Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	244×	body	80	valid
2.0ms	13×	body	1280	valid
2.0ms	15×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	6×	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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
14.7b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite17.0ms

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:

14.0ms	(/ (- t x) (- a z))
0.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series140.0ms

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

prune200.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
14.6b	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite33.0ms

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:

5.0ms	(/ 1 (- a z))
24.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series182.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
93.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify44.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	350	602
1	1497	525
2	5001	481

prune255.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
14.6b	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

rewrite41.0ms

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:

12.0ms	(/ (- a z) (- t x))
17.0ms	(/ 1 (/ (- a z) (- t x)))
0.0ms	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

series368.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- a z) (- t x))
201.0ms	(/ 1 (/ (- a z) (- t x)))
117.0ms	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (48.0ms)

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

prune378.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
3.7b	(+ (/ (- y z) (/ (- a z) (- t x))) x)
5.6b	(/ (- y z) (/ (- a z) (- t x)))

rewrite203.0ms

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:

11.0ms	(/ (- a z) (- t x))
134.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
21.0ms	(/ (- y z) (/ (- a z) (- t x)))

series528.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- a z) (- t x))
176.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
298.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify107.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (77.0ms)

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

prune972.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.0b

regimes403.0ms

Accuracy

13.7% (7.2b remaining)

Error of 10.6b against oracle of 3.4b and baseline of 11.7b

bsearch105.0ms

Steps

Iters	Range		Point
6	7.430386586940111e-220	7.99723010196292e-219	2.711353491124064e-219
10	-2.452597579073626e-67	-7.90650715848996e-79	-8.409742007220424e-79

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	34
1	35	34

end0.0ms

sample932.0ms

Algorithm

intervals

Results

435.0ms	7771×	body	80	valid
76.0ms	484×	body	640	valid
53.0ms	280×	body	1280	valid
46.0ms	385×	body	320	valid
23.0ms	272×	body	160	valid
3.0ms	13×	body	2560	valid