Details

sample24.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	8
1	63	8
2	149	8
3	358	8
4	840	8
5	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: 8.1b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
0.7b	(- (* (* z 2.0) z) (* y t))
16.0b	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

28×	`prod-diff`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cube-cbrt`
12×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-/r/`
7×	`add-log-exp`
6×	`flip3--` `flip--`
4×	`fma-neg` `div-inv`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `associate-/r*` `cbrt-unprod` `log1p-expm1-u`
2×	`sub-neg` `diff-log`
1×	`frac-2neg` `clear-num` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 89

Calls

3 calls:

9.0ms	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
8.0ms	(- (* (* z 2.0) z) (* y t))
10.0ms	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

series296.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
35.0ms	(- (* (* z 2.0) z) (* y t))
180.0ms	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

simplify85.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	506	1970
1	2392	1402
2	5002	1401

prune202.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Merged error: 3.3b

Counts

99 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow z 2))
0.7b	(- (* 2.0 (pow z 2)) (* t y))
3.4b	(* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y))))
15.7b	(/ z (- (* 2.0 (pow z 2)) (* t y)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`add-exp-log` `associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
18×	`times-frac`
9×	`pow1` `prod-exp`
7×	`cbrt-unprod`
6×	`add-log-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `associate-l` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `associate-/r` `flip--` `associate-/l`
2×	`*-commutative` `div-inv` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `pow-exp` `clear-num`

Counts

4 → 113

Calls

4 calls:

6.0ms	(* 2.0 (pow z 2))
4.0ms	(- (* 2.0 (pow z 2)) (* t y))
10.0ms	(* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y))))
6.0ms	(/ z (- (* 2.0 (pow z 2)) (* t y)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 2.0 (pow z 2))
40.0ms	(- (* 2.0 (pow z 2)) (* t y))
178.0ms	(* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y))))
48.0ms	(/ z (- (* 2.0 (pow z 2)) (* t y)))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	433	877
1	2208	755
2	5001	753

prune253.0ms

Filtered

125 candidates to 87 candidates (69.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	125	7	132

Merged error: 3.3b

Counts

132 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* 2.0 (pow z 2)) (* t y))
0.8b	(/ 1 (- (* 2.0 (pow z 2)) (* t y)))
3.4b	(* (* y 2.0) (* z (/ 1 (- (* 2.0 (pow z 2)) (* t y)))))
15.2b	(* z (/ 1 (- (* 2.0 (pow z 2)) (* t y))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
32×	`add-cbrt-cube`
27×	`add-sqr-sqrt` `prod-exp`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
19×	`pow1`
16×	`associate-r`
15×	`cbrt-unprod`
9×	`pow-prod-down`
8×	`div-exp`
6×	`add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `associate-r/` `associate-l*` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `inv-pow`

Counts

4 → 125

Calls

4 calls:

5.0ms	(- (* 2.0 (pow z 2)) (* t y))
6.0ms	(/ 1 (- (* 2.0 (pow z 2)) (* t y)))
12.0ms	(* (* y 2.0) (* z (/ 1 (- (* 2.0 (pow z 2)) (* t y)))))
10.0ms	(* z (/ 1 (- (* 2.0 (pow z 2)) (* t y))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* 2.0 (pow z 2)) (* t y))
31.0ms	(/ 1 (- (* 2.0 (pow z 2)) (* t y)))
176.0ms	(* (* y 2.0) (* z (/ 1 (- (* 2.0 (pow z 2)) (* t y)))))
50.0ms	(* z (/ 1 (- (* 2.0 (pow z 2)) (* t y))))

simplify64.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	436	1137
1	2042	924
2	5001	890

prune236.0ms

Filtered

137 candidates to 78 candidates (56.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	137	7	144

Merged error: 3.3b

Counts

144 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

20.9b	(cbrt (- (* (* z 2.0) z) (* y t)))
20.9b	(cbrt (- (* (* z 2.0) z) (* y t)))
20.9b	(cbrt (- (* (* z 2.0) z) (* y t)))
20.9b	(cbrt (- (* (* z 2.0) z) (* y t)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

5.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
5.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
5.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
5.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
121.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
120.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
123.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))

simplify65.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	180	716
1	539	672
2	2091	664
3	5001	644

prune354.0ms

Filtered

72 candidates to 68 candidates (94.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Merged error: 3.3b

Counts

79 → 7

regimes217.0ms

Accuracy

0% (2.1b remaining)

Error of 6.8b against oracle of 4.7b and baseline of 6.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms

sample600.0ms

Algorithm

intervals

Results

392.0ms

8000×

body

valid