Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	241×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	6×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (11.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
11.7b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite7.0ms

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))

series103.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ y (- a t))
76.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify42.0ms

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

prune166.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
0.4b	(/ 1 (/ (- a t) y))
11.7b	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

rewrite25.0ms

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

series180.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ (- a t) y)
70.0ms	(/ 1 (/ (- a t) y))
84.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

simplify51.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (40.0ms)

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

prune318.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
2.8b	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
8.5b	(/ (- t z) (/ (- a t) y))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

370×	`times-frac`
309×	`*-un-lft-identity`
304×	`add-sqr-sqrt`
152×	`add-cube-cbrt`
100×	`fma-def`
76×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
14×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
8×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `sum-log` `log1p-expm1-u` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `flip3-+` `frac-add` `clear-num` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `associate-+l-` `associate-+r+`

Counts

3 → 299

Calls

3 calls:

8.0ms	(/ (- a t) y)
99.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
16.0ms	(/ (- t z) (/ (- a t) y))

series307.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ (- a t) y)
189.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
93.0ms	(/ (- t z) (/ (- a t) y))

simplify85.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	892	1815
1	3565	1754
2	5001	1752

prune813.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
10.0b	(fma (/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(cbrt y)
1.0ms	(cbrt y)
0.0ms	(fma (/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

series1.5s

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt y)
183.0ms	(cbrt y)
187.0ms	(cbrt y)
947.0ms	(fma (/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

simplify74.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	217	460
1	606	409
2	2824	387
3	5001	360

prune248.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

regimes375.0ms

Accuracy

43.9% (4.3b remaining)

Error of 7.5b against oracle of 3.2b and baseline of 10.9b

bsearch99.0ms

Steps

Iters	Range		Point
9	4.0830906405882634e+82	2.0286648894327507e+90	3.723145648712411e+89
9	-5.401771755051308e+132	-3.374811773836171e+123	-4.807356171593076e+132

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	20
1	32	20

end0.0ms

sample639.0ms

Algorithm

intervals

Results

240.0ms	7337×	body	80	valid
57.0ms	466×	body	640	valid
36.0ms	256×	body	1280	valid
31.0ms	364×	body	320	valid
18.0ms	294×	body	160	valid
2.0ms	12×	body	2560	valid