Details

sample42.0ms

Algorithm

intervals

Results

14.0ms	218×	body	80	valid
4.0ms	17×	body	640	valid
3.0ms	17×	body	320	valid
3.0ms	10×	body	1280	valid
2.0ms	14×	body	160	valid
1.0ms	2×	body	2560	valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (13.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	111	6
3	213	6
4	517	5
5	1051	5
6	2055	5
7	3280	5
8	5002	5

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
16.1b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 49

Calls

2 calls:

5.0ms	(/ y (- a t))
0.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series34.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ y (- a t))
26.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify48.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	170	278
1	468	257
2	1400	257
3	5002	257

prune484.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
0.4b	(/ 1 (/ (- a t) y))
16.1b	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
101×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
22×	`associate-/r*`
16×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`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×	`flip3--` `pow-flip` `div-sub` `associate-/r/` `flip--` `fma-udef` `inv-pow`

Counts

3 → 152

Calls

3 calls:

9.0ms	(/ (- a t) y)
10.0ms	(/ 1 (/ (- a t) y))
0.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

series47.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/ (- a t) y)
13.0ms	(/ 1 (/ (- a t) y))
26.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

simplify54.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	466	1086
1	1950	958
2	5001	852

prune923.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (/ 1 (- a t)) y)
16.1b	(fma (* (/ 1 (- a t)) y) (- t z) (+ x y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-l`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `flip--` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 98

Calls

3 calls:

6.0ms	(/ 1 (- a t))
19.0ms	(* (/ 1 (- a t)) y)
0.0ms	(fma (* (/ 1 (- a t)) y) (- t z) (+ x y))

series46.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ 1 (- a t))
13.0ms	(* (/ 1 (- a t)) y)
29.0ms	(fma (* (/ 1 (- a t)) y) (- t z) (+ x y))

simplify74.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	293	501
1	1108	433
2	3417	397
3	5001	395

prune750.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 7.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(/ (/ 1 (- a t)) (/ 1 y))
16.0b	(fma (/ (/ 1 (- a t)) (/ 1 y)) (- t z) (+ x y))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

696×	`times-frac`
385×	`add-sqr-sqrt` `*-un-lft-identity`
293×	`add-cube-cbrt`
47×	`add-exp-log`
46×	`distribute-lft-out--` `difference-of-squares`
38×	`div-inv`
34×	`div-exp`
31×	`associate-/r/`
24×	`associate-/l*`
18×	`associate-/r*`
17×	`add-cbrt-cube`
15×	`flip3--` `flip--`
9×	`cbrt-undiv` `rec-exp` `1-exp`
4×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

3 → 394

Calls

3 calls:

6.0ms	(/ 1 (- a t))
21.0ms	(/ (/ 1 (- a t)) (/ 1 y))
0.0ms	(fma (/ (/ 1 (- a t)) (/ 1 y)) (- t z) (+ x y))

series44.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ 1 (- a t))
13.0ms	(/ (/ 1 (- a t)) (/ 1 y))
27.0ms	(fma (/ (/ 1 (- a t)) (/ 1 y)) (- t z) (+ x y))

simplify83.0ms

Algorithm

egg-herbie

Counts

403 → 403

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1628	4228
1	5002	3606

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.2b

regimes954.0ms

Accuracy

13.2% (4.9b remaining)

Error of 11.4b against oracle of 6.5b and baseline of 12.1b

bsearch48.0ms

Steps

Iters	Range		Point
6	9.532258889053878e+219	5.919803248124498e+220	1.2628511277499446e+220
7	-8.2522539580275235e+127	-4.759549154242407e+125	-6.098989235421839e+126

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	6
1	25	6

end0.0ms

sample1.1s

Algorithm

intervals

Results

479.0ms	7346×	body	80	valid
117.0ms	461×	body	640	valid
87.0ms	277×	body	1280	valid
79.0ms	431×	body	320	valid
31.0ms	253×	body	160	valid
4.0ms	11×	body	2560	valid