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)

sample26.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	79×	body	1024	valid
6.0ms	140×	body	128	valid
3.0ms	24×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify176.0ms (2.4%)

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%)

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: 18.3b

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))
2.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite80.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_2509`
118×	`times-frac_binary64_2493`
117×	`*-un-lft-identity_binary64_2487`
76×	`sqrt-prod_binary64_2503`
56×	`add-cube-cbrt_binary64_2522`
27×	`cancel-sign-sub-inv_binary64_2453`
25×	`difference-of-squares_binary64_2456`
13×	`associate-/r*_binary64_2431` `distribute-lft-out--_binary64_2439`
12×	`add-exp-log_binary64_2525`
11×	`distribute-lft-out_binary64_2438`
9×	`pow1_binary64_2548`
8×	`add-cbrt-cube_binary64_2523`
7×	`div-inv_binary64_2484`
6×	`pow-flip_binary64_2561` `associate-/l*_binary64_2432` `add-log-exp_binary64_2526` `sqrt-div_binary64_2504`
4×	`associate-/r/_binary64_2433` `div-exp_binary64_2538`
3×	`flip-+_binary64_2461` `sqrt-pow1_binary64_2505` `flip3-+_binary64_2490` `pow1/2_binary64_2567`
2×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `rec-exp_binary64_2537` `inv-pow_binary64_2572` `1-exp_binary64_2531` `cbrt-undiv_binary64_2521`
1×	`flip--_binary64_2462` `sub-neg_binary64_2480` `frac-sub_binary64_2496` `diff-log_binary64_2579` `rem-sqrt-square_binary64_2500` `flip3--_binary64_2491`

Counts

4 → 189

Calls

4 calls:

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

series189.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
59.0ms	(/.f64 1 (sqrt.f64 x))
35.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4913	3696
1	4913	3696

prune677.0ms (9.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	191	10	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	192	10	202

Merged error: 17.7b

Counts

202 → 10

Compiler

Compiled 11159 to 8958 computations (19.7% saved)

localize12.0ms (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))
0.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
2.7b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite237.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

1332×	`*-un-lft-identity_binary64_2487`
1249×	`times-frac_binary64_2493`
725×	`add-sqr-sqrt_binary64_2509`
429×	`distribute-lft-out_binary64_2438`
304×	`sqrt-prod_binary64_2503`
293×	`add-cube-cbrt_binary64_2522`
180×	`distribute-lft-out--_binary64_2439`
168×	`div-inv_binary64_2484`
162×	`difference-of-squares_binary64_2456`
29×	`associate-/r*_binary64_2431`
28×	`associate-/l*_binary64_2432`
18×	`cancel-sign-sub-inv_binary64_2453`
14×	`add-exp-log_binary64_2525`
10×	`add-cbrt-cube_binary64_2523`
8×	`pow1_binary64_2548`
7×	`associate-/r/_binary64_2433`
6×	`pow-flip_binary64_2561` `add-log-exp_binary64_2526`
5×	`div-exp_binary64_2538`
3×	`frac-2neg_binary64_2498` `flip-+_binary64_2461` `clear-num_binary64_2486` `flip3-+_binary64_2490` `associate-/l/_binary64_2434` `cbrt-undiv_binary64_2521`
2×	`flip--_binary64_2462` `frac-sub_binary64_2496` `sqrt-pow1_binary64_2505` `sqrt-div_binary64_2504` `rec-exp_binary64_2537` `inv-pow_binary64_2572` `pow1/2_binary64_2567` `flip3--_binary64_2491` `1-exp_binary64_2531`
1×	`sub-neg_binary64_2480` `diff-log_binary64_2579` `div-sub_binary64_2492` `frac-add_binary64_2495`

Counts

4 → 554

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))

series247.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
60.0ms	(/.f64 1 (sqrt.f64 x))
35.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
29.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

simplify249.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

566 → 566

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4952	22251
1	4952	22251

prune1.9s (25.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	564	2	566
Fresh	8	1	9
Picked	0	1	1
Done	0	0	0
Total	572	4	576

Merged error: 5.0b

Counts

576 → 4

Compiler

Compiled 18766 to 14682 computations (21.8% 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))
0.5b	(/.f64 1 (*.f64 x (+.f64 1 x)))
5.2b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite120.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

417×	`times-frac_binary64_2493`
399×	`*-un-lft-identity_binary64_2487`
164×	`distribute-lft-out_binary64_2438`
148×	`sqrt-prod_binary64_2503`
141×	`add-cube-cbrt_binary64_2522` `add-sqr-sqrt_binary64_2509`
61×	`div-inv_binary64_2484`
42×	`add-exp-log_binary64_2525`
41×	`associate-/r/_binary64_2433`
36×	`associate-*r/_binary64_2429`
30×	`associate-/r*_binary64_2431`
22×	`add-cbrt-cube_binary64_2523`
20×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
19×	`div-exp_binary64_2538`
18×	`associate-/l*_binary64_2432`
11×	`pow1_binary64_2548`
9×	`cbrt-undiv_binary64_2521`
8×	`pow-flip_binary64_2561`
6×	`prod-exp_binary64_2536` `rec-exp_binary64_2537` `1-exp_binary64_2531`
4×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `add-log-exp_binary64_2526`
3×	`inv-pow_binary64_2572`
2×	`sqrt-pow1_binary64_2505` `cbrt-unprod_binary64_2520` `sqrt-div_binary64_2504` `pow1/2_binary64_2567`
1×	`pow-prod-down_binary64_2558` `associate-/l/_binary64_2434` `frac-add_binary64_2495`

Counts

4 → 319

Calls

4 calls:

51.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
8.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series267.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
54.0ms	(/.f64 1 (sqrt.f64 x))
34.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
21.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))

simplify152.0ms (2%)

Algorithm

1×	egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4947	9579
1	4947	9579

prune1.1s (14.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	325	6	331
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	328	7	335

Merged error: 0.0b

Counts

335 → 7

Compiler

Compiled 17299 to 13636 computations (21.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.2b	(/.f64 1 (sqrt.f64 x))
0.4b	(/.f64 (/.f64 (sqrt.f64 1) x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite134.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`times-frac_binary64_2493`
104×	`*-un-lft-identity_binary64_2487`
71×	`add-sqr-sqrt_binary64_2509`
69×	`add-cube-cbrt_binary64_2522`
58×	`sqrt-prod_binary64_2503`
28×	`associate-/l*_binary64_2432`
26×	`add-exp-log_binary64_2525`
22×	`add-cbrt-cube_binary64_2523`
21×	`distribute-lft-out_binary64_2438`
16×	`associate-r_binary64_2427`
15×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
14×	`associate-/r*_binary64_2431`
13×	`associate-/r/_binary64_2433`
12×	`frac-times_binary64_2497`
10×	`div-exp_binary64_2538` `pow1_binary64_2548`
9×	`div-inv_binary64_2484`
8×	`cbrt-undiv_binary64_2521`
6×	`pow-flip_binary64_2561` `associate-*r/_binary64_2429` `frac-add_binary64_2495`
4×	`associate-l/_binary64_2430` `add-log-exp_binary64_2526` `associate-l*_binary64_2428`
3×	`prod-exp_binary64_2536` `frac-2neg_binary64_2498` `clear-num_binary64_2486` `cbrt-unprod_binary64_2520`
2×	`sqrt-pow1_binary64_2505` `sqrt-div_binary64_2504` `rec-exp_binary64_2537` `inv-pow_binary64_2572` `pow1/2_binary64_2567` `1-exp_binary64_2531`
1×	`unswap-sqr_binary64_2455` `distribute-rgt-in_binary64_2437` `distribute-lft-in_binary64_2436` `*-commutative_binary64_2418` `pow-prod-down_binary64_2558` `associate-/l/_binary64_2434`

Counts

4 → 216

Calls

4 calls:

49.0ms	(/.f64 (/.f64 (sqrt.f64 1) x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
47.0ms	(*.f64 (+.f64 x 1) (+.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))

series284.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(/.f64 (/.f64 (sqrt.f64 1) x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
59.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
44.0ms	(/.f64 1 (sqrt.f64 x))
35.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5187	4942

prune529.0ms (7.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	225	3	228
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	229	6	235

Merged error: 0.0b

Counts

235 → 6

Compiler

Compiled 9135 to 6909 computations (24.4% saved)

regimes17.0ms (0.2%)

Compiler: Compiled 102 to 83 computations (18.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	30
1	15	30

end0.0ms (0%)

sample897.0ms (12%)

Algorithm

1×

intervals

Results

341.0ms	2270×	body	1024	valid
165.0ms	4315×	body	128	valid
102.0ms	934×	body	512	valid
36.0ms	481×	body	256	valid

Compiler

Compiled 146 to 118 computations (19.2% saved)

Details

analyze1.0ms (0%)

sample26.0ms (0.3%)

simplify176.0ms (2.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite80.0ms (1.1%)

series189.0ms (2.5%)

simplify82.0ms (1.1%)

prune677.0ms (9.1%)

localize12.0ms (0.2%)

rewrite237.0ms (3.2%)

series247.0ms (3.3%)

simplify249.0ms (3.3%)

prune1.9s (25.5%)

localize11.0ms (0.1%)

rewrite120.0ms (1.6%)

series267.0ms (3.6%)

simplify152.0ms (2%)

prune1.1s (14.3%)

localize11.0ms (0.1%)

rewrite134.0ms (1.8%)

series284.0ms (3.8%)

simplify86.0ms (1.2%)

prune529.0ms (7.1%)

regimes17.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample897.0ms (12%)

Profiling