Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

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: 30.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* re re) (* im im))
137.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	256	741
1	895	697
2	2846	694
3	5001	694

prune232.0ms

Filtered

83 candidates to 55 candidates (66.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	14	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	14	84

Merged error: 7.3b

Counts

84 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
108×	`add-sqr-sqrt`
78×	`sqrt-prod`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt` `log-pow`
53×	`pow1`
46×	`associate-r`
28×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`flip3-+` `flip-+` `div-inv`
2×	`log-div` `rec-exp` `1-exp` `div-sub`
1×	`+-commutative` `frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 205

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
31.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
8.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* re re) (* im im))
141.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
218.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	648	2798
1	2878	2493
2	5002	2395

prune464.0ms

Filtered

217 candidates to 111 candidates (51.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	207	10	217
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	217	14	231

Merged error: 7.1b

Counts

231 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.8b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
46×	`times-frac`
44×	`*-un-lft-identity`
42×	`add-cube-cbrt`
38×	`sqrt-prod`
25×	`pow-unpow` `associate-l`
20×	`log-prod`
18×	`unpow-prod-down`
15×	`pow1`
14×	`add-exp-log`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-cbrt-cube`
7×	`log-pow`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`associate-r` `prod-exp`
3×	`pow-pow` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `sum-log` `-commutative` `sqrt-pow2`

Counts

4 → 141

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
15.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
8.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series824.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
391.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
368.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	593	2050
1	2744	1681
2	5001	1554

prune422.0ms

Filtered

153 candidates to 94 candidates (61.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	150	17	167

Merged error: 7.1b

Counts

167 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
3.8b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
27.5b	(sqrt (+ (* re re) (* im im)))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow-unpow`
42×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `*-un-lft-identity`
36×	`sqrt-prod`
16×	`pow1`
12×	`unpow-prod-down`
6×	`add-exp-log` `pow-pow` `log-pow`
4×	`sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `flip3-+` `pow-exp` `sqrt-pow2` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

8.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
8.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series802.0ms

Counts

4 → 12

Calls

4 calls:

365.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
360.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
36.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	305	1184
1	1001	1106
2	3338	1032
3	5001	1028

prune551.0ms

Filtered

132 candidates to 86 candidates (65.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	4	11	15
Picked	1	0	1
Done	1	0	1
Total	136	13	149

Merged error: 7.1b

Counts

149 → 13

regimes631.0ms

Accuracy

58.7% (10.0b remaining)

Error of 17.3b against oracle of 7.3b and baseline of 31.5b

bsearch221.0ms

Steps

Iters	Range		Point
6	8.386220925578828e+143	4.316820422997054e+144	1.3030602997104563e+144
10	8.660844906217239e-175	7.0021986566734e-156	4.3188726636303697e-169
9	3.2439511425214304e-251	1.5200205730203393e-242	9.860139717477679e-245
9	-1.5222152192366948e+103	-1.1953863104538045e+95	-2.9954377646446586e+97

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	111
1	62	111
2	62	111

end0.0ms

sample500.0ms

Algorithm

intervals

Results

362.0ms

8000×

body

valid