Details

sample116.0ms

Algorithm

intervals

Results

47.0ms	779×	body	80	nan
11.0ms	176×	body	80	valid
10.0ms	28×	body	640	valid
6.0ms	9×	body	1280	valid
5.0ms	26×	body	320	valid
2.0ms	18×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 8.0b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.1b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
5.9b	(log (- 1.0 y))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`log-prod`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`log-div` `log-pow`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 59

Calls

3 calls:

6.0ms	(* z (log (- 1.0 y)))
1.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
4.0ms	(log (- 1.0 y))

series231.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* z (log (- 1.0 y)))
116.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
47.0ms	(log (- 1.0 y))

simplify102.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	332	427
1	1128	376
2	4553	369
3	5001	366

prune203.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 0.2b

Counts

69 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
0.0b	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
0.1b	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
6.8b	(* z (pow y 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
25×	`prod-exp`
20×	`associate-r`
19×	`add-sqr-sqrt`
15×	`add-cbrt-cube`
12×	`div-exp`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow-to-exp` `times-frac` `pow-exp`
7×	`unpow-prod-down`
6×	`pow1` `associate-l`
5×	`cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow2` `sqr-pow`
2×	`cbrt-undiv` `*-commutative` `fma-udef`
1×	`associate-*r/` `pow-prod-down` `div-inv`

Counts

4 → 93

Calls

4 calls:

10.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
1.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
1.0ms	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
9.0ms	(* z (pow y 2))

series351.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
104.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
159.0ms	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
28.0ms	(* z (pow y 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	380	697
1	1716	603
2	5001	603

prune359.0ms

Filtered

105 candidates to 67 candidates (63.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	104	8	112

Merged error: 0.1b

Counts

112 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)))
6.8b	(* z (pow y 2))
6.8b	(* z (pow y 2))
6.8b	(* z (pow y 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
19×	`add-exp-log`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `unswap-sqr`
10×	`add-cbrt-cube`
9×	`associate-l` `prod-exp`
6×	`unpow2` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`pow1/3`

Counts

4 → 100

Calls

4 calls:

1.0ms	(cbrt (fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)))
6.0ms	(* z (pow y 2))
6.0ms	(* z (pow y 2))
7.0ms	(* z (pow y 2))

series411.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(cbrt (fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)))
28.0ms	(* z (pow y 2))
34.0ms	(* z (pow y 2))
30.0ms	(* z (pow y 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	322	726
1	1088	651
2	5001	624

prune586.0ms

Filtered

112 candidates to 74 candidates (66.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	109	11	120

Merged error: 0.1b

Counts

120 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

6.8b	(* z (pow y 2))
6.8b	(* z (pow y 2))
6.8b	(* z (pow y 2))
6.8b	(* z (pow y 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
32×	`associate-r`
24×	`add-exp-log`
16×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
12×	`associate-l` `prod-exp` `add-cbrt-cube`
8×	`unpow2` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

4 → 116

Calls

4 calls:

6.0ms	(* z (pow y 2))
6.0ms	(* z (pow y 2))
6.0ms	(* z (pow y 2))
6.0ms	(* z (pow y 2))

series117.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* z (pow y 2))
33.0ms	(* z (pow y 2))
28.0ms	(* z (pow y 2))
28.0ms	(* z (pow y 2))

simplify75.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	109	432
1	408	372
2	2002	372
3	5001	368

prune788.0ms

Filtered

128 candidates to 80 candidates (62.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	128	11	139

Merged error: 0.1b

Counts

139 → 11

regimes274.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	13
1	23	13

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	24398×	body	80	nan
354.0ms	5521×	body	80	valid
302.0ms	884×	body	640	valid
283.0ms	425×	body	1280	valid
162.0ms	753×	body	320	valid
62.0ms	448×	body	160	valid