Details

analyze12.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample25.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify223.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4787	28
1	4787	28

prune3.0ms (0.1%)

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: 33.0b

Counts

2 → 1

Compiler

Compiled 38 to 24 computations (36.8% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
4.5b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
32.4b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64_14435` `add-sqr-sqrt_binary64_14422` `*-un-lft-identity_binary64_14400`
9×	`times-frac_binary64_14406`
7×	`add-log-exp_binary64_14439`
5×	`add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
3×	`associate-/r_binary64_14344` `pow1_binary64_14461` `associate-/l_binary64_14345`
2×	`associate-/l/_binary64_14347` `flip3-+_binary64_14403` `flip--_binary64_14375` `flip3--_binary64_14404` `flip-+_binary64_14374` `associate-/r/_binary64_14346`
1×	`sub-neg_binary64_14393` `+-commutative_binary64_14330` `cancel-sign-sub-inv_binary64_14366` `frac-2neg_binary64_14411` `cbrt-undiv_binary64_14434` `clear-num_binary64_14399` `div-exp_binary64_14451` `div-inv_binary64_14397` `diff-log_binary64_14492` `sum-log_binary64_14491` `div-sub_binary64_14405`

Counts

3 → 55

Calls

3 calls:

11.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
4.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
4.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

series125.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

51.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
37.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
36.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

simplify91.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4917	1786
1	4917	1786

prune87.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	6	65

Merged error: 0.4b

Counts

65 → 6

Compiler

Compiled 1851 to 990 computations (46.5% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune4.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Merged error: 0.4b

Counts

6 → 6

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
0.0b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4)))) (/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))))
22.5b	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))
25.6b	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))

rewrite52.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
14×	`add-sqr-sqrt_binary64_14422`
12×	`*-un-lft-identity_binary64_14400`
10×	`add-cube-cbrt_binary64_14435` `associate-/r/_binary64_14346` `times-frac_binary64_14406`
9×	`cancel-sign-sub-inv_binary64_14366`
8×	`add-log-exp_binary64_14439`
6×	`associate-/r*_binary64_14344` `flip3-+_binary64_14403` `flip-+_binary64_14374`
5×	`cbrt-undiv_binary64_14434` `div-exp_binary64_14451` `div-inv_binary64_14397`
4×	`cbrt-unprod_binary64_14433` `prod-exp_binary64_14449` `pow1_binary64_14461`
3×	`distribute-rgt-out--_binary64_14354`
2×	`frac-2neg_binary64_14411` `difference-of-squares_binary64_14369` `clear-num_binary64_14399` `associate-/l*_binary64_14345`
1×	`sub-neg_binary64_14393` `frac-sub_binary64_14409` `+-commutative_binary64_14330` `sub-div_binary64_14407` `flip--_binary64_14375` `flip3--_binary64_14404` `distribute-lft-out--_binary64_14352` `diff-log_binary64_14492` `sum-log_binary64_14491`

Counts

4 → 87

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4)))) (/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))))
15.0ms	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
7.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))
4.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

series185.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4)))) (/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))))
50.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))
39.0ms	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
27.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5156	2756

prune149.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	98	7	105

Merged error: 0.4b

Counts

105 → 7

Compiler

Compiled 3657 to 1927 computations (47.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))) (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))))
25.6b	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
30.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
30.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))

rewrite105.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64_14422`
99×	`times-frac_binary64_14406`
64×	`add-cube-cbrt_binary64_14435` `*-un-lft-identity_binary64_14400`
54×	`sqrt-prod_binary64_14416`
30×	`swap-sqr_binary64_14367`
25×	`add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
24×	`associate-l_binary64_14341` `associate-r_binary64_14340`
13×	`pow1_binary64_14461`
12×	`sqrt-div_binary64_14417`
10×	`associate-/r/_binary64_14346`
9×	`unswap-sqr_binary64_14368`
7×	`cbrt-unprod_binary64_14433` `flip3-+_binary64_14403` `prod-exp_binary64_14449` `cbrt-undiv_binary64_14434` `div-exp_binary64_14451` `flip-+_binary64_14374`
5×	`div-inv_binary64_14397`
4×	`add-log-exp_binary64_14439`
3×	`associate-/r*_binary64_14344`
2×	`sqrt-pow1_binary64_14418` `pow1/2_binary64_14480` `rem-sqrt-square_binary64_14413`
1×	`associate-l/_binary64_14343` `pow-plus_binary64_14463` `pow-prod-down_binary64_14471` `frac-2neg_binary64_14411` `pow2_binary64_14481` `frac-times_binary64_14410` `clear-num_binary64_14399` `associate-r/_binary64_14342` `pow-prod-up_binary64_14470` `pow-sqr_binary64_14373` `-commutative_binary64_14331` `associate-/l_binary64_14345`

Counts

4 → 166

Calls

4 calls:

48.0ms	(.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))) (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))))
9.0ms	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))

series145.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))) (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))))
38.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
33.0ms	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
31.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))

simplify140.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5034	5878

prune440.0ms (13.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	178	7	185

Merged error: 0.4b

Counts

185 → 7

Compiler

Compiled 8712 to 4797 computations (44.9% saved)

regimes367.0ms (11.1%)

Compiler: Compiled 2373 to 1503 computations (36.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	98
1	65	98

end0.0ms (0%)

sample986.0ms (29.9%)

Algorithm

1×

intervals

Results

398.0ms

8000×

body

128

valid

Compiler

Compiled 613 to 371 computations (39.5% saved)

Details

analyze12.0ms (0.4%)

sample25.0ms (0.8%)

simplify223.0ms (6.8%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

rewrite24.0ms (0.7%)

series125.0ms (3.8%)

simplify91.0ms (2.7%)

prune87.0ms (2.6%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.2%)

prune4.0ms (0.1%)

localize20.0ms (0.6%)

rewrite52.0ms (1.6%)

series185.0ms (5.6%)

simplify78.0ms (2.4%)

prune149.0ms (4.5%)

localize12.0ms (0.4%)

rewrite105.0ms (3.2%)

series145.0ms (4.4%)

simplify140.0ms (4.2%)

prune440.0ms (13.4%)

regimes367.0ms (11.1%)

bsearch1.0ms (0%)

simplify5.0ms (0.2%)

end0.0ms (0%)

sample986.0ms (29.9%)

Profiling