Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	24	6
2	28	6
3	28	6

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: 4.3b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1.1283791670955126 (exp z))
1.4b	(- (* 1.1283791670955126 (exp z)) (* x y))
7.6b	(/ y (- (* 1.1283791670955126 (exp z)) (* x y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 67

Calls

3 calls:

5.0ms	(* 1.1283791670955126 (exp z))
5.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
6.0ms	(/ y (- (* 1.1283791670955126 (exp z)) (* x y)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(* 1.1283791670955126 (exp z))
53.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
72.0ms	(/ y (- (* 1.1283791670955126 (exp z)) (* x y)))

simplify35.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	290	501
1	1077	461
2	5001	459

prune196.0ms

Filtered

76 candidates to 59 candidates (77.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 2.5b

Counts

77 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1.1283791670955126 (exp z))
0.1b	(/ 1 (/ (- (* 1.1283791670955126 (exp z)) (* x y)) y))
1.4b	(- (* 1.1283791670955126 (exp z)) (* x y))
7.5b	(/ (- (* 1.1283791670955126 (exp z)) (* x y)) y)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log`
16×	`associate-/r*`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

5.0ms	(* 1.1283791670955126 (exp z))
8.0ms	(/ 1 (/ (- (* 1.1283791670955126 (exp z)) (* x y)) y))
5.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
7.0ms	(/ (- (* 1.1283791670955126 (exp z)) (* x y)) y)

series190.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* 1.1283791670955126 (exp z))
50.0ms	(/ 1 (/ (- (* 1.1283791670955126 (exp z)) (* x y)) y))
53.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
71.0ms	(/ (- (* 1.1283791670955126 (exp z)) (* x y)) y)

simplify67.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	547	1434
1	2526	1298
2	5002	1226

prune327.0ms

Filtered

158 candidates to 98 candidates (62.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	162	3	165

Merged error: 0b

Counts

165 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp z) y)
0.0b	(- (* 1.1283791670955126 (/ (exp z) y)) (/ x 1))
0.1b	(/ 1 (- (* 1.1283791670955126 (/ (exp z) y)) (/ x 1)))
0.1b	(* 1.1283791670955126 (/ (exp z) y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `associate-r` `prod-diff` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `div-inv`
3×	`cbrt-undiv` `associate-r/` `associate-l*` `associate-/r/`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rec-exp` `pow-flip` `fma-neg` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 128

Calls

4 calls:

4.0ms	(/ (exp z) y)
8.0ms	(- (* 1.1283791670955126 (/ (exp z) y)) (/ x 1))
10.0ms	(/ 1 (- (* 1.1283791670955126 (/ (exp z) y)) (/ x 1)))
7.0ms	(* 1.1283791670955126 (/ (exp z) y))

series144.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (exp z) y)
45.0ms	(- (* 1.1283791670955126 (/ (exp z) y)) (/ x 1))
59.0ms	(/ 1 (- (* 1.1283791670955126 (/ (exp z) y)) (/ x 1)))
24.0ms	(* 1.1283791670955126 (/ (exp z) y))

simplify67.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	644	1094
1	2837	805
2	5001	797

prune307.0ms

Filtered

140 candidates to 93 candidates (66.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	141	2	143

Merged error: 0b

Counts

143 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp z))
0.0b	(* (cbrt (exp z)) (cbrt (exp z)))
0.1b	(/ 1 (- (* (* (* (cbrt (exp z)) (cbrt (exp z))) 1.1283791670955126) (/ (cbrt (exp z)) y)) (/ x 1)))
0.1b	(* (* (* (cbrt (exp z)) (cbrt (exp z))) 1.1283791670955126) (/ (cbrt (exp z)) y))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log`
28×	`cbrt-prod` `associate-r`
27×	`times-frac`
21×	`pow1`
20×	`add-cbrt-cube`
13×	`prod-exp` `cbrt-unprod`
8×	`pow-prod-down`
7×	`pow1/3` `associate-l`
6×	`swap-sqr`
5×	`div-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/r/` `associate-/l`
2×	`associate-r/` `pow-sqr` `-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `pow-plus` `1-exp` `clear-num` `frac-sub` `flip--` `inv-pow`

Counts

4 → 140

Calls

4 calls:

2.0ms	(cbrt (exp z))
6.0ms	(* (cbrt (exp z)) (cbrt (exp z)))
15.0ms	(/ 1 (- (* (* (* (cbrt (exp z)) (cbrt (exp z))) 1.1283791670955126) (/ (cbrt (exp z)) y)) (/ x 1)))
14.0ms	(* (* (* (cbrt (exp z)) (cbrt (exp z))) 1.1283791670955126) (/ (cbrt (exp z)) y))

series258.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt (exp z))
93.0ms	(* (cbrt (exp z)) (cbrt (exp z)))
65.0ms	(/ 1 (- (* (* (* (cbrt (exp z)) (cbrt (exp z))) 1.1283791670955126) (/ (cbrt (exp z)) y)) (/ x 1)))
21.0ms	(* (* (* (cbrt (exp z)) (cbrt (exp z))) 1.1283791670955126) (/ (cbrt (exp z)) y))

simplify92.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	621	1688
1	3196	1471
2	5002	1394

prune369.0ms

Filtered

152 candidates to 96 candidates (63.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	152	2	154

Merged error: 0b

Counts

154 → 2

regimes72.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	14
1	22	14
2	22	14

end0.0ms

sample410.0ms

Algorithm

intervals

Results

241.0ms

8000×

body

valid