Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	200×	body	80	valid
5.0ms	26×	body	2560	valid
2.0ms	8×	body	5120	valid
2.0ms	12×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	1×	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: 38.0b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series266.0ms

Counts

3 → 9

Calls

3 calls:

172.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344

prune132.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Merged error: 17.0b

Counts

53 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.9b	(exp (log (sqrt (+ (* re re) (* im im)))))
13.5b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

14.0ms	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
10.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
35.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
49.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	283	630
1	843	573
2	2616	551
3	5001	542

prune195.0ms

Filtered

78 candidates to 56 candidates (71.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	75	10	85

Merged error: 16.8b

Counts

85 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
5.1b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.7b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

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:

9.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
198.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
68.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

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

prune271.0ms

Filtered

111 candidates to 78 candidates (70.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	110	11	121

Merged error: 5.0b

Counts

121 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
5.1b	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`associate-r`
14×	`add-cube-cbrt`
13×	`pow1` `times-frac`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`sqrt-pow1` `pow-prod-down` `sqrt-prod` `distribute-lft-out`
3×	`flip3-+` `sqrt-div` `associate-r/` `associate-l*` `flip-+`
2×	`pow1/2` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `div-exp` `sum-log` `*-commutative` `div-inv`

Counts

4 → 77

Calls

4 calls:

13.0ms	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
198.0ms	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	428	701
1	1831	618
2	5002	614

prune189.0ms

Filtered

89 candidates to 66 candidates (74.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	90	10	100

Merged error: 4.4b

Counts

100 → 10

regimes190.0ms

Accuracy

41.5% (20.6b remaining)

Error of 25.8b against oracle of 5.2b and baseline of 40.3b

bsearch142.0ms

Steps

Iters	Range		Point
10	3.49360888869625e+131	2.723523126945292e+144	6.205680054743451e+137
5	4.0291542564501787e-181	1.2228561371258793e-180	4.089276534834089e-181
3	3.7412437811481085e-298	4.965075808081927e-298	4.883498556383496e-298
6	-5.4082340853716294e-104	-5.091613400763011e-105	-2.393156389015936e-104

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	38
1	59	38

end0.0ms

sample673.0ms

Algorithm

intervals

Results

198.0ms	6000×	body	80	valid
135.0ms	694×	body	2560	valid
82.0ms	499×	body	1280	valid
65.0ms	262×	body	5120	valid
39.0ms	297×	body	640	valid
15.0ms	164×	body	320	valid
5.0ms	84×	body	160	valid