Details

sample18.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune2.0ms

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: 30.1b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
20×	`pow1`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
4×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`log-div` `flip3-+` `div-sub` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

2 → 63

Calls

2 calls:

7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))

series167.0ms

Counts

2 → 6

Calls

2 calls:

128.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify130.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (121.0ms)

Iter	Nodes	Cost
0	221	664
1	556	631
2	1309	628
3	4047	628
4	5001	627

prune183.0ms

Filtered

69 candidates to 45 candidates (65.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 7.2b

Counts

70 → 12

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
28.8b	(log (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
82×	`add-sqr-sqrt`
54×	`sqrt-prod`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 153

Calls

3 calls:

22.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
3.0ms	(log (+ (* re re) (* im im)))

series366.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
182.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
46.0ms	(log (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	528	2082
1	2065	1915
2	5001	1832

prune353.0ms

Filtered

162 candidates to 93 candidates (57.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	153	9	162
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	162	12	174

Merged error: 7.1b

Counts

174 → 12

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

14.3b

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

15.9b

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`times-frac`
39×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`log-pow` `add-cbrt-cube`
7×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `pow-pow` `div-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 117

Calls

3 calls:

15.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

4.0ms

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

7.0ms

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series986.0ms

Counts

3 → 9

Calls

3 calls:

390.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

291.0ms

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

305.0ms

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	463	1699
1	1990	1501
2	5001	1310

prune327.0ms

Filtered

126 candidates to 78 candidates (61.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	123	15	138

Merged error: 7.0b

Counts

138 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0))))
1.0b	(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
1.6b	(* (cbrt (log 10.0)) (cbrt (log 10.0)))
28.8b	(log (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
24×	`cbrt-prod`
23×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
12×	`add-exp-log` `pow1/3`
9×	`sqrt-pow1` `swap-sqr`
7×	`associate-r` `associate-l` `log-pow` `add-cbrt-cube`
4×	`times-frac` `pow-prod-down` `associate-/r*` `pow-sqr` `pow-prod-up` `add-log-exp` `unswap-sqr`
3×	`log-prod` `sqrt-prod`
2×	`cbrt-undiv` `pow2` `log-div` `pow-plus` `div-exp` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `frac-2neg` `flip3-+` `pow1/2` `rem-log-exp` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 101

Calls

4 calls:

7.0ms	(sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0))))
10.0ms	(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
6.0ms	(* (cbrt (log 10.0)) (cbrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series47.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0))))
0.0ms	(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
0.0ms	(* (cbrt (log 10.0)) (cbrt (log 10.0)))
47.0ms	(log (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	294	812
1	1129	727
2	5001	669

prune370.0ms

Filtered

107 candidates to 70 candidates (65.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	3	10	13
Picked	0	1	1
Done	1	0	1
Total	107	15	122

Merged error: 7.0b

Counts

122 → 15

regimes465.0ms

Accuracy

59.5% (9.9b remaining)

Error of 17.2b against oracle of 7.2b and baseline of 31.8b

bsearch97.0ms

Steps

Iters	Range		Point
9	1.441855190865374e+102	1.6710656672296886e+109	8.215111750981571e+102
6	-3.245969229886643e+141	-4.4689590379865175e+140	-4.555058156204304e+140

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	59
1	69	59
2	80	59
3	85	59
4	87	59
5	89	59
6	89	59

end0.0ms

sample605.0ms

Algorithm

intervals

Results

472.0ms

8000×

body

valid