Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	244×	body	80	valid
2.0ms	15×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	9×	body	640	valid
0.0ms	2×	body	2560	valid
0.0ms	3×	body	160	valid

simplify53.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.0b	(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)

series141.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- t x) (- a z))
91.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune201.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.2b	(/ 1 (/ (- a z) (- t x)))
12.9b	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

rewrite38.0ms

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:

8.0ms	(/ (- a z) (- t x))
12.0ms	(/ 1 (/ (- a z) (- t x)))
1.0ms	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

series362.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- a z) (- t x))
194.0ms	(/ 1 (/ (- a z) (- t x)))
115.0ms	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	632	1907
1	2802	1722
2	5001	1551

prune395.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
3.0b	(+ (/ (- y z) (/ (- a z) (- t x))) x)
4.0b	(/ (- y z) (/ (- a z) (- t x)))

rewrite131.0ms

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) (- t x))
65.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
16.0ms	(/ (- y z) (/ (- a z) (- t x)))

series534.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- a z) (- t x))
171.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
310.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify106.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1035	3079
1	4296	3003
2	5001	3001

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.3b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
2.7b	(* (/ (- y z) (- a z)) (- t x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

12.0ms	(/ (- y z) (- a z))
15.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
17.0ms	(* (/ (- y z) (- a z)) (- t x))

series528.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- y z) (- a z))
175.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
301.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify71.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	682	1497
1	2657	1254
2	5002	1252

prune417.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.3b

regimes299.0ms

Accuracy

5.7% (3.8b remaining)

Error of 7.5b against oracle of 3.7b and baseline of 7.7b

bsearch93.0ms

Steps

Iters	Range		Point
8	1.557424007302578e-241	6.23434962018428e-238	4.956504028535711e-241
8	-1.0308405028667604e-278	-7.876890058089722e-283	-7.454512941735669e-281

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	29	15

end0.0ms

sample698.0ms

Algorithm

intervals

Results

265.0ms	7743×	body	80	valid
66.0ms	525×	body	640	valid
41.0ms	259×	body	1280	valid
38.0ms	414×	body	320	valid
14.0ms	219×	body	160	valid
3.0ms	17×	body	2560	valid