Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	235×	body	80	valid
2.0ms	11×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	111	6
3	213	6
4	517	5
5	1051	5
6	2055	5
7	3280	5
8	5002	5

prune11.0ms

Filtered

1 candidates to 1 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: 9.6b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
11.0b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 49

Calls

2 calls:

5.0ms	(/ y (- a t))
1.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series119.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ y (- a t))
87.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify59.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	168	278
1	465	257
2	1396	257
3	5001	257

prune138.0ms

Filtered

55 candidates to 43 candidates (21.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	44	11	55
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	45	12	57

Merged error: 6.3b

Counts

57 → 12

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
11.0b	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
11×	`associate-*r/`
10×	`associate-/r*` `add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`associate-/l*`
6×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `associate-l` `clear-num` `un-div-inv` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3--` `frac-2neg` `1-exp` `flip--` `cbrt-unprod` `div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

3 → 111

Calls

3 calls:

6.0ms	(/ 1 (- a t))
13.0ms	(* y (/ 1 (- a t)))
1.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

series161.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (- a t))
32.0ms	(* y (/ 1 (- a t)))
88.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify104.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	293	530
1	1159	458
2	4304	408
3	5001	405

prune209.0ms

Filtered

120 candidates to 69 candidates (42.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	120	12	132

Merged error: 6.3b

Counts

132 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
11.0b	(fma (/ (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) (- t z) (+ x y))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
1.0ms	(fma (/ (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) (- t z) (+ x y))

series629.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt (- a t))
176.0ms	(cbrt (- a t))
173.0ms	(cbrt (- a t))
91.0ms	(fma (/ (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) (- t z) (+ x y))

simplify67.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	187	514
1	426	469
2	1365	454
3	5002	431

prune259.0ms

Filtered

73 candidates to 65 candidates (11.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	74	11	85

Merged error: 6.3b

Counts

85 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
11.0b	(fma (/ (/ y (* (* 1 (cbrt (- a t))) (cbrt (- a t)))) (cbrt (- a t))) (- t z) (+ x y))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
1.0ms	(fma (/ (/ y (* (* 1 (cbrt (- a t))) (cbrt (- a t)))) (cbrt (- a t))) (- t z) (+ x y))

series620.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (- a t))
173.0ms	(cbrt (- a t))
179.0ms	(cbrt (- a t))
94.0ms	(fma (/ (/ y (* (* 1 (cbrt (- a t))) (cbrt (- a t)))) (cbrt (- a t))) (- t z) (+ x y))

simplify73.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	193	527
1	496	479
2	1708	463
3	5003	428

prune218.0ms

Filtered

73 candidates to 62 candidates (15.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	73	11	84

Merged error: 6.3b

Counts

84 → 11

regimes281.0ms

Accuracy

34.7% (4.0b remaining)

Error of 10.3b against oracle of 6.3b and baseline of 12.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	18
1	30	18

end0.0ms

sample667.0ms

Algorithm

intervals

Results

244.0ms	7263×	body	80	valid
61.0ms	479×	body	640	valid
45.0ms	281×	body	1280	valid
37.0ms	406×	body	320	valid
16.0ms	255×	body	160	valid
2.0ms	13×	body	2560	valid