Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	196×	body	80	valid
5.0ms	23×	body	2560	valid
2.0ms	16×	body	640	valid
2.0ms	10×	body	1280	valid
1.0ms	4×	body	5120	valid
0.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 40.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
171.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune174.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 19.5b

Counts

67 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (+ (* re re) (* im im))) re)
0.4b	(* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
32.7b	(sqrt (+ (* re re) (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
51×	`sqrt-prod`
30×	`*-un-lft-identity`
21×	`pow1`
16×	`sqrt-div`
15×	`swap-sqr`
14×	`add-cube-cbrt` `difference-of-squares`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
7×	`flip3--` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `flip3-+` `associate-r/` `associate-l/` `flip-+`
1×	`pow2` `sub-neg` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 115

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
19.0ms	(* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
46.0ms	(* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
38.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify179.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (166.0ms)

Iter	Nodes	Cost
0	231	1095
1	763	1015
2	4107	975
3	5002	952

prune272.0ms

Filtered

127 candidates to 73 candidates (57.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	127	8	135

Merged error: 19.5b

Counts

135 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.6b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.7b	(sqrt (+ (* re re) (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

15.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
18.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
46.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune272.0ms

Filtered

138 candidates to 74 candidates (53.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	138	8	146

Merged error: 19.5b

Counts

146 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
11.0b	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
32.7b	(sqrt (+ (* re re) (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`cube-div` `rem-sqrt-square`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `sqrt-pow2` `flip--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
16.0ms	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
52.0ms	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	381	993
1	1279	875
2	5002	845

prune287.0ms

Filtered

104 candidates to 64 candidates (61.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	103	9	112

Merged error: 19.5b

Counts

112 → 9

regimes216.0ms

Accuracy

50.7% (10.4b remaining)

Error of 28.0b against oracle of 17.5b and baseline of 38.7b

bsearch138.0ms

Steps

Iters	Range	Point
8	2.555487769507404e-297	9.204367104374754e-295	2.3367351856997066e-296
9	-4.0298841896469914e-94	-3.744556309116812e-103	-3.8099669373079583e-103
10	-8.777387788220042e+125	-4.2027485674795273e+114	-8.15615961666859e+125

Iters

Range

Point

2.555487769507404e-297

9.204367104374754e-295

2.3367351856997066e-296

-4.0298841896469914e-94

-3.744556309116812e-103

-3.8099669373079583e-103

-8.777387788220042e+125

-4.2027485674795273e+114

-8.15615961666859e+125

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	34
1	54	34

end0.0ms

sample701.0ms

Algorithm

intervals

Results

211.0ms	5992×	body	80	valid
142.0ms	721×	body	2560	valid
90.0ms	517×	body	1280	valid
64.0ms	265×	body	5120	valid
34.0ms	272×	body	640	valid
17.0ms	150×	body	320	valid
6.0ms	83×	body	160	valid