Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	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: 24.9b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(- (* b c) (* a d))
24.5b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

260×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
92×	`associate-l`
88×	`times-frac`
65×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
26×	`swap-sqr`
24×	`add-cube-cbrt`
11×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 160

Calls

3 calls:

17.0ms	(+ (* c c) (* d d))
13.0ms	(- (* b c) (* a d))
34.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
39.0ms	(- (* b c) (* a d))
88.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify55.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	403	1751
1	1527	1703
2	5001	1701

prune271.0ms

Filtered

169 candidates to 72 candidates (42.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	158	11	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Merged error: 23.5b

Counts

170 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.5b	(sqrt (+ (* c c) (* d d)))
28.5b	(sqrt (+ (* c c) (* d d)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

314×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
121×	`times-frac`
112×	`sqrt-prod`
108×	`associate-l`
70×	`distribute-lft-out`
52×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
42×	`add-cube-cbrt`
28×	`swap-sqr`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 220

Calls

4 calls:

14.0ms	(- (* b c) (* a d))
38.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
17.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b c) (* a d))
114.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))

simplify121.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	428	2698
1	1238	2613
2	4267	2607
3	5001	2602

prune402.0ms

Filtered

232 candidates to 99 candidates (42.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	222	10	232
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	228	15	243

Merged error: 22.0b

Counts

243 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
15.0b	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
28.5b	(sqrt (+ (* c c) (* d d)))
28.5b	(sqrt (+ (* c c) (* d d)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

149×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
66×	`sqrt-prod`
51×	`associate-l`
40×	`distribute-lft-out`
39×	`associate-r`
37×	`times-frac`
34×	`frac-times` `add-cube-cbrt`
33×	`associate-/r*`
19×	`flip3--` `flip--`
17×	`associate-*r/`
16×	`swap-sqr`
13×	`add-exp-log` `unswap-sqr`
10×	`associate-/l*`
9×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`sqrt-div` `add-log-exp`
4×	`prod-exp` `clear-num`
3×	`frac-2neg` `flip3-+` `un-div-inv` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 186

Calls

4 calls:

13.0ms	(- (* b c) (* a d))
53.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
17.0ms	(sqrt (+ (* c c) (* d d)))
20.0ms	(sqrt (+ (* c c) (* d d)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* b c) (* a d))
114.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
40.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify74.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	540	1852
1	2109	1781
2	5001	1721

prune401.0ms

Filtered

198 candidates to 96 candidates (48.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	5	9	14
Picked	0	1	1
Done	0	0	0
Total	199	14	213

Merged error: 22.0b

Counts

213 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.5b	(sqrt (+ (* c c) (* d d)))
28.5b	(sqrt (+ (* c c) (* d d)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

314×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
121×	`times-frac`
112×	`sqrt-prod`
108×	`associate-l`
70×	`distribute-lft-out`
52×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
42×	`add-cube-cbrt`
28×	`swap-sqr`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 220

Calls

4 calls:

13.0ms	(- (* b c) (* a d))
38.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b c) (* a d))
116.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))

simplify122.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	428	2698
1	1238	2613
2	4267	2607
3	5001	2602

prune393.0ms

Filtered

232 candidates to 99 candidates (42.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	232	14	246

Merged error: 22.0b

Counts

246 → 14

regimes219.0ms

Accuracy

0% (2.9b remaining)

Error of 26.2b against oracle of 23.3b and baseline of 26.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

sample514.0ms

Algorithm

intervals

Results

305.0ms

8500×

body

valid