Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	227×	body	80	valid
2.0ms	16×	body	1280	valid
2.0ms	16×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid

simplify123.0ms

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: 18.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.6b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.7b	(/ (* (- z t) y) (- a t))

rewrite48.0ms

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:

12.0ms	(* (- z t) y)
25.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series205.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* (- z t) y)
115.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
61.0ms	(/ (* (- z t) y) (- a t))

simplify50.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (12.0ms)

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

prune212.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(* (cbrt (- a t)) (cbrt (- a t)))
2.9b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.9b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`cbrt-prod`
38×	`associate-r`
36×	`times-frac`
30×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
15×	`flip3--` `flip--`
13×	`pow1`
11×	`frac-times` `distribute-lft-out--`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares`
7×	`cbrt-undiv` `pow1/3` `associate-r/` `div-exp` `associate-l/`
6×	`frac-sub`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`diff-log` `pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `sub-neg` `pow-plus` `associate--l+` `sum-log`

Counts

4 → 168

Calls

4 calls:

2.0ms	(cbrt (- a t))
19.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
64.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
18.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (- a t))
124.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
103.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
117.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify125.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	886	2068
1	4326	1890
2	5001	1779

prune560.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
2.7b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
5.0b	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `frac-times` `-un-lft-identity` `associate-r/`
14×	`associate-l` `frac-sub`
9×	`pow1` `add-cube-cbrt` `associate-*l/` `add-log-exp`
8×	`times-frac`
7×	`flip3-+` `flip-+`
6×	`cbrt-div`
4×	`flip3--` `flip--`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `diff-log` `associate-/r/`
1×	`sub-neg` `associate-r` `associate--l+` `sum-log` `*-commutative` `div-inv`

Counts

4 → 120

Calls

4 calls:

2.0ms	(cbrt (- z t))
2.0ms	(cbrt (- z t))
79.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
20.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (- z t))
151.0ms	(cbrt (- z t))
106.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
115.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify88.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	796	2499
1	3082	2071
2	5001	1925

prune386.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
2.7b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
6.9b	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac`
6×	`cbrt-div` `add-log-exp`
5×	`frac-times` `associate-*r/`
4×	`flip3--` `flip--`
3×	`pow-prod-down` `associate-*l/` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `associate-/r/`
1×	`sub-neg` `diff-log` `associate-r` `*-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

2.0ms	(cbrt (- z t))
2.0ms	(cbrt (- z t))
79.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
2.0ms	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- z t))
149.0ms	(cbrt (- z t))
108.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
84.0ms	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	621	1977
1	2350	1562
2	5001	1406

prune307.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.0b

regimes344.0ms

Accuracy

26.5% (3.7b remaining)

Error of 7.7b against oracle of 4.0b and baseline of 9.0b

bsearch96.0ms

Steps

Iters	Range		Point
8	7.822312363142053e-194	1.998992656231707e-189	4.987953603449975e-192
9	-1.7500594794839567e-124	-1.6036634392402047e-131	-1.323154873685477e-128

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	23
1	34	23

end0.0ms

sample652.0ms

Algorithm

intervals

Results

240.0ms	7343×	body	80	valid
56.0ms	461×	body	640	valid
42.0ms	260×	body	1280	valid
36.0ms	407×	body	320	valid
15.0ms	247×	body	160	valid
2.0ms	11×	body	2560	valid