Details

analyze265.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample60.0ms (1.5%)

Algorithm

1×

intervals

Results

19.0ms	99×	body	2560	nan
14.0ms	87×	body	1280	nan
11.0ms	256×	body	80	valid
4.0ms	32×	body	640	nan
2.0ms	16×	body	320	nan
1.0ms	11×	body	160	nan
0.0ms	13×	body	80	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify255.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (240.0ms)

Iter	Nodes	Cost
0	5151	14

prune2.0ms (0.1%)

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: 32.1b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
29.8b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`pow1_binary64` `log-prod_binary64` `add-cube-cbrt_binary64`
3×	`add-exp-log_binary64`
2×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `log-div_binary64` `insert-posit16` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `log-pow_binary64` `difference-of-sqr-1_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 35

Calls

2 calls:

8.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
8.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series133.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

91.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
42.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify97.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4935	693
1	4935	693

prune39.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 0b

Counts

42 → 2

Compiler

Compiled 637 to 426 computations (33.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `sqrt-div_binary64`
10×	`associate-r_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64` `associate-l_binary64`
5×	`add-exp-log_binary64`
4×	`flip3-+_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `log-prod_binary64` `flip--_binary64`
2×	`add-log-exp_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `log-div_binary64` `insert-posit16` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `log-pow_binary64` `difference-of-sqr-1_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

2 → 59

Calls

2 calls:

15.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series162.0ms (4.1%)

Counts

2 → 6

Calls

2 calls:

85.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
78.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

simplify182.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	4897	1414
1	4897	1414

prune73.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	2	67

Merged error: 0b

Counts

67 → 2

Compiler

Compiled 1298 to 985 computations (24.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
0.1b	(/.f64 3/32 (pow.f64 x 4))
0.2b	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
0.3b	(/.f64 1/4 (*.f64 x x))

rewrite58.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
12×	`unpow-prod-down_binary64`
11×	`pow1_binary64` `add-cbrt-cube_binary64`
10×	`add-log-exp_binary64`
8×	`associate-/r*_binary64`
7×	`log-pow_binary64`
6×	`distribute-lft-out_binary64` `log-prod_binary64` `associate-/l*_binary64`
5×	`diff-log_binary64` `div-exp_binary64`
4×	`associate--r+_binary64` `sqr-pow_binary64` `insert-posit16`
3×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `associate--l+_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `associate-+r-_binary64` `cbrt-unprod_binary64` `associate--r-_binary64` `prod-exp_binary64` `pow-exp_binary64`

Counts

4 → 115

Calls

4 calls:

29.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
13.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
6.0ms	(/.f64 1/4 (*.f64 x x))
5.0ms	(/.f64 3/32 (pow.f64 x 4))

series363.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
81.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
52.0ms	(/.f64 3/32 (pow.f64 x 4))
36.0ms	(/.f64 1/4 (*.f64 x x))

simplify109.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4931	2226
1	4931	2226

prune155.0ms (3.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	127	2	129

Merged error: 0b

Counts

129 → 2

Compiler

Compiled 2838 to 1922 computations (32.3% saved)

regimes8.0ms (0.2%)

Compiler: Compiled 31 to 26 computations (16.1% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19

end0.0ms (0%)

sample1.9s (48.9%)

Algorithm

1×

intervals

Results

603.0ms	3113×	body	2560	nan
413.0ms	2554×	body	1280	nan
343.0ms	8000×	body	80	valid
166.0ms	1276×	body	640	nan
59.0ms	609×	body	320	nan
22.0ms	321×	body	160	nan
11.0ms	318×	body	80	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

Details

analyze265.0ms (6.6%)

sample60.0ms (1.5%)

simplify255.0ms (6.4%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite18.0ms (0.4%)

series133.0ms (3.3%)

simplify97.0ms (2.4%)

prune39.0ms (1%)

localize9.0ms (0.2%)

rewrite23.0ms (0.6%)

series162.0ms (4.1%)

simplify182.0ms (4.6%)

prune73.0ms (1.8%)

localize13.0ms (0.3%)

rewrite58.0ms (1.5%)

series363.0ms (9.1%)

simplify109.0ms (2.7%)

prune155.0ms (3.9%)

regimes8.0ms (0.2%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.9s (48.9%)

Profiling