Details

analyze5.0ms (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 7 to 6 computations (14.3% saved)

sample13.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify102.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

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

Error

29.4b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 2 (.f64 x x))
28.3b	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite40.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

29.3b

Rules

13×	`pow1_binary64_139`
7×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
6×	`pow-prod-down_binary64_149`
4×	`add-sqr-sqrt_binary64_100`
3×	`add-cube-cbrt_binary64_113` `sqrt-pow1_binary64_96` `-un-lft-identity_binary64_78` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `associate-l*_binary64_19`
2×	`add-log-exp_binary64_117`
1×	`pow1/2_binary64_158` `sqrt-prod_binary64_94` `unswap-sqr_binary64_46` `associate-r_binary64_18` `*-commutative_binary64_9`

Counts

2 → 31

Calls

2 calls:

5.0ms	(.f64 2 (.f64 x x))
5.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 344 to 213 computations (38.1% saved)

series72.0ms (2.5%)

Error

0.2b

Counts

2 → 6

Calls

2 calls:

41.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
25.0ms	(.f64 2 (.f64 x x))

Compiler

Compiled 96 to 91 computations (5.2% saved)

simplify52.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4932	300
1	4932	300

prune29.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	5	38

Error

0.2b

Counts

38 → 5

Compiler

Compiled 349 to 233 computations (33.2% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
28.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
28.3b	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite175.0ms (6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

158×	`pow1_binary64_139`
154×	`sqrt-pow1_binary64_96`
82×	`pow-prod-down_binary64_149`
33×	`sqrt-prod_binary64_94`
28×	`add-sqr-sqrt_binary64_100`
24×	`pow1/2_binary64_158`
21×	`pow-prod-up_binary64_148`
13×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow-sqr_binary64_51`
9×	`swap-sqr_binary64_45`
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` `unswap-sqr_binary64_46`
3×	`rem-sqrt-square_binary64_91`
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 → 131

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
5.0ms	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 2665 to 1778 computations (33.3% saved)

series121.0ms (4.1%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
29.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
29.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
23.0ms	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))

Compiler

Compiled 437 to 362 computations (17.2% saved)

simplify75.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5188	1158

prune110.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	144	4	148

Error

0.2b

Counts

148 → 4

Compiler

Compiled 1900 to 1245 computations (34.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x))))) 3))
0.8b	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))) 3)
28.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
28.3b	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite301.0ms (10.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

104×	`sqrt-prod_binary64_94`
66×	`add-sqr-sqrt_binary64_100`
29×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
26×	`pow1_binary64_139` `associate-r_binary64_18`
24×	`unswap-sqr_binary64_46`
21×	`add-cube-cbrt_binary64_113` `sqrt-pow1_binary64_96` `*-un-lft-identity_binary64_78`
10×	`add-exp-log_binary64_116` `associate-l_binary64_19`
9×	`pow-prod-down_binary64_149` `pow-pow_binary64_150`
7×	`add-cbrt-cube_binary64_114`
5×	`pow1/2_binary64_158` `sqr-pow_binary64_50`
4×	`add-log-exp_binary64_117`
3×	`pow-unpow_binary64_155` `prod-exp_binary64_127`
2×	`pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow3_binary64_144` `cube-mult_binary64_108`
1×	`rem-cube-cbrt_binary64_101` `sqrt-pow2_binary64_97` `pow-prod-up_binary64_148` `cbrt-unprod_binary64_111` `*-commutative_binary64_9`

Counts

4 → 143

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x))))) 3))
8.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))) 3)
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 4448 to 3170 computations (28.7% saved)

series253.0ms (8.6%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))) 3)
32.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
32.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
27.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x))))) 3))

Compiler

Compiled 552 to 479 computations (13.2% saved)

simplify116.0ms (4%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4882	2529
1	4882	2529

prune182.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	155	4	159

Error

0.2b

Counts

159 → 4

Compiler

Compiled 3203 to 2220 computations (30.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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:

5.0ms

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

Compiler

Compiled 206 to 166 computations (19.4% saved)

series34.0ms (1.2%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

32.0ms

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

Compiler

Compiled 36 to 34 computations (5.6% saved)

simplify43.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5010	211

prune20.0ms (0.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	23	6	29

Error

0.1b

Counts

29 → 6

Compiler

Compiled 193 to 154 computations (20.2% saved)

regimes294.0ms (10.1%)

Accuracy

Total 0.3b remaining (74%)

Threshold costs 0.3b (74%)

Compiler

Compiled 1884 to 1489 computations (21% saved)

bsearch17.0ms (0.6%)

Steps

Iters	Range		Point
10	-6.611580846772381e-302	2.1885311794389874e-302	2.6083400758351e-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	39	29
1	39	29

end0.0ms (0%)

sample819.0ms (28%)

Algorithm

1×

intervals

Results

185.0ms

8000×

body

128

valid

Compiler

Compiled 375 to 304 computations (18.9% saved)

Details

analyze5.0ms (0.2%)

sample13.0ms (0.4%)

simplify102.0ms (3.5%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite40.0ms (1.4%)

series72.0ms (2.5%)

simplify52.0ms (1.8%)

prune29.0ms (1%)

localize6.0ms (0.2%)

rewrite175.0ms (6%)

series121.0ms (4.1%)

simplify75.0ms (2.6%)

prune110.0ms (3.8%)

localize11.0ms (0.4%)

rewrite301.0ms (10.3%)

series253.0ms (8.6%)

simplify116.0ms (4%)

prune182.0ms (6.2%)

localize3.0ms (0.1%)

rewrite23.0ms (0.8%)

series34.0ms (1.2%)

simplify43.0ms (1.5%)

prune20.0ms (0.7%)

regimes294.0ms (10.1%)

bsearch17.0ms (0.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample819.0ms (28%)

Profiling