Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

285×

body

valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	5
1	37	4
2	60	4
3	104	4
4	174	4
5	237	4
6	266	4
7	312	4
8	375	4
9	507	4
10	666	4
11	1117	4
12	1341	4
13	1513	4
14	1535	4
15	1535	4

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: 1.6b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- z a))
1.5b	(fma y (/ (- z t) (- z a)) 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	(/ (- z t) (- z a))
1.0ms	(fma y (/ (- z t) (- z a)) x)

series119.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- z t) (- z a))
75.0ms	(fma y (/ (- z t) (- z a)) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	260	433
1	705	410
2	2411	410
3	5001	410

prune396.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	9	71

Merged error: 1.2b

Counts

71 → 9

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z a) (- z t))
0.5b	(/ 1 (/ (- z a) (- z t)))
1.5b	(fma y (/ 1 (/ (- z a) (- z t))) x)

rewrite39.0ms

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

series225.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (- z a) (- z t))
100.0ms	(/ 1 (/ (- z a) (- z t)))
82.0ms	(fma y (/ 1 (/ (- z a) (- z t))) x)

simplify76.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	624	1890
1	2773	1707
2	5003	1538

prune354.0ms

Filtered

223 candidates to 104 candidates (46.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	224	8	232

Merged error: 1.2b

Counts

232 → 8

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z a) (- z t))
2.8b	(/ y (/ (- z a) (- z t)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
194×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
11×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`div-sub`

Counts

2 → 198

Calls

2 calls:

9.0ms	(/ (- z a) (- z t))
13.0ms	(/ y (/ (- z a) (- z t)))

series162.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- z a) (- z t))
117.0ms	(/ y (/ (- z a) (- z t)))

simplify86.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	639	1797
1	2867	1744
2	5001	1741

prune453.0ms

Filtered

204 candidates to 137 candidates (67.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	206	6	212

Merged error: 0b

Counts

212 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- z a))
0.2b	(* (- z t) (/ 1 (- z a)))
1.5b	(fma y (* (- z t) (/ 1 (- z a))) x)

rewrite25.0ms

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

series163.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 1 (- z a))
49.0ms	(* (- z t) (/ 1 (- z a)))
77.0ms	(fma y (* (- z t) (/ 1 (- z a))) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	337	585
1	1465	510
2	5001	468

prune211.0ms

Filtered

114 candidates to 71 candidates (62.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	114	6	120

Merged error: 0b

Counts

120 → 6

regimes175.0ms

Accuracy

15.5% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 1.5b

bsearch76.0ms

Steps

Iters	Range		Point
9	1.6220373225649038e-164	1.88939424872283e-159	2.803087658643117e-161
3	-8.266584531325709e-277	-6.056026182056047e-277	-7.023145459861525e-277

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample621.0ms

Algorithm

intervals

Results

336.0ms

8746×

body

valid