Details

analyze99.0ms (3.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9
0	1	1
1	1	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

Symmetry

Compiler

Compiled 9 to 5 computations (44.4% saved)

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify7.0ms (0.3%)

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

29.0b

Counts

2 → 1

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

27.9b

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

rewrite17.0ms (0.7%)

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:

5.0ms

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

Compiler

Compiled 161 to 50 computations (68.9% saved)

series32.0ms (1.3%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

28.0ms

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

Compiler

Compiled 42 to 40 computations (4.8% saved)

simplify74.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5009	140

prune16.0ms (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

0.2b

Counts

17 → 6

Compiler

Compiled 174 to 79 computations (54.6% saved)

localize6.0ms (0.2%)

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)))))
27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite144.0ms (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:

19.0ms	(.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)

series122.0ms (4.8%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
30.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
30.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
22.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))

Compiler

Compiled 437 to 311 computations (28.8% saved)

simplify85.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4704	1347
1	4704	1347

prune88.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	136	7	143

Error

0.2b

Counts

143 → 7

Compiler

Compiled 1987 to 507 computations (74.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite77.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

13×	`pow1_binary64_139`
8×	`associate-*r/_binary64_20` `sqrt-div_binary64_95`
6×	`sqrt-pow1_binary64_96`
5×	`add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `flip-+_binary64_52` `sqrt-prod_binary64_94` `cbrt-prod_binary64_109`
3×	`pow1/2_binary64_158` `pow-prod-down_binary64_149`
2×	`cbrt-div_binary64_110`
1×	`pow1/3_binary64_160`

Counts

4 → 53

Calls

4 calls:

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

Compiler

Compiled 1637 to 269 computations (83.6% saved)

series211.0ms (8.3%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
34.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
32.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
31.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 858 to 446 computations (48% saved)

simplify88.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4793	624
1	4793	624

prune64.0ms (2.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	63	9	72

Error

0.2b

Counts

72 → 9

Compiler

Compiled 1813 to 398 computations (78% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite92.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

16×	`pow1_binary64_139`
8×	`sqrt-pow1_binary64_96` `associate-*r/_binary64_20` `sqrt-div_binary64_95`
4×	`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

4 → 52

Calls

4 calls:

5.0ms	(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)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 2152 to 518 computations (75.9% saved)

series143.0ms (5.6%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
34.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
31.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
29.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 1212 to 564 computations (53.5% saved)

simplify75.0ms (3%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5009	560

prune75.0ms (3%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	63	10	73

Error

0.1b

Counts

73 → 10

Compiler

Compiled 2392 to 655 computations (72.6% saved)

regimes211.0ms (8.3%)

Accuracy

Total 0.2b remaining (61.5%)

Threshold costs 0.2b (61.5%)

Compiler

Compiled 1934 to 860 computations (55.5% saved)

bsearch19.0ms (0.8%)

Steps

Iters	Range		Point
11	-4.0589427805015366e-297	2.337969904445149e-300	1.8744063510754e-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

Removed

()

end0.0ms (0%)

sample740.0ms (29.2%)

Algorithm

1×

intervals

Results

181.0ms

8000×

body

128

valid

Compiler

Compiled 499 to 228 computations (54.3% saved)

Details

analyze99.0ms (3.9%)

sample12.0ms (0.5%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

rewrite17.0ms (0.7%)

series32.0ms (1.3%)

simplify74.0ms (2.9%)

prune16.0ms (0.6%)

localize6.0ms (0.2%)

rewrite144.0ms (5.7%)

series122.0ms (4.8%)

simplify85.0ms (3.4%)

prune88.0ms (3.5%)

localize11.0ms (0.4%)

rewrite77.0ms (3%)

series211.0ms (8.3%)

simplify88.0ms (3.5%)

prune64.0ms (2.5%)

localize14.0ms (0.5%)

rewrite92.0ms (3.7%)

series143.0ms (5.6%)

simplify75.0ms (3%)

prune75.0ms (3%)

regimes211.0ms (8.3%)

bsearch19.0ms (0.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample740.0ms (29.2%)

Profiling