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

6.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify164.0ms (8.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

prune7.0ms (0.4%)

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 26 to 16 computations (38.5% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

27.6b

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

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_140`
2×	`associate-*r/_binary64_21` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96`
1×	`sqrt-prod_binary64_95` `add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `flip-+_binary64_53` `add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101` `pow-prod-down_binary64_150` `add-log-exp_binary64_118` `pow1/2_binary64_159` `flip3-+_binary64_82` `*-un-lft-identity_binary64_79`

Counts

1 → 13

Calls

1 calls:

5.0ms

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

series48.0ms (2.5%)

Counts

1 → 3

Calls

1 calls:

48.0ms

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

simplify69.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4711	140
1	4711	140

prune55.0ms (2.8%)

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 608 to 351 computations (42.3% 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 (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-pow1_binary64_97`
71×	`pow1_binary64_140`
33×	`sqrt-prod_binary64_95`
32×	`sqrt-div_binary64_96`
28×	`add-sqr-sqrt_binary64_101`
25×	`pow-prod-down_binary64_150`
22×	`pow1/2_binary64_159`
20×	`associate-*r/_binary64_21`
14×	`pow-prod-up_binary64_149`
13×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
9×	`flip-+_binary64_53` `swap-sqr_binary64_46` `flip3-+_binary64_82`
8×	`pow-sqr_binary64_52`
7×	`associate-l_binary64_20` `associate-r_binary64_19`
6×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
4×	`frac-times_binary64_89` `unswap-sqr_binary64_47` `add-log-exp_binary64_118`
3×	`rem-sqrt-square_binary64_92`
2×	`associate-*l/_binary64_22`
1×	`sqrt-unprod_binary64_99` `rem-square-sqrt_binary64_91` `sqr-abs_binary64_94` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-plus_binary64_142` `pow2_binary64_160`

Counts

4 → 125

Calls

4 calls:

20.0ms	(.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)))

series191.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
49.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
43.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
42.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify74.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4874	1431
1	4874	1431

prune94.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	137	7	144

Merged error: 0.2b

Counts

144 → 7

Compiler

Compiled 2087 to 590 computations (71.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite7.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_101`
6×	`associate-r_binary64_19`
4×	`sqrt-prod_binary64_95` `add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
3×	`add-exp-log_binary64_117` `associate-l_binary64_20` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
2×	`unswap-sqr_binary64_47`
1×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `add-log-exp_binary64_118`

Counts

1 → 22

Calls

1 calls:

6.0ms

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

series57.0ms (2.9%)

Counts

1 → 3

Calls

1 calls:

57.0ms

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

simplify44.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4987	211
1	4987	211

prune63.0ms (3.2%)

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 712 to 564 computations (20.8% saved)

localize7.0ms (0.4%)

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)))

rewrite27.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_117` `pow1_binary64_140`
10×	`associate-r_binary64_19`
9×	`add-cbrt-cube_binary64_115` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150`
7×	`add-sqr-sqrt_binary64_101`
6×	`add-cube-cbrt_binary64_114` `cbrt-prod_binary64_110` `*-un-lft-identity_binary64_79`
4×	`associate-l_binary64_20`
3×	`sqrt-prod_binary64_95`
2×	`*-commutative_binary64_10` `add-log-exp_binary64_118`
1×	`unswap-sqr_binary64_47`

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))))

series333.0ms (16.9%)

Counts

2 → 6

Calls

2 calls:

278.0ms	(.f64 x (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
55.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

simplify56.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4902	577
1	4902	577

prune68.0ms (3.4%)

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 896 to 791 computations (11.7% saved)

regimes27.0ms (1.4%)

Compiler: Compiled 107 to 88 computations (17.8% 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	61	41
1	61	41

end0.0ms (0%)

sample479.0ms (24.3%)

Algorithm

1×

intervals

Results

183.0ms

8000×

body

128

valid

Compiler

Compiled 139 to 113 computations (18.7% saved)

Details

analyze4.0ms (0.2%)

sample10.0ms (0.5%)

simplify164.0ms (8.3%)

prune7.0ms (0.4%)

localize4.0ms (0.2%)

rewrite6.0ms (0.3%)

series48.0ms (2.5%)

simplify69.0ms (3.5%)

prune55.0ms (2.8%)

localize6.0ms (0.3%)

rewrite53.0ms (2.7%)

series191.0ms (9.7%)

simplify74.0ms (3.7%)

prune94.0ms (4.8%)

localize4.0ms (0.2%)

rewrite7.0ms (0.4%)

series57.0ms (2.9%)

simplify44.0ms (2.2%)

prune63.0ms (3.2%)

localize7.0ms (0.4%)

rewrite27.0ms (1.3%)

series333.0ms (16.9%)

simplify56.0ms (2.8%)

prune68.0ms (3.4%)

regimes27.0ms (1.4%)

bsearch15.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample479.0ms (24.3%)

Profiling