Details

analyze7.0ms (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)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify170.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

prune13.0ms (0.3%)

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

Error

27.4b

Counts

2 → 1

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

26.4b

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

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

13.4b

Rules

4×	`pow1_binary64_139`
2×	`sqrt-pow1_binary64_96` `associate-*r/_binary64_20` `sqrt-div_binary64_95`
1×	`pow1/2_binary64_158` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `pow-prod-down_binary64_149` `flip3-+_binary64_81` `flip-+_binary64_52` `sqrt-prod_binary64_94` `*-un-lft-identity_binary64_78`

Counts

1 → 13

Calls

1 calls:

9.0ms

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

Compiler

Compiled 161 to 50 computations (68.9% saved)

series59.0ms (1.3%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

52.0ms

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

Compiler

Compiled 42 to 40 computations (4.8% saved)

simplify133.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	5009	140

prune34.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	6	17

Error

0.1b

Counts

17 → 6

Compiler

Compiled 174 to 79 computations (54.6% saved)

localize12.0ms (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)))))
26.4b	(sqrt.f64 (*.f64 x (+.f64 x x)))
26.4b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite258.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

84×	`sqrt-pow1_binary64_96`
71×	`pow1_binary64_139`
33×	`sqrt-prod_binary64_94`
32×	`sqrt-div_binary64_95`
28×	`add-sqr-sqrt_binary64_100`
25×	`pow-prod-down_binary64_149`
22×	`pow1/2_binary64_158`
20×	`associate-*r/_binary64_20`
14×	`pow-prod-up_binary64_148`
13×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`flip3-+_binary64_81` `flip-+_binary64_52` `swap-sqr_binary64_45`
8×	`pow-sqr_binary64_51`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `frac-times_binary64_88` `unswap-sqr_binary64_46`
3×	`rem-sqrt-square_binary64_91`
2×	`associate-*l/_binary64_21`
1×	`pow2_binary64_159` `pow-plus_binary64_141` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `sqrt-unprod_binary64_98` `sqr-abs_binary64_93` `rem-square-sqrt_binary64_90` `*-commutative_binary64_9`

Counts

4 → 125

Calls

4 calls:

38.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
11.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
10.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
9.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 2803 to 549 computations (80.4% saved)

series210.0ms (4.6%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
54.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
49.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
37.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))

Compiler

Compiled 437 to 311 computations (28.8% saved)

simplify170.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4704	1347
1	4704	1347

prune163.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	135	8	143

Error

0.1b

Counts

143 → 8

Compiler

Compiled 1998 to 518 computations (74.1% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3)))
19.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))
26.4b	(sqrt.f64 (*.f64 x (+.f64 x x)))
26.4b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite330.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

52×	`cbrt-prod_binary64_109`
43×	`add-sqr-sqrt_binary64_100`
38×	`sqrt-prod_binary64_94`
32×	`sqrt-div_binary64_95`
23×	`associate-r_binary64_18`
20×	`associate-*r/_binary64_20`
18×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
17×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
14×	`unswap-sqr_binary64_46`
12×	`pow1_binary64_139`
9×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`cube-div_binary64_107` `cbrt-div_binary64_110`
7×	`associate-l_binary64_19`
6×	`add-exp-log_binary64_116`
5×	`add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `sqr-pow_binary64_50` `frac-times_binary64_88`
3×	`pow-prod-down_binary64_149`
2×	`pow1/2_binary64_158` `unpow3_binary64_144` `cube-mult_binary64_108` `associate-*l/_binary64_21`
1×	`pow1/3_binary64_160` `rem-cbrt-cube_binary64_102` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `*-commutative_binary64_9`

Counts

4 → 120

Calls

4 calls:

41.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3)))
10.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
9.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
9.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))

Compiler

Compiled 3683 to 1037 computations (71.8% saved)

series219.0ms (4.8%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
52.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
51.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3)))
39.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))

Compiler

Compiled 491 to 365 computations (25.7% saved)

simplify136.0ms (3%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4497	2135
1	4497	2135

prune193.0ms (4.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	132	8	140

Error

0.1b

Counts

140 → 8

Compiler

Compiled 2652 to 710 computations (73.2% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-sqr-sqrt_binary64_100`
6×	`associate-r_binary64_18`
4×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `sqrt-prod_binary64_94`
3×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `associate-l_binary64_19`
2×	`unswap-sqr_binary64_46`
1×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `*-commutative_binary64_9`

Counts

1 → 22

Calls

1 calls:

10.0ms

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

Compiler

Compiled 228 to 188 computations (17.5% saved)

series58.0ms (1.3%)

Error

0.1b

Counts

1 → 3

Calls

1 calls:

55.0ms

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

Compiler

Compiled 45 to 43 computations (4.4% saved)

simplify88.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5010	211

prune33.0ms (0.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	1	3	4
Picked	0	1	1
Done	1	2	3
Total	25	8	33

Error

0.0b

Counts

33 → 8

Compiler

Compiled 218 to 179 computations (17.9% saved)

regimes509.0ms (11.2%)

Accuracy

Total 0.3b remaining (88.2%)

Threshold costs 0.3b (88.2%)

Compiler

Compiled 1878 to 1036 computations (44.8% saved)

bsearch33.0ms (0.7%)

Steps

Iters	Range		Point
8	-2.294159949323056e-307	3.373081245366399e-305	-1.7163347373368e-310

Compiler

Compiled 1 to 1 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	61	41
1	61	41

end0.0ms (0%)

sample1.6s (34.4%)

Algorithm

1×

intervals

Results

341.0ms

8000×

body

128

valid

Compiler

Compiled 494 to 281 computations (43.1% saved)

Details

analyze7.0ms (0.2%)

sample23.0ms (0.5%)

simplify170.0ms (3.7%)

prune13.0ms (0.3%)

localize8.0ms (0.2%)

rewrite34.0ms (0.8%)

series59.0ms (1.3%)

simplify133.0ms (2.9%)

prune34.0ms (0.7%)

localize12.0ms (0.3%)

rewrite258.0ms (5.7%)

series210.0ms (4.6%)

simplify170.0ms (3.7%)

prune163.0ms (3.6%)

localize19.0ms (0.4%)

rewrite330.0ms (7.3%)

series219.0ms (4.8%)

simplify136.0ms (3%)

prune193.0ms (4.3%)

localize8.0ms (0.2%)

rewrite47.0ms (1%)

series58.0ms (1.3%)

simplify88.0ms (1.9%)

prune33.0ms (0.7%)

regimes509.0ms (11.2%)

bsearch33.0ms (0.7%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.6s (34.4%)

Profiling