Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	255×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	12×	body	320	valid
0.0ms	6×	body	160	valid

simplify93.0ms

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

prune8.0ms

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: 10.5b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.3b	(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:

10.0ms	(/ (- 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))
124.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (63.0ms)

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

prune226.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	10	72

Merged error: 3.8b

Counts

72 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- y z) (/ 1 (- a z)))
3.3b	(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:

6.0ms	(/ 1 (- a z))
15.0ms	(* (- y z) (/ 1 (- a z)))
1.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series214.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ 1 (- a z))
54.0ms	(* (- y z) (/ 1 (- a z)))
125.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (37.0ms)

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

prune306.0ms

Filtered

114 candidates to 70 candidates (61.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	113	11	124

Merged error: 3.8b

Counts

124 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
8.7b	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

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

series634.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (- y z))
170.0ms	(cbrt (- y z))
163.0ms	(cbrt (- y z))
131.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	199	519
1	454	479
2	1395	458
3	5001	435

prune329.0ms

Filtered

73 candidates to 66 candidates (90.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	72	12	84

Merged error: 3.8b

Counts

84 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (/ (- y z) (- a z)) (- t x) x))
2.3b	(fma (/ (- y z) (- a z)) (- t x) x)
2.3b	(fma (/ (- y z) (- a z)) (- t x) x)
2.3b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

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

series5.9s

Counts

4 → 12

Calls

4 calls:

5.5s	(cbrt (fma (/ (- y z) (- a z)) (- t x) x))
124.0ms	(fma (/ (- y z) (- a z)) (- t x) x)
132.0ms	(fma (/ (- y z) (- a z)) (- t x) x)
125.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify47.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	125	416
1	298	370
2	1149	361
3	5002	352

prune213.0ms

Filtered

55 candidates to 51 candidates (92.7%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	55	12	67

Merged error: 3.8b

Counts

67 → 12

regimes305.0ms

Accuracy

22.4% (6.1b remaining)

Error of 10.0b against oracle of 3.9b and baseline of 11.8b

bsearch109.0ms

Steps

Iters	Range		Point
7	4.5639512795403315e-201	2.5859239974450258e-199	2.0281642037679978e-199
10	-1.7794668257788558e-146	-1.4120361073866138e-161	-2.0837690743295162e-147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample722.0ms

Algorithm

intervals

Results

258.0ms	7852×	body	80	valid
68.0ms	477×	body	640	valid
49.0ms	275×	body	1280	valid
38.0ms	423×	body	320	valid
19.0ms	247×	body	160	valid
3.0ms	14×	body	2560	valid