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 (0.4%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify162.0ms (6.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

prune4.0ms (0.2%)

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:

27.5b

(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)))

series46.0ms (1.9%)

Counts

1 → 3

Calls

1 calls:

45.0ms

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

simplify69.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4711	140
1	4711	140

prune55.0ms (2.3%)

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 652 to 333 computations (48.9% 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)))))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite53.0ms (2.2%)

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:

21.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
9.0ms	(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)))

series185.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(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)))))
45.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
42.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify74.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4874	1431
1	4874	1431

prune119.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	136	8	144

Merged error: 0.2b

Counts

144 → 8

Compiler

Compiled 2466 to 777 computations (68.5% saved)

localize10.0ms (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)))
19.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite54.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`cbrt-prod_binary64_110`
43×	`add-sqr-sqrt_binary64_101`
38×	`sqrt-prod_binary64_95`
32×	`sqrt-div_binary64_96`
23×	`associate-r_binary64_19`
20×	`associate-*r/_binary64_21`
18×	`unpow-prod-down_binary64_158` `cube-prod_binary64_107`
17×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
14×	`unswap-sqr_binary64_47`
12×	`pow1_binary64_140`
9×	`flip-+_binary64_53` `flip3-+_binary64_82`
8×	`cube-div_binary64_108` `cbrt-div_binary64_111`
7×	`associate-l_binary64_20`
6×	`add-exp-log_binary64_117`
5×	`add-cbrt-cube_binary64_115`
4×	`sqr-pow_binary64_51` `frac-times_binary64_89` `sqrt-pow1_binary64_97` `add-log-exp_binary64_118`
3×	`pow-prod-down_binary64_150`
2×	`associate-*l/_binary64_22` `cube-mult_binary64_109` `pow1/2_binary64_159` `unpow3_binary64_145`
1×	`rem-cbrt-cube_binary64_103` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow1/3_binary64_161`

Counts

4 → 120

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series187.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))
48.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3)))
47.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
42.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify73.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4819	2235
1	4819	2235

prune128.0ms (5.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	132	8	140

Merged error: 0.2b

Counts

140 → 8

Compiler

Compiled 2967 to 892 computations (69.9% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.9b	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite31.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64_140`
10×	`unpow-prod-down_binary64_158`
8×	`sqrt-prod_binary64_95` `add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
7×	`cbrt-prod_binary64_110`
6×	`associate-*r/_binary64_21` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96`
5×	`add-exp-log_binary64_117`
4×	`add-cbrt-cube_binary64_115` `add-log-exp_binary64_118`
3×	`pow-unpow_binary64_156` `flip-+_binary64_53` `pow-prod-down_binary64_150` `pow1/2_binary64_159` `flip3-+_binary64_82`
2×	`pow-pow_binary64_151`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `sqr-pow_binary64_51` `pow1/3_binary64_161`

Counts

4 → 64

Calls

4 calls:

8.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series432.0ms (18.3%)

Counts

4 → 12

Calls

4 calls:

302.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
45.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
42.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
42.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify84.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4992	903
1	4992	903

prune80.0ms (3.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	76	8	84

Merged error: 0.2b

Counts

84 → 8

Compiler

Compiled 2257 to 633 computations (72% saved)

regimes24.0ms (1%)

Compiler: Compiled 95 to 57 computations (40% saved)

bsearch14.0ms (0.6%)

Steps

Iters	Range		Point
9	-3.7200702278433635e-302	2.1738515532578095e-306	-2.1487218123004e-310

Compiler

Compiled 1 to 1 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	25
1	39	25

end0.0ms (0%)

sample432.0ms (18.3%)

Algorithm

1×

intervals

Results

186.0ms

8000×

body

128

valid

Compiler

Compiled 118 to 73 computations (38.1% saved)

Details

analyze4.0ms (0.2%)

sample10.0ms (0.4%)

simplify162.0ms (6.9%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

rewrite6.0ms (0.3%)

series46.0ms (1.9%)

simplify69.0ms (2.9%)

prune55.0ms (2.3%)

localize6.0ms (0.3%)

rewrite53.0ms (2.2%)

series185.0ms (7.8%)

simplify74.0ms (3.1%)

prune119.0ms (5%)

localize10.0ms (0.4%)

rewrite54.0ms (2.3%)

series187.0ms (7.9%)

simplify73.0ms (3.1%)

prune128.0ms (5.4%)

localize13.0ms (0.6%)

rewrite31.0ms (1.3%)

series432.0ms (18.3%)

simplify84.0ms (3.6%)

prune80.0ms (3.4%)

regimes24.0ms (1%)

bsearch14.0ms (0.6%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample432.0ms (18.3%)

Profiling