Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	252×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	13×	body	1280	valid
1.0ms	15×	body	320	valid
0.0ms	4×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 13.2b

Counts

2 → 2

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.4b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 64

Calls

2 calls:

9.0ms	(/ (- t x) (- a z))
1.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series140.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- t x) (- a z))
92.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune200.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	57	13	70
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 5.5b

Counts

72 → 13

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
13.4b	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (- a z))
14.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series180.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
93.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	350	602
1	1497	525
2	5001	481

prune271.0ms

Filtered

114 candidates to 69 candidates (60.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	6	6	12
Picked	0	1	1
Done	0	0	0
Total	113	14	127

Merged error: 5.2b

Counts

127 → 14

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.0b	(* (/ (- t x) (- a z)) (- y z))
3.2b	(+ (* (/ (- t x) (- a z)) (- y z)) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`add-cube-cbrt` `times-frac`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

9.0ms	(/ (- t x) (- a z))
18.0ms	(* (/ (- t x) (- a z)) (- y z))
20.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)

series401.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- t x) (- a z))
200.0ms	(* (/ (- t x) (- a z)) (- y z))
148.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)

simplify73.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	682	1508
1	2581	1283
2	5002	1263

prune447.0ms

Filtered

179 candidates to 119 candidates (66.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	170	9	179
Fresh	7	5	12
Picked	1	0	1
Done	0	1	1
Total	178	15	193

Merged error: 4.6b

Counts

193 → 15

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.8b	(* (- t x) (/ (- y z) (- a z)))
2.0b	(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

9.0ms	(/ (- y z) (- a z))
18.0ms	(* (- t x) (/ (- y z) (- a z)))
14.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series319.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- y z) (- a z))
113.0ms	(* (- t x) (/ (- y z) (- a z)))
154.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	490	904
1	2053	854
2	5003	852

prune323.0ms

Filtered

135 candidates to 94 candidates (69.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	4	9	13
Picked	1	0	1
Done	0	1	1
Total	136	14	150

Merged error: 4.5b

Counts

150 → 14

regimes302.0ms

Accuracy

8.5% (7.4b remaining)

Error of 11.5b against oracle of 4.1b and baseline of 12.2b

bsearch71.0ms

Steps

Iters	Range		Point
6	2.715832765458057e-111	3.689100597225875e-110	1.0238132444880358e-110
6	-6.172682213460419e-74	-4.559231648305547e-75	-6.227068275249967e-75

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	16
1	29	16

end0.0ms

sample708.0ms

Algorithm

intervals

Results

255.0ms	7746×	body	80	valid
64.0ms	503×	body	640	valid
44.0ms	282×	body	1280	valid
40.0ms	432×	body	320	valid
24.0ms	281×	body	160	valid
3.0ms	16×	body	2560	valid