Details

analyze59.0ms (2%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample13.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify161.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

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: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_5842`
1×	`pow1_binary64_5864` `flip3-+_binary64_5809` `flip-+_binary64_5780` `+-commutative_binary64_5738` `add-sqr-sqrt_binary64_5827` `add-exp-log_binary64_5841` `add-cbrt-cube_binary64_5839` `add-cube-cbrt_binary64_5838` `*-un-lft-identity_binary64_5806` `sum-log_binary64_5894`

Counts

1 → 11

Calls

1 calls:

4.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

series40.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

40.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

simplify31.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5014	193

prune12.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	11	3	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	4	15

Merged error: 0.0b

Counts

15 → 4

Compiler

Compiled 222 to 68 computations (69.4% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
6.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
6.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite21.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_5827` `add-log-exp_binary64_5842`
6×	`pow1_binary64_5864` `sqrt-prod_binary64_5821` `add-cube-cbrt_binary64_5838` `*-un-lft-identity_binary64_5806`
4×	`flip3-+_binary64_5809` `sqrt-div_binary64_5822` `flip-+_binary64_5780` `add-exp-log_binary64_5841` `add-cbrt-cube_binary64_5839`
2×	`+-commutative_binary64_5738` `rem-sqrt-square_binary64_5819` `pow1/2_binary64_5883` `sqrt-pow1_binary64_5823` `sum-log_binary64_5894`

Counts

4 → 52

Calls

4 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series306.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
47.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
38.0ms	(+.f64 (.f64 x x) (.f64 y y))
36.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify98.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4913	886
1	4913	886

prune49.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	64	4	68

Merged error: 0.0b

Counts

68 → 4

Compiler

Compiled 1413 to 238 computations (83.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
7.0b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite34.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_5834`
23×	`add-sqr-sqrt_binary64_5827`
18×	`cbrt-div_binary64_5835`
15×	`add-cube-cbrt_binary64_5838` `*-un-lft-identity_binary64_5806`
11×	`pow1_binary64_5864`
9×	`flip3-+_binary64_5809` `flip-+_binary64_5780` `pow1/3_binary64_5885`
6×	`swap-sqr_binary64_5773` `associate-l_binary64_5749` `associate-r_binary64_5748` `add-exp-log_binary64_5841`
4×	`frac-times_binary64_5816` `unswap-sqr_binary64_5774` `add-log-exp_binary64_5842` `add-cbrt-cube_binary64_5839`
2×	`pow-prod-up_binary64_5873` `pow-sqr_binary64_5779` `associate-r/_binary64_5750` `pow-prod-down_binary64_5874` `associate-l/_binary64_5751`
1×	`prod-exp_binary64_5852` `cbrt-unprod_binary64_5836` `pow-plus_binary64_5866` `pow2_binary64_5884` `*-commutative_binary64_5739`

Counts

4 → 87

Calls

4 calls:

12.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series549.0ms (19%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
141.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
138.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
118.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify86.0ms (3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4890	2047
1	4890	2047

prune98.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	100	3	103

Merged error: 0b

Counts

103 → 3

Compiler

Compiled 3134 to 585 computations (81.3% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) 4)
7.0b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64_5834`
11×	`add-sqr-sqrt_binary64_5827` `add-cube-cbrt_binary64_5838` `*-un-lft-identity_binary64_5806`
9×	`unpow-prod-down_binary64_5882`
6×	`cbrt-div_binary64_5835`
5×	`pow1_binary64_5864` `add-exp-log_binary64_5841`
4×	`add-log-exp_binary64_5842` `add-cbrt-cube_binary64_5839` `pow1/3_binary64_5885`
3×	`flip3-+_binary64_5809` `flip-+_binary64_5780` `pow-unpow_binary64_5880`
2×	`pow-pow_binary64_5875`
1×	`pow-exp_binary64_5871` `sqr-pow_binary64_5778` `pow-to-exp_binary64_5872`

Counts

4 → 63

Calls

4 calls:

7.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) 4)
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series580.0ms (20.1%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) 4)
131.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
123.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
122.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify49.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4889	1421
1	4889	1421

prune93.0ms (3.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	75	3	78

Merged error: 0b

Counts

78 → 3

Compiler

Compiled 2831 to 752 computations (73.4% saved)

regimes76.0ms (2.6%)

Compiler: Compiled 760 to 350 computations (53.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

end0.0ms (0%)

sample463.0ms (16%)

Algorithm

1×

intervals

Results

179.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 161 to 77 computations (52.2% saved)

Details

analyze59.0ms (2%)

sample13.0ms (0.4%)

simplify161.0ms (5.6%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

rewrite5.0ms (0.2%)

series40.0ms (1.4%)

simplify31.0ms (1.1%)

prune12.0ms (0.4%)

localize6.0ms (0.2%)

rewrite21.0ms (0.7%)

series306.0ms (10.6%)

simplify98.0ms (3.4%)

prune49.0ms (1.7%)

localize8.0ms (0.3%)

rewrite34.0ms (1.2%)

series549.0ms (19%)

simplify86.0ms (3%)

prune98.0ms (3.4%)

localize14.0ms (0.5%)

rewrite30.0ms (1%)

series580.0ms (20.1%)

simplify49.0ms (1.7%)

prune93.0ms (3.2%)

regimes76.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample463.0ms (16%)

Profiling