Details

analyze40.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify181.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	487	18
1	487	18

prune4.0ms (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: 0.2b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
0.2b	(/.f64 1 (*.f64 x 9))
0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64_10896`
18×	`*-un-lft-identity_binary64_10861`
17×	`add-sqr-sqrt_binary64_10882`
16×	`add-cbrt-cube_binary64_10894`
11×	`add-cube-cbrt_binary64_10893`
9×	`pow1_binary64_10919` `add-log-exp_binary64_10897`
6×	`associate-r_binary64_10803` `associate-/l*_binary64_10808` `times-frac_binary64_10867` `div-exp_binary64_10909`
5×	`prod-exp_binary64_10907` `distribute-lft-out--_binary64_10815`
4×	`cbrt-undiv_binary64_10892` `sqrt-prod_binary64_10876`
3×	`diff-log_binary64_10950` `cbrt-unprod_binary64_10891` `div-inv_binary64_10858` `associate-l_binary64_10804`
2×	`pow-flip_binary64_10932` `sub-neg_binary64_10854` `pow-prod-down_binary64_10929` `1-exp_binary64_10902` `flip--_binary64_10836` `unswap-sqr_binary64_10829` `frac-2neg_binary64_10872` `frac-sub_binary64_10870` `associate-/r*_binary64_10807` `clear-num_binary64_10860` `flip3--_binary64_10865` `rec-exp_binary64_10908`
1×	`associate--l+_binary64_10800` `*-commutative_binary64_10794` `associate--l-_binary64_10801` `difference-of-squares_binary64_10830` `inv-pow_binary64_10943`

Counts

4 → 91

Calls

4 calls:

14.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
6.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
6.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(/.f64 1 (*.f64 x 9))

series202.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
65.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
33.0ms	(*.f64 3 (sqrt.f64 x))
21.0ms	(/.f64 1 (*.f64 x 9))

simplify74.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4918	1401
1	4918	1401

prune133.0ms (3.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0.0b

Counts

105 → 9

Compiler

Compiled 2000 to 1441 computations (28% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
0.2b	(/.f64 1 (*.f64 x 9))
0.2b	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
0.4b	(/.f64 1/3 (sqrt.f64 x))

rewrite44.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_10882`
41×	`times-frac_binary64_10867`
35×	`*-un-lft-identity_binary64_10861` `add-cube-cbrt_binary64_10893`
22×	`associate-r_binary64_10803` `add-exp-log_binary64_10896` `sqrt-prod_binary64_10876`
16×	`add-cbrt-cube_binary64_10894`
9×	`pow1_binary64_10919` `add-log-exp_binary64_10897`
7×	`associate-/r*_binary64_10807`
6×	`associate-/l*_binary64_10808` `div-exp_binary64_10909`
5×	`prod-exp_binary64_10907`
4×	`cbrt-undiv_binary64_10892`
3×	`associate-r/_binary64_10805` `diff-log_binary64_10950` `cbrt-unprod_binary64_10891` `div-inv_binary64_10858` `unswap-sqr_binary64_10829` `associate-l*_binary64_10804`
2×	`pow-flip_binary64_10932` `sub-neg_binary64_10854` `pow-prod-down_binary64_10929` `1-exp_binary64_10902` `flip--_binary64_10836` `frac-2neg_binary64_10872` `frac-sub_binary64_10870` `clear-num_binary64_10860` `flip3--_binary64_10865` `rec-exp_binary64_10908`
1×	`associate--l+_binary64_10800` `*-commutative_binary64_10794` `associate--l-_binary64_10801` `inv-pow_binary64_10943`

Counts

4 → 125

Calls

4 calls:

13.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
10.0ms	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
5.0ms	(/.f64 1 (*.f64 x 9))
4.0ms	(/.f64 1/3 (sqrt.f64 x))

series221.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
62.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
53.0ms	(/.f64 1/3 (sqrt.f64 x))
21.0ms	(/.f64 1 (*.f64 x 9))

simplify80.0ms (2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4901	1867
1	4901	1867

prune161.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	137	9	146

Merged error: 0.0b

Counts

146 → 9

Compiler

Compiled 2760 to 1938 computations (29.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(*.f64 3 (sqrt.f64 x))
0.4b	(/.f64 1/9 x)

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_10882`
22×	`*-un-lft-identity_binary64_10861`
17×	`add-cube-cbrt_binary64_10893`
13×	`add-exp-log_binary64_10896` `add-cbrt-cube_binary64_10894`
12×	`times-frac_binary64_10867`
9×	`add-log-exp_binary64_10897`
6×	`associate-r_binary64_10803` `associate-/l*_binary64_10808` `pow1_binary64_10919`
4×	`associate-/r*_binary64_10807` `sqrt-prod_binary64_10876`
3×	`cbrt-undiv_binary64_10892` `distribute-lft-out--_binary64_10815` `diff-log_binary64_10950` `div-exp_binary64_10909` `associate-l_binary64_10804`
2×	`prod-exp_binary64_10907` `sub-neg_binary64_10854` `cbrt-unprod_binary64_10891` `flip--_binary64_10836` `div-inv_binary64_10858` `unswap-sqr_binary64_10829` `frac-2neg_binary64_10872` `frac-sub_binary64_10870` `clear-num_binary64_10860` `flip3--_binary64_10865`
1×	`pow-prod-down_binary64_10929` `associate--l+_binary64_10800` `*-commutative_binary64_10794` `associate--l-_binary64_10801` `difference-of-squares_binary64_10830`

Counts

4 → 89

Calls

4 calls:

15.0ms	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
5.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1/9 x)

series192.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
63.0ms	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
27.0ms	(*.f64 3 (sqrt.f64 x))
22.0ms	(/.f64 1/9 x)

simplify60.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4922	1447
1	4922	1447

prune106.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	101	9	110

Merged error: 0.0b

Counts

110 → 9

Compiler

Compiled 1877 to 1292 computations (31.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 y (.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x)))))
0.4b	(/.f64 1/3 (sqrt.f64 x))
0.4b	(/.f64 1/3 (sqrt.f64 x))
0.5b	(*.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))))

rewrite87.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

200×	`sqrt-prod_binary64_10876`
160×	`add-sqr-sqrt_binary64_10882`
136×	`times-frac_binary64_10867`
95×	`*-un-lft-identity_binary64_10861` `add-cube-cbrt_binary64_10893`
33×	`swap-sqr_binary64_10828`
28×	`associate-l_binary64_10804`
26×	`associate-r_binary64_10803`
24×	`pow1_binary64_10919`
17×	`unswap-sqr_binary64_10829`
15×	`add-exp-log_binary64_10896` `add-cbrt-cube_binary64_10894`
12×	`associate-/r*_binary64_10807`
8×	`pow1/2_binary64_10938` `sqrt-pow1_binary64_10878` `sqrt-div_binary64_10877`
6×	`pow-prod-down_binary64_10929` `associate-/l*_binary64_10808` `div-inv_binary64_10858`
5×	`associate-*r/_binary64_10805` `pow-prod-up_binary64_10928`
4×	`prod-exp_binary64_10907` `cbrt-unprod_binary64_10891` `add-log-exp_binary64_10897`
3×	`pow-sqr_binary64_10834`
2×	`cbrt-undiv_binary64_10892` `frac-times_binary64_10871` `-commutative_binary64_10794` `associate-l/_binary64_10806` `frac-2neg_binary64_10872` `clear-num_binary64_10860` `div-exp_binary64_10909`
1×	`pow-plus_binary64_10921` `sqrt-unprod_binary64_10880` `pow2_binary64_10939` `rem-square-sqrt_binary64_10873`

Counts

4 → 227

Calls

4 calls:

26.0ms	(*.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))))
21.0ms	(.f64 y (.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x)))))
5.0ms	(/.f64 1/3 (sqrt.f64 x))
5.0ms	(/.f64 1/3 (sqrt.f64 x))

series386.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(.f64 y (.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x)))))
122.0ms	(*.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))))
52.0ms	(/.f64 1/3 (sqrt.f64 x))
51.0ms	(/.f64 1/3 (sqrt.f64 x))

simplify92.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5064	3637

prune348.0ms (8.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	239	9	248

Merged error: 0.0b

Counts

248 → 9

Compiler

Compiled 5965 to 4205 computations (29.5% saved)

regimes197.0ms (5%)

Compiler: Compiled 1880 to 1651 computations (12.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	21
1	57	21

end0.0ms (0%)

sample1.2s (31.2%)

Algorithm

1×

intervals

Results

364.0ms	8000×	body	128	valid
5.0ms	103×	body	128	invalid

Compiler

Compiled 659 to 581 computations (11.8% saved)

Details

analyze40.0ms (1%)

sample19.0ms (0.5%)

simplify181.0ms (4.5%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite38.0ms (1%)

series202.0ms (5.1%)

simplify74.0ms (1.8%)

prune133.0ms (3.3%)

localize9.0ms (0.2%)

rewrite44.0ms (1.1%)

series221.0ms (5.5%)

simplify80.0ms (2%)

prune161.0ms (4%)

localize8.0ms (0.2%)

rewrite35.0ms (0.9%)

series192.0ms (4.8%)

simplify60.0ms (1.5%)

prune106.0ms (2.7%)

localize12.0ms (0.3%)

rewrite87.0ms (2.2%)

series386.0ms (9.7%)

simplify92.0ms (2.3%)

prune348.0ms (8.7%)

regimes197.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (31.2%)

Profiling