-/l*_binary64_2046` `div-inv_binary64_2096`
4×	`div-exp_binary64_2147` `sqrt-div_binary64_2115`
3×	`pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`
2×	`cbrt-undiv_binary64_2130` `flip3-+_binary64_2102` `1-exp_binary64_2140` `inv-pow_binary64_2181` `rec-exp_binary64_2146` `frac-2neg_binary64_2110` `associate-/r/_binary64_2047` `clear-num_binary64_2098` `flip-+_binary64_2073`
1×	`sub-neg_binary64_2092` `frac-sub_binary64_2108` `rem-sqrt-square_binary64_2112` `flip3--_binary64_2103` `flip--_binary64_2074` `diff-log_binary64_2188`

Counts

4 → 162

Calls

4 calls:

37.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 x))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series176.0ms (2%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
50.0ms	(/.f64 1 (sqrt.f64 x))
32.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
28.0ms	(sqrt.f64 (+.f64 x 1))

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4950	3382
1	4950	3382

prune234.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	161	13	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	13	175

Merged error: 18.8b

Counts

175 → 13

Compiler

Compiled 3524 to 2608 computations (26% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
2.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
2.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))

rewrite299.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

831×	`add-sqr-sqrt_binary64_2120`
666×	`sqrt-prod_binary64_2114`
598×	`times-frac_binary64_2105`
515×	`*-un-lft-identity_binary64_2099`
262×	`difference-of-squares_binary64_2068`
128×	`swap-sqr_binary64_2066`
122×	`distribute-lft-out--_binary64_2053`
71×	`add-cube-cbrt_binary64_2131`
57×	`div-inv_binary64_2096`
44×	`associate-l_binary64_2042` `associate-r_binary64_2041`
24×	`distribute-lft-out_binary64_2052` `sqrt-div_binary64_2115`
21×	`pow1_binary64_2157`
10×	`frac-sub_binary64_2108` `flip3--_binary64_2103` `flip--_binary64_2074` `add-exp-log_binary64_2134`
9×	`pow1/2_binary64_2176` `frac-times_binary64_2109` `sqrt-pow1_binary64_2116`
8×	`add-cbrt-cube_binary64_2132` `add-log-exp_binary64_2135`
6×	`associate-/r*_binary64_2045`
5×	`pow-prod-up_binary64_2166`
4×	`unswap-sqr_binary64_2067`
3×	`pow-flip_binary64_2170` `associate-r/_binary64_2043` `associate-l/_binary64_2044` `pow-prod-down_binary64_2167` `associate-/l*_binary64_2046` `pow-sqr_binary64_2072`
2×	`sub-neg_binary64_2092` `div-exp_binary64_2147` `diff-log_binary64_2188`
1×	`sqrt-unprod_binary64_2118` `rem-square-sqrt_binary64_2111` `cbrt-undiv_binary64_2130` `1-exp_binary64_2140` `inv-pow_binary64_2181` `*-commutative_binary64_2032` `rec-exp_binary64_2146` `frac-2neg_binary64_2110` `prod-exp_binary64_2145` `pow2_binary64_2177` `pow-plus_binary64_2159` `clear-num_binary64_2098` `cbrt-unprod_binary64_2129`

Counts

4 → 405

Calls

4 calls:

118.0ms	(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
40.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
37.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
5.0ms	(/.f64 1 (sqrt.f64 x))

series249.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
68.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
62.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
46.0ms	(/.f64 1 (sqrt.f64 x))

simplify186.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4923	12848
1	4923	12848

prune930.0ms (10.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	417	13	430

Merged error: 18.8b

Counts

430 → 13

Compiler

Compiled 12852 to 9651 computations (24.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (sqrt.f64 x))
0.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
2.6b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite224.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1318×	`*-un-lft-identity_binary64_2099`
1237×	`times-frac_binary64_2105`
717×	`add-sqr-sqrt_binary64_2120`
426×	`distribute-lft-out_binary64_2052`
304×	`sqrt-prod_binary64_2114`
285×	`add-cube-cbrt_binary64_2131`
180×	`distribute-lft-out--_binary64_2053`
167×	`div-inv_binary64_2096`
162×	`difference-of-squares_binary64_2068`
29×	`associate-/r*_binary64_2045`
28×	`associate-/l*_binary64_2046`
14×	`add-exp-log_binary64_2134`
10×	`add-cbrt-cube_binary64_2132`
8×	`pow1_binary64_2157`
6×	`pow-flip_binary64_2170` `add-log-exp_binary64_2135`
5×	`div-exp_binary64_2147` `associate-/r/_binary64_2047`
3×	`cbrt-undiv_binary64_2130` `associate-/l/_binary64_2048` `frac-2neg_binary64_2110` `clear-num_binary64_2098`
2×	`flip3-+_binary64_2102` `1-exp_binary64_2140` `frac-sub_binary64_2108` `inv-pow_binary64_2181` `rec-exp_binary64_2146` `sqrt-div_binary64_2115` `pow1/2_binary64_2176` `flip3--_binary64_2103` `flip--_binary64_2074` `sqrt-pow1_binary64_2116` `flip-+_binary64_2073`
1×	`sub-neg_binary64_2092` `div-sub_binary64_2104` `diff-log_binary64_2188` `frac-add_binary64_2107`

Counts

4 → 536

Calls

4 calls:

70.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
21.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series240.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
48.0ms	(/.f64 1 (sqrt.f64 x))
35.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
30.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

simplify247.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4935	22059
1	4935	22059

prune1.5s (17.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	544	4	548
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	556	5	561

Merged error: 4.0b

Counts

561 → 5

Compiler

Compiled 17564 to 13703 computations (22% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (sqrt.f64 x))
0.2b	(/.f64 1 (*.f64 x (+.f64 1 x)))
4.5b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite121.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

417×	`times-frac_binary64_2105`
399×	`*-un-lft-identity_binary64_2099`
164×	`distribute-lft-out_binary64_2052`
148×	`sqrt-prod_binary64_2114`
141×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131`
61×	`div-inv_binary64_2096`
42×	`add-exp-log_binary64_2134`
41×	`associate-/r/_binary64_2047`
36×	`associate-*r/_binary64_2043`
30×	`associate-/r*_binary64_2045`
22×	`add-cbrt-cube_binary64_2132`
20×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
19×	`div-exp_binary64_2147`
18×	`associate-/l*_binary64_2046`
11×	`pow1_binary64_2157`
9×	`cbrt-undiv_binary64_2130`
8×	`pow-flip_binary64_2170`
6×	`1-exp_binary64_2140` `rec-exp_binary64_2146` `prod-exp_binary64_2145`
4×	`frac-2neg_binary64_2110` `add-log-exp_binary64_2135` `clear-num_binary64_2098`
3×	`inv-pow_binary64_2181`
2×	`sqrt-div_binary64_2115` `pow1/2_binary64_2176` `sqrt-pow1_binary64_2116` `cbrt-unprod_binary64_2129`
1×	`associate-/l/_binary64_2048` `pow-prod-down_binary64_2167` `frac-add_binary64_2107`

Counts

4 → 319

Calls

4 calls:

50.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
7.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

series249.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
52.0ms	(/.f64 1 (sqrt.f64 x))
32.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
20.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))

simplify131.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4966	9578
1	4966	9578

prune644.0ms (7.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	324	7	331
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	328	8	336

Merged error: 0.0b

Counts

336 → 8

Compiler

Compiled 8869 to 6663 computations (24.9% saved)

regimes297.0ms (3.5%)

Compiler: Compiled 3932 to 3266 computations (16.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	16	29

end0.0ms (0%)

sample2.5s (28.8%)

Algorithm

1×

intervals

Results

361.0ms	2352×	body	1024	valid
167.0ms	4192×	body	128	valid
104.0ms	955×	body	512	valid
39.0ms	501×	body	256	valid

Compiler

Compiled 2000 to 1662 computations (16.9% saved)

Details

analyze2.0ms (0%)

sample27.0ms (0.3%)

simplify170.0ms (2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite72.0ms (0.8%)

series176.0ms (2%)

simplify72.0ms (0.8%)

prune234.0ms (2.7%)

localize10.0ms (0.1%)

rewrite299.0ms (3.5%)

series249.0ms (2.9%)

simplify186.0ms (2.2%)

prune930.0ms (10.8%)

localize15.0ms (0.2%)

rewrite224.0ms (2.6%)

series240.0ms (2.8%)

simplify247.0ms (2.9%)

prune1.5s (17.6%)

localize11.0ms (0.1%)

rewrite121.0ms (1.4%)

series249.0ms (2.9%)

simplify131.0ms (1.5%)

prune644.0ms (7.5%)

regimes297.0ms (3.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.5s (28.8%)

Profiling