Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	248×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	12×	body	160	valid

simplify55.0ms

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

prune10.0ms

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: 14.4b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
14.4b	(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)

series149.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- t x) (- a z))
95.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	266	450
1	730	425
2	2486	423
3	5003	421

prune145.0ms

Filtered

70 candidates to 51 candidates (27.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	60	12	72

Merged error: 6.0b

Counts

72 → 12

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
14.4b	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 137

Calls

3 calls:

5.0ms	(/ 1 (- a z))
15.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series187.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (- a z))
56.0ms	(* (- t x) (/ 1 (- a z)))
93.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	431	830
1	2055	743
2	5002	683

prune236.0ms

Filtered

146 candidates to 84 candidates (42.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	146	12	158

Merged error: 6.0b

Counts

158 → 12

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 176

Calls

3 calls:

9.0ms	(/ (- t x) (- a z))
23.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
21.0ms	(* (- y z) (/ (- t x) (- a z)))

series355.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (- t x) (- a z))
159.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
139.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify93.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	647	1324
1	3278	1269
2	5002	1267

prune335.0ms

Filtered

185 candidates to 125 candidates (32.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	178	7	185
Fresh	5	4	9
Picked	1	0	1
Done	1	1	2
Total	185	12	197

Merged error: 4.0b

Counts

197 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
4.1b	(+ x (/ (- y z) (/ (- a z) (- t x))))
5.6b	(/ (- y z) (/ (- a z) (- t x)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

330×	`*-un-lft-identity` `times-frac`
328×	`add-sqr-sqrt`
116×	`add-cube-cbrt`
106×	`distribute-lft-out--` `difference-of-squares`
41×	`associate-/r*`
29×	`associate-/r/`
15×	`associate-/l*`
10×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
8×	`div-inv`
6×	`associate-/l/`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-def` `frac-2neg` `div-sub` `clear-num` `log1p-expm1-u`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 297

Calls

3 calls:

9.0ms	(/ (- a z) (- t x))
47.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
19.0ms	(/ (- y z) (/ (- a z) (- t x)))

series541.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- a z) (- t x))
163.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
323.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify119.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1085	3135
1	4461	3058
2	5002	3056

prune477.0ms

Filtered

306 candidates to 189 candidates (38.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	302	4	306
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	307	11	318

Merged error: 4.0b

Counts

318 → 11

regimes265.0ms

Accuracy

19.4% (6.6b remaining)

Error of 10.3b against oracle of 3.7b and baseline of 11.8b

bsearch98.0ms

Steps

Iters	Range		Point
8	1.4236453659511324e-150	9.308336965525908e-147	1.2797340449318303e-148
8	-3.2624607372148336e-246	-2.4572477418168722e-250	-2.957055597426421e-246

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	34	12
2	37	12
3	37	12

end0.0ms

sample689.0ms

Algorithm

intervals

Results

263.0ms	7786×	body	80	valid
61.0ms	518×	body	640	valid
39.0ms	258×	body	1280	valid
33.0ms	376×	body	320	valid
19.0ms	321×	body	160	valid
4.0ms	21×	body	2560	valid