Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	191×	body	80	valid
5.0ms	25×	body	2560	valid
3.0ms	16×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	6×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	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: 39.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))
0.1b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-r/` `associate-r*` `sqrt-prod` `flip-+`
3×	`sqrt-pow1` `associate-l`
2×	`pow1/2` `pow-prod-down` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

9.0ms	(* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))
170.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify121.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	305	544
1	1140	488
2	4905	474
3	5001	474

prune180.0ms

Filtered

75 candidates to 60 candidates (80.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 18.1b

Counts

76 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3)
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
15.6b	(cbrt (pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod`
7×	`sqrt-prod`
6×	`sqrt-div` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`cube-div` `pow-pow` `flip3-+` `associate-*r/` `flip-+`
3×	`pow-unpow` `sqrt-pow1`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-prod-down` `pow-exp` `sum-log` `sqrt-pow2` `rem-cbrt-cube` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 83

Calls

4 calls:

10.0ms	(pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3)
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(cbrt (pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3))
4.0ms	(sqrt (+ (* re re) (* im im)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

431.0ms	(pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3)
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
172.0ms	(cbrt (pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	433	886
1	1632	846
2	5001	828

prune218.0ms

Filtered

95 candidates to 64 candidates (67.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	95	7	102

Merged error: 18.1b

Counts

102 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

8.7b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
15.7b	(cbrt (pow (sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))) 3))
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-prod`
6×	`pow1` `sqrt-div` `add-log-exp`
4×	`add-exp-log` `unpow-prod-down` `flip3-+` `cube-prod` `add-cbrt-cube` `flip-+`
2×	`cube-div` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`+-commutative` `cube-mult` `pow1/3` `unpow3` `sum-log` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

14.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
7.0ms	(cbrt (pow (sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))) 3))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
176.0ms	(cbrt (pow (sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))) 3))
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	348	1075
1	1138	999
2	3944	975
3	5001	974

prune250.0ms

Filtered

78 candidates to 61 candidates (78.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Merged error: 18.1b

Counts

85 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

8.7b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
15.7b	(cbrt (pow (sqrt (* 2.0 (exp (log (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))))) 3))
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-prod`
6×	`pow1` `sqrt-div` `add-log-exp`
4×	`add-exp-log` `unpow-prod-down` `flip3-+` `cube-prod` `add-cbrt-cube` `flip-+`
2×	`cube-div` `rem-sqrt-square` `log-div` `cbrt-div` `sqrt-pow1` `pow1/2` `exp-diff` `associate-*r/`
1×	`+-commutative` `cube-mult` `pow1/3` `unpow3` `sum-log` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

15.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
7.0ms	(cbrt (pow (sqrt (* 2.0 (exp (log (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))))) 3))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
177.0ms	(cbrt (pow (sqrt (* 2.0 (exp (log (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))))) 3))
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify102.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	346	1156
1	1133	1059
2	3885	1047
3	5002	1046

prune268.0ms

Filtered

78 candidates to 61 candidates (78.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	77	9	86

Merged error: 18.1b

Counts

86 → 9

regimes207.0ms

Accuracy

55.5% (9.5b remaining)

Error of 27.3b against oracle of 17.8b and baseline of 39.1b

bsearch125.0ms

Steps

Iters	Range	Point
10	1.2902098347601735e+154	3.4696428002669553e+165	1.3638911906358806e+154
7	4.890145485880173e-169	5.979285330824152e-167	9.206347815971593e-169
9	-2.280053641928557e-301	-1.6123238595482796e-307	-1.3029551315611556e-303

Iters

Range

Point

1.2902098347601735e+154

3.4696428002669553e+165

1.3638911906358806e+154

4.890145485880173e-169

5.979285330824152e-167

9.206347815971593e-169

-2.280053641928557e-301

-1.6123238595482796e-307

-1.3029551315611556e-303

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	35
1	57	35
2	57	35

end0.0ms

sample673.0ms

Algorithm

intervals

Results

198.0ms	6040×	body	80	valid
150.0ms	717×	body	2560	valid
77.0ms	487×	body	1280	valid
67.0ms	268×	body	5120	valid
34.0ms	266×	body	640	valid
14.0ms	153×	body	320	valid
4.0ms	69×	body	160	valid