Details

sample18.0ms

Algorithm

intervals

Results

11.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
32.6b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

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:

13.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))

series163.0ms

Counts

2 → 6

Calls

2 calls:

129.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify125.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (118.0ms)

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

prune190.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize14.0ms

Local error

Found 3 expressions with local error:

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)))
32.6b	(sqrt (+ (* re re) (* im im)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 194

Calls

3 calls:

42.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
11.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series376.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
198.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	613	2721
1	2460	2427
2	5001	2325

prune429.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.2b	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
32.6b	(sqrt (+ (* re re) (* im im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
45×	`add-cube-cbrt`
41×	`sqrt-prod`
30×	`log-prod`
25×	`pow-unpow` `associate-l`
24×	`unpow-prod-down`
16×	`add-exp-log`
15×	`pow1`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-cbrt-cube`
8×	`log-pow`
5×	`unswap-sqr`
4×	`associate-r` `prod-exp` `add-log-exp` `sqr-pow`
3×	`pow-pow` `rem-log-exp`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `flip3-+` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `sqrt-pow2` `flip-+`

Counts

4 → 151

Calls

4 calls:

5.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
24.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
7.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

308.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
357.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
337.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	558	2291
1	2343	1895
2	5002	1744

prune416.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.4b

localize29.0ms

Local error

Found 4 expressions with local error:

3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
32.6b	(sqrt (+ (* re re) (* im im)))
32.6b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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:

7.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
7.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series890.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
341.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
35.0ms	(sqrt (+ (* re re) (* im im)))
171.0ms	(sqrt (+ (* re re) (* im im)))

simplify78.0ms

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

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 7.4b

regimes786.0ms

Accuracy

58.1% (10.1b remaining)

Error of 17.8b against oracle of 7.7b and baseline of 31.8b

bsearch121.0ms

Steps

Iters	Range		Point
9	251.47950061764826	104248118811.33417	5087537.920258233
8	-4.8974339249696285e+155	-4.1579563909415707e+152	-2.5872918038759956e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	57
1	57	57

end0.0ms

sample482.0ms

Algorithm

intervals

Results

347.0ms

8000×

body

valid