Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

263×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 24.3b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (* b c) (* a d))
23.8b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

247×	`*-un-lft-identity`
143×	`add-sqr-sqrt`
88×	`times-frac` `associate-l`
60×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
24×	`swap-sqr`
23×	`add-cube-cbrt`
11×	`associate-/l*`
8×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 144

Calls

2 calls:

16.0ms	(- (* b c) (* a d))
33.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (* b c) (* a d))
96.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify133.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	350	1659
1	1115	1622
2	4162	1622
3	5003	1621

prune177.0ms

Filtered

150 candidates to 59 candidates (60.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	142	8	150
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	9	151

Merged error: 22.7b

Counts

151 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b c) (* a d))
15.6b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
26.9b	(sqrt (+ (* c c) (* d d)))
26.9b	(sqrt (+ (* c c) (* d d)))

rewrite97.0ms

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))
37.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b c) (* a d))
123.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
44.0ms	(sqrt (+ (* c c) (* d d)))

simplify134.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	416	2698
1	1181	2613
2	3957	2607
3	5001	2602

prune301.0ms

Filtered

232 candidates to 99 candidates (57.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	227	5	232
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	232	9	241

Merged error: 20.4b

Counts

241 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

15.6b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
26.9b	(sqrt (+ (* c c) (* d d)))
26.9b	(sqrt (+ (* c c) (* d d)))
26.9b	(sqrt (+ (* c c) (* d d)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

319×	`*-un-lft-identity`
190×	`add-sqr-sqrt`
121×	`times-frac`
120×	`sqrt-prod`
108×	`associate-l`
75×	`distribute-lft-out`
48×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
43×	`add-cube-cbrt`
30×	`swap-sqr`
11×	`associate-/r` `associate-/l`
8×	`sqrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 220

Calls

4 calls:

34.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
19.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
43.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify125.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	387	2679
1	1081	2598
2	3350	2592
3	5002	2587

prune347.0ms

Filtered

232 candidates to 99 candidates (57.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	233	8	241

Merged error: 20.4b

Counts

241 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

26.9b	(sqrt (+ (* c c) (* d d)))
26.9b	(sqrt (+ (* c c) (* d d)))
26.9b	(sqrt (+ (* c c) (* d d)))
26.9b	(sqrt (+ (* c c) (* d d)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
32×	`sqrt-prod`
20×	`distribute-lft-out`
16×	`associate-l`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `sqrt-div` `swap-sqr`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 80

Calls

4 calls:

16.0ms	(sqrt (+ (* c c) (* d d)))
19.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify153.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	86	476
1	202	464
2	465	464
3	1174	464
4	3616	464
5	5001	464

prune255.0ms

Filtered

92 candidates to 60 candidates (34.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	92	8	100

Merged error: 20.4b

Counts

100 → 8

regimes193.0ms

Accuracy

28% (2.1b remaining)

Error of 25.1b against oracle of 23.0b and baseline of 25.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	26
1	27	26
2	27	26

end0.0ms

sample549.0ms

Algorithm

intervals

Results

323.0ms

8440×

body

valid