Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample20.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms	62×	body	1024	valid
4.0ms	141×	body	128	valid
2.0ms	22×	body	512	valid
1.0ms	11×	body	2048	valid
1.0ms	20×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_10665`
14×	`*-un-lft-identity_binary64_10649` `add-sqr-sqrt_binary64_10671`
6×	`cancel-sign-sub-inv_binary64_10615`
5×	`add-cube-cbrt_binary64_10684`
4×	`add-log-exp_binary64_10688` `difference-of-squares_binary64_10618`
3×	`pow1_binary64_10710` `distribute-lft-out--_binary64_10601`
2×	`add-cbrt-cube_binary64_10685` `add-exp-log_binary64_10687` `distribute-lft-out_binary64_10600` `sqrt-div_binary64_10666`
1×	`sqrt-pow1_binary64_10667` `pow1/2_binary64_10729` `sub-neg_binary64_10642` `flip-+_binary64_10623` `flip3--_binary64_10653` `flip--_binary64_10624` `flip3-+_binary64_10652` `rem-sqrt-square_binary64_10662` `diff-log_binary64_10741`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 x 1))

series45.0ms (0.6%)

Counts

2 → 9

Calls

2 calls:

29.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
16.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 168 to 140 computations (16.7% saved)

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4802	589
1	4802	589

prune46.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	4	50

Merged error: 0.2b

Counts

50 → 4

Compiler

Compiled 591 to 388 computations (34.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_10649`
24×	`sqrt-prod_binary64_10665`
21×	`distribute-lft-out_binary64_10600`
18×	`times-frac_binary64_10655`
16×	`add-sqr-sqrt_binary64_10671`
15×	`add-cube-cbrt_binary64_10684`
7×	`add-exp-log_binary64_10687`
6×	`associate-/r*_binary64_10593`
5×	`add-log-exp_binary64_10688` `pow1_binary64_10710` `add-cbrt-cube_binary64_10685`
3×	`associate-/l*_binary64_10594` `flip-+_binary64_10623` `flip3-+_binary64_10652`
2×	`associate-/r/_binary64_10595` `div-exp_binary64_10700` `sqrt-div_binary64_10666`
1×	`sum-log_binary64_10740` `clear-num_binary64_10648` `sqrt-pow1_binary64_10667` `pow1/2_binary64_10729` `+-commutative_binary64_10579` `cbrt-undiv_binary64_10683` `frac-2neg_binary64_10660` `inv-pow_binary64_10734` `1-exp_binary64_10693` `div-inv_binary64_10646` `rec-exp_binary64_10699` `rem-sqrt-square_binary64_10662` `pow-flip_binary64_10723`

Counts

3 → 75

Calls

3 calls:

10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series50.0ms (0.7%)

Counts

3 → 12

Calls

3 calls:

18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
17.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
16.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 178 to 164 computations (7.9% saved)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4911	1227
1	4911	1227

prune92.0ms (1.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	81	10	91

Merged error: 0.1b

Counts

91 → 10

Compiler

Compiled 1342 to 981 computations (26.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite148.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64_10649`
700×	`sqrt-prod_binary64_10665`
594×	`times-frac_binary64_10655`
280×	`distribute-lft-out_binary64_10600`
254×	`add-sqr-sqrt_binary64_10671`
252×	`add-cube-cbrt_binary64_10684`
36×	`associate-/l*_binary64_10594`
28×	`sqrt-div_binary64_10666`
24×	`associate-/r/_binary64_10595`
18×	`associate-/r*_binary64_10593`
17×	`add-exp-log_binary64_10687`
14×	`flip-+_binary64_10623` `flip3-+_binary64_10652`
12×	`div-inv_binary64_10646`
11×	`add-cbrt-cube_binary64_10685`
8×	`pow1_binary64_10710` `div-exp_binary64_10700`
4×	`add-log-exp_binary64_10688` `cbrt-undiv_binary64_10683`
3×	`sqrt-pow1_binary64_10667` `pow1/2_binary64_10729` `pow-flip_binary64_10723`
2×	`clear-num_binary64_10648` `frac-2neg_binary64_10660` `1-exp_binary64_10693` `rec-exp_binary64_10699` `rem-sqrt-square_binary64_10662`
1×	`inv-pow_binary64_10734` `associate-/l/_binary64_10596`

Counts

4 → 453

Calls

4 calls:

30.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
12.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series87.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
22.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
20.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
19.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 392 to 352 computations (10.2% saved)

simplify220.0ms (3%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4875	14766
1	4875	14766

prune972.0ms (13.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	460	5	465
Fresh	4	3	7
Picked	1	0	1
Done	1	1	2
Total	466	9	475

Merged error: 0b

Counts

475 → 9

Compiler

Compiled 11606 to 8545 computations (26.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite192.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

887×	`*-un-lft-identity_binary64_10649`
880×	`sqrt-prod_binary64_10665`
774×	`times-frac_binary64_10655`
334×	`add-sqr-sqrt_binary64_10671` `add-cube-cbrt_binary64_10684`
316×	`distribute-lft-out_binary64_10600`
216×	`cbrt-prod_binary64_10680`
36×	`associate-/l*_binary64_10594`
30×	`associate-/r/_binary64_10595` `sqrt-div_binary64_10666`
21×	`associate-/r*_binary64_10593`
17×	`add-exp-log_binary64_10687` `flip-+_binary64_10623` `flip3-+_binary64_10652`
15×	`div-inv_binary64_10646`
11×	`add-cbrt-cube_binary64_10685`
8×	`div-exp_binary64_10700`
7×	`pow1_binary64_10710`
6×	`cbrt-div_binary64_10681`
5×	`pow-flip_binary64_10723`
4×	`add-log-exp_binary64_10688` `sqrt-pow1_binary64_10667` `cbrt-undiv_binary64_10683` `pow1/3_binary64_10731`
2×	`pow-div_binary64_10724` `clear-num_binary64_10648` `pow1/2_binary64_10729` `frac-2neg_binary64_10660` `1-exp_binary64_10693` `rec-exp_binary64_10699`
1×	`inv-pow_binary64_10734` `associate-/l/_binary64_10596`

Counts

4 → 553

Calls

4 calls:

33.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
15.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
8.0ms	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series138.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
37.0ms	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
30.0ms	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
29.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

Compiler

Compiled 724 to 622 computations (14.1% saved)

simplify299.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

565 → 565

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4878	28200
1	4878	28200

prune2.6s (35.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	565	0	565
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	565	9	574

Merged error: 0b

Counts

574 → 9

Compiler

Compiled 26146 to 19496 computations (25.4% saved)

regimes220.0ms (3%)

Compiler: Compiled 2732 to 2180 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.8s (25.1%)

Algorithm

1×

intervals

Results

204.0ms	1981×	body	1024	valid
128.0ms	4332×	body	128	valid
78.0ms	963×	body	512	valid
29.0ms	513×	body	256	valid
27.0ms	211×	body	2048	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 1355 to 1082 computations (20.1% saved)

Details

analyze3.0ms (0%)

sample20.0ms (0.3%)

simplify101.0ms (1.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite19.0ms (0.3%)

series45.0ms (0.6%)

simplify92.0ms (1.3%)

prune46.0ms (0.6%)

localize6.0ms (0.1%)

rewrite27.0ms (0.4%)

series50.0ms (0.7%)

simplify74.0ms (1%)

prune92.0ms (1.3%)

localize12.0ms (0.2%)

rewrite148.0ms (2%)

series87.0ms (1.2%)

simplify220.0ms (3%)

prune972.0ms (13.4%)

localize15.0ms (0.2%)

rewrite192.0ms (2.6%)

series138.0ms (1.9%)

simplify299.0ms (4.1%)

prune2.6s (35.2%)

regimes220.0ms (3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (25.1%)

Profiling