Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 9 to 5 computations (44.4% saved)

sample10.0ms (0.5%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify157.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.6b

Counts

2 → 1

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

27.6b

(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_135`
2×	`sqrt-pow1_binary64_94` `sqrt-div_binary64_93` `associate-*r/_binary64_21`
1×	`add-exp-log_binary64_112` `sqrt-prod_binary64_92` `add-cbrt-cube_binary64_110` `pow-prod-down_binary64_145` `add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80` `add-cube-cbrt_binary64_109` `pow1/2_binary64_154` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`

Counts

1 → 13

Calls

1 calls:

9.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

series51.0ms (2.4%)

Counts

1 → 3

Calls

1 calls:

50.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify66.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4711	140
1	4711	140

prune20.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	10	6	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	7	17

Merged error: 0.2b

Counts

17 → 7

Compiler

Compiled 183 to 86 computations (53% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
27.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite53.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-pow1_binary64_94`
71×	`pow1_binary64_135`
33×	`sqrt-prod_binary64_92`
32×	`sqrt-div_binary64_93`
26×	`add-sqr-sqrt_binary64_98`
25×	`pow-prod-down_binary64_145`
22×	`pow1/2_binary64_154`
20×	`associate-*r/_binary64_21`
14×	`pow-prod-up_binary64_144`
13×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
9×	`flip-+_binary64_51` `flip3-+_binary64_80` `swap-sqr_binary64_44`
8×	`pow-sqr_binary64_50`
7×	`associate-l_binary64_20` `associate-r_binary64_19`
6×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
4×	`add-log-exp_binary64_113` `frac-times_binary64_87` `unswap-sqr_binary64_45`
2×	`associate-*l/_binary64_22`
1×	`rem-square-sqrt_binary64_89` `pow2_binary64_155` `rem-sqrt-square_binary64_90` `cbrt-unprod_binary64_107` `pow-plus_binary64_137` `prod-exp_binary64_123` `*-commutative_binary64_10` `sqrt-unprod_binary64_96`

Counts

4 → 124

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series197.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
52.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
44.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
44.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify51.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4890	1465
1	4890	1465

prune87.0ms (4.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	136	7	143

Merged error: 0.2b

Counts

143 → 7

Compiler

Compiled 2028 to 544 computations (73.2% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 2))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_98`
6×	`associate-r_binary64_19`
4×	`sqrt-prod_binary64_92` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
3×	`add-exp-log_binary64_112` `associate-l_binary64_20` `add-cbrt-cube_binary64_110` `pow1_binary64_135`
2×	`unswap-sqr_binary64_45`
1×	`pow-prod-down_binary64_145` `add-log-exp_binary64_113` `cbrt-unprod_binary64_107` `prod-exp_binary64_123` `*-commutative_binary64_10`

Counts

1 → 22

Calls

1 calls:

6.0ms

(*.f64 x (sqrt.f64 2))

series45.0ms (2.1%)

Counts

1 → 3

Calls

1 calls:

45.0ms

(*.f64 x (sqrt.f64 2))

simplify45.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4987	211
1	4987	211

prune23.0ms (1.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	22	10	32

Merged error: 0.1b

Counts

32 → 10

Compiler

Compiled 283 to 235 computations (17% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 x (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite26.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_112` `pow1_binary64_135`
10×	`associate-r_binary64_19`
9×	`add-cbrt-cube_binary64_110` `pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123`
7×	`add-sqr-sqrt_binary64_98`
6×	`cbrt-prod_binary64_105` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
4×	`associate-l_binary64_20`
3×	`sqrt-prod_binary64_92`
2×	`add-log-exp_binary64_113` `*-commutative_binary64_10`
1×	`unswap-sqr_binary64_45`

Counts

2 → 46

Calls

2 calls:

14.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
9.0ms	(.f64 x (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series339.0ms (16%)

Counts

2 → 6

Calls

2 calls:

282.0ms	(.f64 x (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
56.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

simplify70.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5074	577

prune49.0ms (2.3%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	5	6
Picked	0	1	1
Done	0	3	3
Total	52	10	62

Merged error: 0.1b

Counts

62 → 10

Compiler

Compiled 665 to 599 computations (9.9% saved)

regimes187.0ms (8.8%)

Compiler: Compiled 933 to 708 computations (24.1% saved)

bsearch15.0ms (0.7%)

Steps

Iters	Range		Point
8	-1.127321002485621e-305	5.20687394484729e-309	3.2457638208323e-310

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	37
1	59	37

end0.0ms (0%)

sample576.0ms (27.2%)

Algorithm

1×

intervals

Results

176.0ms

8000×

body

128

valid

Compiler

Compiled 237 to 185 computations (21.9% saved)

Details

analyze4.0ms (0.2%)

sample10.0ms (0.5%)

simplify157.0ms (7.4%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

rewrite10.0ms (0.5%)

series51.0ms (2.4%)

simplify66.0ms (3.1%)

prune20.0ms (0.9%)

localize6.0ms (0.3%)

rewrite53.0ms (2.5%)

series197.0ms (9.3%)

simplify51.0ms (2.4%)

prune87.0ms (4.1%)

localize4.0ms (0.2%)

rewrite7.0ms (0.3%)

series45.0ms (2.1%)

simplify45.0ms (2.1%)

prune23.0ms (1.1%)

localize7.0ms (0.3%)

rewrite26.0ms (1.2%)

series339.0ms (16%)

simplify70.0ms (3.3%)

prune49.0ms (2.3%)

regimes187.0ms (8.8%)

bsearch15.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample576.0ms (27.2%)

Profiling