Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	190×	body	80	valid
6.0ms	22×	body	2560	valid
3.0ms	16×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	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: 38.7b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.4b	(+ (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

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)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312

prune146.0ms

Filtered

49 candidates to 42 candidates (85.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Merged error: 18.9b

Counts

50 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (+ (* re re) (* im im))) re)
5.0b	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
20.4b	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
7×	`add-cube-cbrt` `sqrt-prod`
6×	`times-frac` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`sqrt-pow1` `sqrt-div` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `pow1/2` `div-exp` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `flip3-+` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l`

Counts

4 → 71

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
10.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
185.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
71.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	369	696
1	1474	620
2	5001	611

prune220.0ms

Filtered

83 candidates to 65 candidates (78.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	80	8	88

Merged error: 13.8b

Counts

88 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (+ (* re re) (* im im))) re)
5.0b	(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
21.0ms	(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
196.0ms	(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
34.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	294	590
1	979	551
2	3232	539
3	5001	536

prune261.0ms

Filtered

72 candidates to 56 candidates (77.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	71	9	80

Merged error: 11.4b

Counts

80 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (sqrt 2.0) (fabs (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re)))))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `sqrt-prod`
27×	`times-frac`
26×	`add-cube-cbrt`
10×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`distribute-lft-out--`
4×	`sqrt-div`
3×	`associate-r` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

10.0ms	(/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(* (sqrt 2.0) (fabs (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re)))))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(* (sqrt 2.0) (fabs (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re)))))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	411	1305
1	1391	1209
2	5001	1185

prune333.0ms

Filtered

117 candidates to 80 candidates (68.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	117	9	126

Merged error: 7.9b

Counts

126 → 9

regimes442.0ms

Accuracy

68.1% (9.9b remaining)

Error of 17.6b against oracle of 7.8b and baseline of 38.7b

bsearch148.0ms

Steps

Iters	Range		Point
7	7.242250218771691e+34	4.0951139157536485e+36	4.034915440264747e+36
7	-7.083727823843107e-308	8.580811661457357e-308	3.8423606990857e-310
9	-2.1109830459205943e+145	-1.356436873356383e+137	-2.1886437731135835e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	34
1	53	34

end0.0ms

sample913.0ms

Algorithm

intervals

Results

290.0ms	6026×	body	80	valid
202.0ms	732×	body	2560	valid
101.0ms	293×	body	5120	valid
99.0ms	453×	body	1280	valid
45.0ms	246×	body	640	valid
21.0ms	159×	body	320	valid
8.0ms	91×	body	160	valid

Details

sample33.0ms

simplify5.0ms

prune3.0ms

localize12.0ms

rewrite19.0ms

series251.0ms

simplify71.0ms

prune146.0ms

localize11.0ms

rewrite36.0ms

series338.0ms

simplify42.0ms

prune220.0ms

localize13.0ms

rewrite38.0ms

series312.0ms

simplify90.0ms

prune261.0ms

localize13.0ms

rewrite30.0ms

series252.0ms

simplify46.0ms

prune333.0ms

regimes442.0ms

bsearch148.0ms

simplify2.0ms

end0.0ms

sample913.0ms

Profiling