Details

sample98.0ms

Algorithm

intervals

Results

30.0ms	681×	body	80	nan
13.0ms	20×	body	1280	valid
9.0ms	30×	body	640	valid
8.0ms	160×	body	80	valid
6.0ms	33×	body	320	valid
2.0ms	15×	body	160	valid

simplify28.0ms

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

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 12.7b

Counts

2 → 1

localize11.0ms

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))
5.0b	(log (- 1.0 y))

rewrite13.0ms

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))

series235.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* z (log (- 1.0 y)))
122.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
47.0ms	(log (- 1.0 y))

simplify108.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	330	427
1	1121	376
2	4527	369
3	5001	366

prune167.0ms

Filtered

68 candidates to 52 candidates (23.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 0.1b

Counts

69 → 4

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))
7.9b	(* z (pow y 2))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

244×	`associate-r`
207×	`add-sqr-sqrt`
180×	`times-frac`
112×	`unpow-prod-down`
89×	`*-un-lft-identity`
87×	`add-cube-cbrt`
77×	`unswap-sqr`
50×	`unpow2` `sqr-pow`
49×	`add-exp-log`
34×	`associate-l`
31×	`associate-*r/`
25×	`prod-exp`
22×	`associate-/l*`
15×	`add-cbrt-cube`
12×	`div-exp`
11×	`*-commutative`
8×	`pow1` `pow-to-exp` `pow-exp` `associate-/r*`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv`
2×	`cbrt-undiv` `pow-prod-down` `clear-num` `fma-udef`
1×	`frac-2neg` `div-inv`

Counts

4 → 299

Calls

4 calls:

57.0ms	(* 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))
7.0ms	(* z (pow y 2))

series386.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
116.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
174.0ms	(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))
32.0ms	(* z (pow y 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1379	1955
1	5002	1715

prune1.0s

Filtered

311 candidates to 208 candidates (33.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	308	3	311
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	311	4	315

Merged error: 0.1b

Counts

315 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (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))) (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))))
7.9b	(* z (pow y 2))
7.9b	(* z (pow y 2))
7.9b	(* z (pow y 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
30×	`associate-r`
21×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
17×	`pow1`
16×	`cbrt-prod` `unswap-sqr`
15×	`associate-l`
14×	`add-cbrt-cube`
12×	`unpow-prod-down`
10×	`prod-exp`
7×	`cbrt-unprod`
6×	`pow1/3` `swap-sqr` `unpow2` `sqr-pow`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp`
2×	`pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 135

Calls

4 calls:

6.0ms	(* (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))) (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))))
10.0ms	(* z (pow y 2))
7.0ms	(* z (pow y 2))
7.0ms	(* z (pow y 2))

series475.0ms

Counts

4 → 12

Calls

4 calls:

374.0ms	(* (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))) (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))))
37.0ms	(* z (pow y 2))
32.0ms	(* z (pow y 2))
32.0ms	(* z (pow y 2))

simplify62.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	371	1987
1	1464	1738
2	5002	1479

prune662.0ms

Filtered

147 candidates to 90 candidates (38.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	144	7	151

Merged error: 0.0b

Counts

151 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

7.9b	(* z (pow y 2))
7.9b	(* z (pow y 2))
7.9b	(* z (pow y 2))
7.9b	(* z (pow y 2))

rewrite35.0ms

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×	`pow1` `associate-l` `prod-exp` `add-cbrt-cube`
8×	`unpow2` `sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

4 → 120

Calls

4 calls:

8.0ms	(* z (pow y 2))
8.0ms	(* z (pow y 2))
7.0ms	(* z (pow y 2))
7.0ms	(* z (pow y 2))

series139.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* z (pow y 2))
38.0ms	(* z (pow y 2))
32.0ms	(* z (pow y 2))
37.0ms	(* z (pow y 2))

simplify83.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	109	440
1	408	380
2	1981	380
3	5002	376

prune718.0ms

Filtered

132 candidates to 80 candidates (39.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	132	7	139

Merged error: 0.0b

Counts

139 → 7

regimes231.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

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	23956×	body	80	nan
279.0ms	5464×	body	80	valid
265.0ms	905×	body	640	valid
245.0ms	414×	body	1280	valid
131.0ms	750×	body	320	valid
53.0ms	502×	body	160	valid