Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	199×	body	80	valid
5.0ms	23×	body	2560	valid
2.0ms	9×	body	5120	valid
1.0ms	11×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 38.1b

Counts

2 → 1

localize13.0ms

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)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
176.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	274	428
1	986	391
2	3089	381
3	5002	379

prune197.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 15.6b

Counts

64 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

10.3b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
31.4b	(sqrt (+ (* re re) (* im im)))
31.4b	(sqrt (+ (* re re) (* im im)))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

21.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	160	641
1	431	527
2	1354	481
3	5001	477

prune259.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Merged error: 15.6b

Counts

74 → 6

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)
15.0b	(cbrt (pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

458.0ms	(pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3)
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
176.0ms	(cbrt (pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (42.0ms)

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

prune262.0ms

Filtered

95 candidates to 63 candidates (66.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	93	8	101

Merged error: 15.6b

Counts

101 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

10.3b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
31.4b	(sqrt (+ (* re re) (* im im)))
31.4b	(sqrt (+ (* re re) (* im im)))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

22.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
41.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	160	644
1	431	530
2	1354	484
3	5001	480

prune310.0ms

Filtered

68 candidates to 64 candidates (94.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	66	10	76

Merged error: 15.6b

Counts

76 → 10

regimes488.0ms

Accuracy

55.5% (10.3b remaining)

Error of 27.9b against oracle of 17.6b and baseline of 40.7b

bsearch242.0ms

Steps

Iters	Range		Point
7	1.1965702813225714e+120	7.306927196198172e+121	1.2114863434718439e+120
10	3.3746055148489886e-168	6.644118788358932e-151	4.692800873959165e-163
7	2.363660519479911e-304	1.3429956514040144e-302	1.3380699708873314e-303
10	-2.5170109662579546e-211	-5.785550335923721e-221	-8.939695392010629e-220
10	-2.368742889503448e-151	-4.8620484299604695e-170	-7.304925653698628e-169

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	48
1	67	48
2	67	48

end0.0ms

sample779.0ms

Algorithm

intervals

Results

226.0ms	6077×	body	80	valid
153.0ms	666×	body	2560	valid
93.0ms	473×	body	1280	valid
89.0ms	293×	body	5120	valid
48.0ms	288×	body	640	valid
13.0ms	129×	body	320	valid
5.0ms	74×	body	160	valid