Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	249×	body	80	valid
3.0ms	7×	body	1280	valid
2.0ms	16×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	3×	body	2560	valid
0.0ms	7×	body	160	valid

simplify50.0ms

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.6b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite11.0ms

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:

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

series139.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- t x) (- a z))
88.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (51.0ms)

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

prune196.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.7b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.1b	(* (- y z) (/ (- t x) (- a z)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 128

Calls

3 calls:

15.0ms	(/ (- t x) (- a z))
7.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
21.0ms	(* (- y z) (/ (- t x) (- a z)))

series327.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- t x) (- a z))
144.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
133.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	488	901
1	2066	849
2	5001	847

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.5b	(/ 1 (/ (- a z) (- t x)))
15.6b	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

rewrite33.0ms

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)

series353.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- a z) (- t x))
187.0ms	(/ 1 (/ (- a z) (- t x)))
115.0ms	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

simplify69.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (50.0ms)

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

prune398.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
5.1b	(* (- y z) (/ (- t x) (- a z)))
12.1b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (- y z) (/ (- t x) (- a z))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
31×	`associate-r`
26×	`times-frac`
18×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-prod`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `pow1/3` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `fma-udef` `div-inv`

Counts

4 → 94

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
16.0ms	(* (- y z) (/ (- t x) (- a z)))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (- y z) (/ (- t x) (- a z))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt x)
170.0ms	(cbrt x)
129.0ms	(* (- y z) (/ (- t x) (- a z)))
157.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (- y z) (/ (- t x) (- a z))))

simplify44.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	363	638
1	1589	575
2	5001	566

prune303.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 3.2b

regimes406.0ms

Accuracy

31% (8.0b remaining)

Error of 11.7b against oracle of 3.8b and baseline of 15.3b

bsearch102.0ms

Steps

Iters	Range		Point
10	1.4008479968077877e-114	5.216915299784966e-99	2.3226627040798955e-101
8	-3.7533434580716932e-112	-4.216507433109753e-116	-9.742147880973151e-116

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	10
1	27	10

end0.0ms

sample710.0ms

Algorithm

intervals

Results

259.0ms	7715×	body	80	valid
65.0ms	545×	body	640	valid
41.0ms	254×	body	1280	valid
41.0ms	414×	body	320	valid
16.0ms	266×	body	160	valid
2.0ms	13×	body	2560	valid