Details

sample94.0ms

Algorithm

intervals

Results

32.0ms	701×	body	80	nan
10.0ms	192×	body	80	valid
9.0ms	15×	body	1280	valid
7.0ms	23×	body	640	valid
4.0ms	19×	body	320	valid
1.0ms	7×	body	160	valid

simplify33.0ms

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

localize13.0ms

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))

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))

series229.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* z (log (- 1.0 y)))
120.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
44.0ms	(log (- 1.0 y))

simplify118.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (112.0ms)

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

prune215.0ms

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

localize22.0ms

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))

rewrite85.0ms

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:

1.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
57.0ms	(* 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))
7.0ms	(* z (pow y 2))

series366.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
61.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
168.0ms	(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))
30.0ms	(* z (pow y 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1379	1955
1	5002	1715

prune1.2s

Filtered

311 candidates to 208 candidates (66.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	308	3	311
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	311	5	316

Merged error: 0.1b

Counts

316 → 5

localize25.0ms

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))

rewrite30.0ms

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×	`pow1` `add-cbrt-cube`
9×	`associate-l` `prod-exp`
6×	`unpow2` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`pow1/3`

Counts

4 → 103

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

series429.0ms

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)))
35.0ms	(* z (pow y 2))
30.0ms	(* z (pow y 2))
30.0ms	(* z (pow y 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	322	732
1	1088	657
2	5001	630

prune643.0ms

Filtered

115 candidates to 74 candidates (64.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	111	9	120

Merged error: 0.1b

Counts

120 → 9

localize30.0ms

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))

rewrite37.0ms

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:

7.0ms	(* z (pow y 2))
8.0ms	(* z (pow y 2))
7.0ms	(* z (pow y 2))
11.0ms	(* z (pow y 2))

series123.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* z (pow y 2))
34.0ms	(* z (pow y 2))
30.0ms	(* z (pow y 2))
30.0ms	(* z (pow y 2))

simplify87.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	109	440
1	408	380
2	2002	380
3	5001	376

prune758.0ms

Filtered

132 candidates to 80 candidates (60.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	132	9	141

Merged error: 0.1b

Counts

141 → 9

regimes252.0ms

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
291.0ms	5537×	body	80	valid
268.0ms	880×	body	640	valid
256.0ms	423×	body	1280	valid
131.0ms	726×	body	320	valid
52.0ms	465×	body	160	valid