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)

sample18.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify92.0ms (3.7%)

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

Error

29.4b

Counts

2 → 1

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

28.3b

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

rewrite22.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

16.3b

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:

6.0ms

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

Compiler

Compiled 161 to 50 computations (68.9% saved)

series32.0ms (1.3%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

28.0ms

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

Compiler

Compiled 42 to 40 computations (4.8% saved)

simplify71.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5009	140

prune15.0ms (0.6%)

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 78 computations (55.2% 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)))))
28.3b	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.3b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite144.0ms (5.8%)

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:

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)))

Compiler

Compiled 2803 to 549 computations (80.4% saved)

series113.0ms (4.6%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
28.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
21.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))

Compiler

Compiled 437 to 311 computations (28.8% saved)

simplify84.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4704	1347
1	4704	1347

prune83.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	138	5	143

Error

0.1b

Counts

143 → 5

Compiler

Compiled 1973 to 499 computations (74.7% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite216.0ms (8.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

104×	`sqrt-prod_binary64_94`
66×	`add-sqr-sqrt_binary64_100`
46×	`sqrt-div_binary64_95`
29×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
26×	`associate-r_binary64_18`
24×	`unswap-sqr_binary64_46`
21×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
20×	`associate-*r/_binary64_20`
17×	`pow1_binary64_139`
16×	`sqrt-pow1_binary64_96`
10×	`add-exp-log_binary64_116` `associate-l_binary64_19`
9×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`pow-pow_binary64_150` `cube-div_binary64_107`
7×	`add-cbrt-cube_binary64_114`
5×	`pow1/2_binary64_158` `sqr-pow_binary64_50`
4×	`add-log-exp_binary64_117` `frac-times_binary64_88`
3×	`pow-prod-down_binary64_149` `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` `associate-*l/_binary64_21`
1×	`rem-cube-cbrt_binary64_101` `sqrt-pow2_binary64_97` `pow-prod-up_binary64_148` `cbrt-unprod_binary64_111` `*-commutative_binary64_9`

Counts

4 → 154

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 3))
9.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 3)
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 4924 to 1116 computations (77.3% saved)

series260.0ms (10.5%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

155.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 3)
33.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
31.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
30.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 3))

Compiler

Compiled 552 to 420 computations (23.9% saved)

simplify127.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4815	2884
1	4815	2884

prune130.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	166	5	171

Error

0.1b

Counts

171 → 5

Compiler

Compiled 3502 to 839 computations (76% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite25.0ms (1%)

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)

series32.0ms (1.3%)

Error

0.1b

Counts

1 → 3

Calls

1 calls:

30.0ms

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

Compiler

Compiled 36 to 34 computations (5.6% saved)

simplify46.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5010	211

prune18.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	23	7	30

Error

0.1b

Counts

30 → 7

Compiler

Compiled 193 to 154 computations (20.2% saved)

regimes202.0ms (8.2%)

Accuracy

Total 0.3b remaining (71.9%)

Threshold costs 0.3b (71.9%)

Compiler

Compiled 1314 to 828 computations (37% saved)

bsearch15.0ms (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	25
1	39	25

end0.0ms (0%)

sample704.0ms (28.4%)

Algorithm

1×

intervals

Results

181.0ms

8000×

body

128

valid

Compiler

Compiled 344 to 220 computations (36% saved)

Details

analyze4.0ms (0.2%)

sample18.0ms (0.7%)

simplify92.0ms (3.7%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

rewrite22.0ms (0.9%)

series32.0ms (1.3%)

simplify71.0ms (2.9%)

prune15.0ms (0.6%)

localize6.0ms (0.3%)

rewrite144.0ms (5.8%)

series113.0ms (4.6%)

simplify84.0ms (3.4%)

prune83.0ms (3.4%)

localize11.0ms (0.5%)

rewrite216.0ms (8.7%)

series260.0ms (10.5%)

simplify127.0ms (5.1%)

prune130.0ms (5.2%)

localize3.0ms (0.1%)

rewrite25.0ms (1%)

series32.0ms (1.3%)

simplify46.0ms (1.8%)

prune18.0ms (0.7%)

regimes202.0ms (8.2%)

bsearch15.0ms (0.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample704.0ms (28.4%)

Profiling