Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	242×	body	80	valid
2.0ms	18×	body	320	valid
2.0ms	12×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	11×	body	160	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.6b	(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))
124.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (64.0ms)

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

prune232.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
6.3b	(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)

series231.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (- a z))
60.0ms	(* (- y z) (/ 1 (- a z)))
129.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (47.0ms)

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

prune289.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
10.9b	(fma (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a 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 (- a z))
4.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
1.0ms	(fma (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z))) (- t x) x)

series678.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (- a z))
177.0ms	(cbrt (- a z))
180.0ms	(cbrt (- a z))
138.0ms	(fma (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z))) (- t x) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	198	519
1	455	474
2	1349	457
3	5002	433

prune335.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite137.0ms

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:

10.0ms	(/ (- a z) (- y z))
18.0ms	(/ (- t x) (/ (- a z) (- y z)))
71.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

series473.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (- a z) (- y z))
243.0ms	(/ (- t x) (/ (- a z) (- y z)))
173.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

simplify141.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (104.0ms)

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

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

regimes387.0ms

Accuracy

-1.2% (4.2b remaining)

Error of 7.6b against oracle of 3.4b and baseline of 7.5b

bsearch105.0ms

Steps

Iters	Range		Point
6	4.7103262021150205e-147	6.7446870861152425e-146	4.7846661919792587e-147
9	-1.626797486195298e-119	-2.444825287532227e-127	-2.6791552713315823e-127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms

sample719.0ms

Algorithm

intervals

Results

274.0ms	7828×	body	80	valid
60.0ms	465×	body	640	valid
43.0ms	416×	body	320	valid
41.0ms	269×	body	1280	valid
18.0ms	287×	body	160	valid
2.0ms	8×	body	2560	valid