Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	229×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	10×	body	160	valid
1.0ms	6×	body	320	valid

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	109	6
3	195	6
4	445	6
5	828	6
6	1434	6
7	2520	6
8	4830	6
9	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.2b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.0b	(/ (* (- z t) y) (- a t))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-l` `associate-/r*` `distribute-lft-out--`
4×	`flip3--` `associate-*l/` `flip--` `difference-of-squares`
3×	`associate-r`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

10.0ms	(* (- z t) y)
27.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series196.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(* (- z t) y)
106.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
62.0ms	(/ (* (- z t) y) (- a t))

simplify47.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	383	461
1	1704	422
2	5001	422

prune191.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
3.2b	(- (+ x y) (/ (- z t) (/ (- a t) y)))
10.0b	(/ (- z t) (/ (- a t) y))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

203×	`times-frac`
180×	`add-sqr-sqrt`
176×	`*-un-lft-identity`
87×	`add-cube-cbrt`
45×	`difference-of-squares`
44×	`distribute-lft-out--`
22×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
8×	`div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `flip3--` `div-sub` `flip--`
2×	`frac-2neg` `diff-log` `clear-num` `frac-sub`
1×	`sub-neg` `flip3-+` `associate--l+` `sum-log` `associate-/r/` `flip-+` `distribute-lft-out` `associate--r-`

Counts

3 → 197

Calls

3 calls:

7.0ms	(/ (- a t) y)
56.0ms	(- (+ x y) (/ (- z t) (/ (- a t) y)))
14.0ms	(/ (- z t) (/ (- a t) y))

series236.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ (- a t) y)
109.0ms	(- (+ x y) (/ (- z t) (/ (- a t) y)))
101.0ms	(/ (- z t) (/ (- a t) y))

simplify84.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	853	1851
1	3326	1798
2	5001	1798

prune518.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
1.9b	(* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (/ (cbrt (- a t)) (cbrt y))))
7.3b	(- (+ x y) (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (/ (cbrt (- a t)) (cbrt y)))))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

525×	`times-frac`
409×	`add-sqr-sqrt`
373×	`*-un-lft-identity`
288×	`cbrt-prod`
265×	`associate-r`
205×	`add-cube-cbrt`
84×	`distribute-lft-out--` `difference-of-squares`
73×	`add-exp-log`
39×	`add-cbrt-cube`
27×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`cbrt-div`
13×	`associate-l`
12×	`unswap-sqr`
9×	`flip3--` `associate-/r/` `flip--` `add-log-exp`
7×	`frac-times` `div-inv`
6×	`pow1` `frac-sub`
5×	`associate-r/` `associate-l/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 382

Calls

4 calls:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
161.0ms	(* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (/ (cbrt (- a t)) (cbrt y))))
17.0ms	(- (+ x y) (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (/ (cbrt (- a t)) (cbrt y)))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- a t))
150.0ms	(cbrt (- a t))
173.0ms	(* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (/ (cbrt (- a t)) (cbrt y))))
124.0ms	(- (+ x y) (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (/ (cbrt (- a t)) (cbrt y)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2281	7251
1	5002	6880

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- a t) (/ 1 y))
6.1b	(- (+ x y) (/ (- z t) (* (- a t) (/ 1 y))))
10.0b	(/ (- z t) (* (- a t) (/ 1 y)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
27×	`add-exp-log`
25×	`*-un-lft-identity`
17×	`add-cbrt-cube`
16×	`times-frac`
13×	`add-cube-cbrt` `associate-r`
9×	`div-exp`
8×	`prod-exp` `add-log-exp`
6×	`flip3--` `associate-/r/` `flip--`
5×	`pow1` `cbrt-undiv` `associate-l` `associate-/l*` `distribute-lft-out--`
4×	`frac-times` `associate-*l/` `cbrt-unprod` `difference-of-squares`
3×	`unswap-sqr`
2×	`rec-exp` `diff-log` `1-exp` `div-sub` `associate-*r/` `un-div-inv` `frac-sub` `div-inv` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `associate-/r` `sum-log` `-commutative` `flip-+` `distribute-lft-out` `associate--r-`

Counts

3 → 100

Calls

3 calls:

14.0ms	(* (- a t) (/ 1 y))
27.0ms	(- (+ x y) (/ (- z t) (* (- a t) (/ 1 y))))
16.0ms	(/ (- z t) (* (- a t) (/ 1 y)))

series240.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* (- a t) (/ 1 y))
116.0ms	(- (+ x y) (/ (- z t) (* (- a t) (/ 1 y))))
98.0ms	(/ (- z t) (* (- a t) (/ 1 y)))

simplify62.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	557	720
1	2427	626
2	5001	609

prune252.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.1b

regimes239.0ms

Accuracy

27.4% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 11.0b

bsearch99.0ms

Steps

Iters	Range		Point
7	3.8546788808116346e-66	6.6796673763652165e-65	4.5065014455694435e-66
10	-1.3465527011938294e-166	-2.7828870664677494e-182	-9.343679842378289e-178

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	21
1	33	21

end0.0ms

sample691.0ms

Algorithm

intervals

Results

258.0ms	7336×	body	80	valid
60.0ms	460×	body	640	valid
50.0ms	289×	body	1280	valid
35.0ms	371×	body	320	valid
17.0ms	260×	body	160	valid
3.0ms	15×	body	2560	valid