Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	9×	body	1280	valid
1.0ms	11×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1912	5
6	4581	5
7	5001	5

prune14.0ms

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: 9.9b

Counts

2 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.2b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite13.0ms

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

series178.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- y z) (- a z))
125.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify76.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	265	450
1	729	425
2	2562	423
3	5002	421

prune233.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 2.7b

Counts

72 → 12

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
3.7b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite26.0ms

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:

7.0ms	(/ 1 (- a z))
14.0ms	(* (- y z) (/ 1 (- a z)))
1.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series216.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (- a z))
50.0ms	(* (- y z) (/ 1 (- a z)))
126.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	340	602
1	1472	525
2	5002	481

prune272.0ms

Filtered

114 candidates to 68 candidates (59.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	114	12	126

Merged error: 2.7b

Counts

126 → 12

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.3b	(/ 1 (/ (- a z) (- y z)))
2.2b	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/ (- a z) (- y z))
13.0ms	(/ 1 (/ (- a z) (- y z)))
1.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

series329.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- a z) (- y z))
144.0ms	(/ 1 (/ (- a z) (- y z)))
131.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

simplify89.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	630	1909
1	2802	1724
2	5003	1553

prune396.0ms

Filtered

223 candidates to 105 candidates (47.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	226	9	235

Merged error: 2.6b

Counts

235 → 9

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
1.9b	(+ (/ (- t x) (/ (- a z) (- y z))) x)
2.8b	(/ (- t x) (/ (- a z) (- y z)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
572×	`*-un-lft-identity`
570×	`add-sqr-sqrt`
200×	`add-cube-cbrt`
185×	`distribute-lft-out--` `difference-of-squares`
160×	`fma-def`
36×	`associate-/r*`
26×	`associate-/r/`
14×	`flip3--` `flip--` `div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

9.0ms	(/ (- a z) (- y z))
69.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
23.0ms	(/ (- t x) (/ (- a z) (- y z)))

series421.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- a z) (- y z))
149.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
219.0ms	(/ (- t x) (/ (- a z) (- y z)))

simplify136.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1043	3090
1	4307	3014
2	5001	3012

prune1.0s

Filtered

449 candidates to 271 candidates (60.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	442	7	449
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	447	11	458

Merged error: 2.6b

Counts

458 → 11

regimes313.0ms

Accuracy

20.3% (6.4b remaining)

Error of 10.0b against oracle of 3.5b and baseline of 11.6b

bsearch101.0ms

Steps

Iters	Range		Point
8	3.276713297361509e-112	4.8666627780759835e-109	2.4030722061005788e-111
7	-1.1151747913850161e-175	-5.795691522746873e-178	-9.840465118612939e-176

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	16
1	29	16

end0.0ms

sample735.0ms

Algorithm

intervals

Results

281.0ms	7835×	body	80	valid
71.0ms	510×	body	640	valid
43.0ms	270×	body	1280	valid
40.0ms	384×	body	320	valid
17.0ms	257×	body	160	valid
3.0ms	16×	body	2560	valid