Details

sample150.0ms

Algorithm

intervals

Results

50.0ms	701×	body	80	nan
19.0ms	192×	body	80	valid
15.0ms	15×	body	1280	valid
11.0ms	23×	body	640	valid
6.0ms	19×	body	320	valid
1.0ms	7×	body	160	valid

simplify26.0ms

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: 7.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.2b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
5.2b	(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:

71.0ms	(* z (log (- 1.0 y)))
114.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
47.0ms	(log (- 1.0 y))

simplify103.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (97.0ms)

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

prune210.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 0.1b

Counts

69 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
0.0b	(* 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))
7.7b	(* z (pow y 2))

rewrite19.0ms

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:

1.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
10.0ms	(* 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))
6.0ms	(* z (pow y 2))

series359.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
62.0ms	(* 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))
33.0ms	(* z (pow y 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (10.0ms)

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

prune544.0ms

Filtered

105 candidates to 67 candidates (63.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	105	5	110

Merged error: 0.1b

Counts

110 → 5

localize26.0ms

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)))
7.7b	(* z (pow y 2))
7.7b	(* z (pow y 2))
7.7b	(* z (pow y 2))

rewrite21.0ms

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

series425.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(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))
29.0ms	(* z (pow y 2))

simplify37.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

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

prune622.0ms

Filtered

112 candidates to 74 candidates (66.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	108	9	117

Merged error: 0.1b

Counts

117 → 9

localize44.0ms

Local error

Found 4 expressions with local error:

7.7b	(* z (pow y 2))
7.7b	(* z (pow y 2))
7.7b	(* z (pow y 2))
7.7b	(* z (pow y 2))

rewrite38.0ms

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))
8.0ms	(* z (pow y 2))
10.0ms	(* z (pow y 2))
10.0ms	(* z (pow y 2))

series123.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* z (pow y 2))
28.0ms	(* z (pow y 2))
29.0ms	(* z (pow y 2))
33.0ms	(* z (pow y 2))

simplify106.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 3 (98.0ms)

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

prune724.0ms

Filtered

128 candidates to 80 candidates (62.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	128	9	137

Merged error: 0.1b

Counts

137 → 9

regimes242.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	13
1	23	13

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	23670×	body	80	nan
284.0ms	5537×	body	80	valid
263.0ms	880×	body	640	valid
256.0ms	423×	body	1280	valid
129.0ms	726×	body	320	valid
50.0ms	465×	body	160	valid