Details

sample22.0ms

Algorithm

intervals

Results

12.0ms

274×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	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: 25.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(+ (* a c) (* b d))
25.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

208×	`*-un-lft-identity`
85×	`distribute-lft-out`
76×	`associate-l`
56×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`swap-sqr`
8×	`associate-/r*`
7×	`associate-/l*` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 118

Calls

3 calls:

19.0ms	(+ (* c c) (* d d))
14.0ms	(+ (* a c) (* b d))
32.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
84.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify148.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	284	1069
1	1203	1021
2	4644	1019
3	5001	1019

prune183.0ms

Filtered

127 candidates to 51 candidates (40.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	7	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	8	128

Merged error: 24.8b

Counts

128 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
15.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

258×	`*-un-lft-identity`
102×	`distribute-lft-out`
92×	`associate-l`
80×	`sqrt-prod`
77×	`times-frac`
36×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
20×	`swap-sqr`
11×	`associate-/r*`
7×	`associate-/l*`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 166

Calls

4 calls:

13.0ms	(+ (* a c) (* b d))
34.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
19.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* a c) (* b d))
109.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify92.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	282	1685
1	888	1616
2	2740	1614
3	5001	1609

prune289.0ms

Filtered

178 candidates to 74 candidates (41.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	170	8	178
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	173	13	186

Merged error: 23.1b

Counts

186 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
15.6b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 177

Calls

4 calls:

13.0ms	(+ (* a c) (* b d))
51.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
16.0ms	(sqrt (+ (* c c) (* d d)))
20.0ms	(sqrt (+ (* c c) (* d d)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a c) (* b d))
115.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
41.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify68.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	503	1751
1	2086	1684
2	5003	1624

prune362.0ms

Filtered

189 candidates to 88 candidates (46.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	4	6	10
Picked	0	1	1
Done	0	2	2
Total	190	12	202

Merged error: 23.1b

Counts

202 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

15.6b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
28.9b	(sqrt (+ (* c c) (* d d)))
29.9b	(cbrt (+ (* c c) (* d d)))
29.9b	(cbrt (+ (* c c) (* d d)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
58×	`sqrt-prod`
49×	`distribute-lft-out`
48×	`add-sqr-sqrt`
47×	`associate-l`
39×	`associate-r`
37×	`times-frac`
35×	`add-cube-cbrt`
34×	`frac-times`
33×	`associate-/r*`
22×	`flip3-+` `flip-+`
18×	`swap-sqr`
17×	`associate-*r/`
16×	`cbrt-prod`
13×	`add-exp-log`
10×	`associate-/l*`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`unswap-sqr`
4×	`cbrt-div` `sqrt-div` `prod-exp` `clear-num` `add-log-exp`
3×	`frac-2neg` `un-div-inv`
2×	`pow1/3` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 178

Calls

4 calls:

47.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
19.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(cbrt (+ (* c c) (* d d)))
16.0ms	(cbrt (+ (* c c) (* d d)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
36.0ms	(sqrt (+ (* c c) (* d d)))
94.0ms	(cbrt (+ (* c c) (* d d)))
96.0ms	(cbrt (+ (* c c) (* d d)))

simplify75.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	544	1840
1	2404	1765
2	5001	1689

prune460.0ms

Filtered

190 candidates to 95 candidates (50.0%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	2	6	8
Picked	0	1	1
Done	0	3	3
Total	190	12	202

Merged error: 23.1b

Counts

202 → 12

regimes248.0ms

Accuracy

0% (2.9b remaining)

Error of 26.2b against oracle of 23.2b and baseline of 26.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample511.0ms

Algorithm

intervals

Results

302.0ms

8506×

body

valid