Details

sample24.0ms

Algorithm

intervals

Results

13.0ms

267×

body

valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	8
1	35	8
2	60	8
3	103	8
4	183	8
5	416	8
6	1194	8
7	5001	8

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: 5.1b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
8.6b	(/ (- (* y z) x) (- (* t z) x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
25×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`distribute-lft-out`
7×	`associate-/r` `associate-/l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`associate-/r/` `associate-/l/`
3×	`div-sub`
2×	`pow1` `cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`
1×	`associate-+r-`

Counts

2 → 73

Calls

2 calls:

17.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
8.0ms	(/ (- (* y z) x) (- (* t z) x))

series166.0ms

Counts

2 → 6

Calls

2 calls:

115.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
51.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify41.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	832
1	1306	776
2	5001	776

prune177.0ms

Filtered

79 candidates to 58 candidates (73.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	8	80

Merged error: 0.8b

Counts

80 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
0.6b	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
8.4b	(/ (- (* t z) x) (- (* y z) x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

110×	`times-frac`
93×	`*-un-lft-identity`
66×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/r*`
18×	`add-exp-log`
16×	`distribute-lft-out`
13×	`associate-/r/`
12×	`add-cbrt-cube` `div-inv`
11×	`associate-/l*`
9×	`div-exp`
6×	`flip3--` `flip--`
5×	`cbrt-undiv`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `add-log-exp`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

3 → 161

Calls

3 calls:

25.0ms	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
10.0ms	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
9.0ms	(/ (- (* t z) x) (- (* y z) x))

series276.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
80.0ms	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
54.0ms	(/ (- (* t z) x) (- (* y z) x))

simplify76.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	615	1965
1	2847	1806
2	5002	1727

prune271.0ms

Filtered

170 candidates to 95 candidates (55.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	169	9	178

Merged error: 0.8b

Counts

178 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (* (cbrt (- (* t z) x)) (cbrt (- (* t z) x))) (/ (cbrt (- (* t z) x)) (- (* y z) x)))
7.4b	(cbrt (- (* t z) x))
7.4b	(cbrt (- (* t z) x))
7.4b	(cbrt (- (* t z) x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-prod`
16×	`add-exp-log` `frac-times` `flip3--` `flip--`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 102

Calls

4 calls:

22.0ms	(* (* (cbrt (- (* t z) x)) (cbrt (- (* t z) x))) (/ (cbrt (- (* t z) x)) (- (* y z) x)))
4.0ms	(cbrt (- (* t z) x))
4.0ms	(cbrt (- (* t z) x))
4.0ms	(cbrt (- (* t z) x))

series412.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* (cbrt (- (* t z) x)) (cbrt (- (* t z) x))) (/ (cbrt (- (* t z) x)) (- (* y z) x)))
114.0ms	(cbrt (- (* t z) x))
116.0ms	(cbrt (- (* t z) x))
122.0ms	(cbrt (- (* t z) x))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	539	1531
1	2034	1378
2	5001	1310

prune354.0ms

Filtered

114 candidates to 93 candidates (81.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	114	9	123

Merged error: 0.8b

Counts

123 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ x (/ (- (* y z) x) (- (* t z) x))))
8.6b	(/ (- (* y z) x) (- (* t z) x))
8.6b	(/ (- (* y z) x) (- (* t z) x))
8.6b	(/ (- (* y z) x) (- (* t z) x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
6×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
4×	`pow1` `cbrt-prod` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 110

Calls

4 calls:

10.0ms	(cbrt (+ x (/ (- (* y z) x) (- (* t z) x))))
9.0ms	(/ (- (* y z) x) (- (* t z) x))
9.0ms	(/ (- (* y z) x) (- (* t z) x))
9.0ms	(/ (- (* y z) x) (- (* t z) x))

series359.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt (+ x (/ (- (* y z) x) (- (* t z) x))))
59.0ms	(/ (- (* y z) x) (- (* t z) x))
54.0ms	(/ (- (* y z) x) (- (* t z) x))
57.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify146.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	322	1078
1	1035	1030
2	4662	1018
3	5002	1018

prune441.0ms

Filtered

122 candidates to 101 candidates (82.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	122	9	131

Merged error: 0.8b

Counts

131 → 9

regimes213.0ms

Accuracy

75.5% (1.6b remaining)

Error of 2.6b against oracle of 0.9b and baseline of 7.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	29
1	38	29

end0.0ms

sample618.0ms

Algorithm

intervals

Results

405.0ms

8322×

body

valid