Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	199×	body	80	valid
4.0ms	20×	body	2560	valid
2.0ms	15×	body	1280	valid
1.0ms	10×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	3×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

3.0ms	(+ (* re re) (* im im))
17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series121.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* re re) (* im im))
53.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	172	305
1	661	282
2	1936	278
3	5002	276

prune155.0ms

Filtered

50 candidates to 38 candidates (76.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.2b

localize14.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
32.5b	(cbrt (+ (* re re) (* im im)))
32.5b	(cbrt (+ (* re re) (* im im)))
32.5b	(cbrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

33.0ms	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
96.0ms	(cbrt (+ (* re re) (* im im)))
96.0ms	(cbrt (+ (* re re) (* im im)))
101.0ms	(cbrt (+ (* re re) (* im im)))

simplify192.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (179.0ms)

Iter	Nodes	Cost
0	287	1509
1	709	1463
2	3077	1446
3	5001	1379

prune289.0ms

Filtered

101 candidates to 65 candidates (64.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.2b

localize17.0ms

Local error

Found 4 expressions with local error:

32.5b	(cbrt (+ (* re re) (* im im)))
32.5b	(cbrt (+ (* re re) (* im im)))
32.5b	(cbrt (+ (* re re) (* im im)))
32.5b	(cbrt (+ (* re re) (* im im)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ (* re re) (* im im)))
96.0ms	(cbrt (+ (* re re) (* im im)))
96.0ms	(cbrt (+ (* re re) (* im im)))
97.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	123	488
1	408	452
2	1386	444
3	5001	444

prune292.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.2b

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (sqrt (+ (* re re) (* im im))) re)
4.1b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
23.5b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
23.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
219.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
69.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune286.0ms

Filtered

111 candidates to 78 candidates (70.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

regimes255.0ms

Accuracy

48.3% (17.6b remaining)

Error of 24.3b against oracle of 6.7b and baseline of 40.8b

bsearch193.0ms

Steps

Iters	Range		Point
6	1.272440175084956e+89	8.312320725607927e+89	7.788470368286171e+89
6	3.0530874406240013e-131	3.4548165133222533e-130	3.103597257167775e-130
4	-5.906043100963754e-260	-3.955409345523615e-260	-5.84508579610625e-260
9	-5.759922189643687e-102	-3.8856404091163327e-107	-1.3179842623367683e-105
9	-5.968619231634867e+127	-5.005393495068343e+122	-4.312262875779433e+124

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	38
1	65	38
2	66	38
3	66	38

end0.0ms

sample651.0ms

Algorithm

intervals

Results

198.0ms	6029×	body	80	valid
132.0ms	707×	body	2560	valid
77.0ms	491×	body	1280	valid
62.0ms	260×	body	5120	valid
36.0ms	275×	body	640	valid
13.0ms	143×	body	320	valid
6.0ms	95×	body	160	valid