Details

sample40.0ms

Algorithm

intervals

Results

17.0ms	227×	body	80	valid
4.0ms	14×	body	640	valid
3.0ms	14×	body	320	valid
2.0ms	7×	body	1280	valid
2.0ms	13×	body	160	valid

simplify120.0ms

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: 18.1b

localize10.0ms

Local error

Found 2 expressions with local error:

4.3b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.9b	(/ (* (- z t) y) (- a t))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

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

series167.0ms

Counts

2 → 6

Calls

2 calls:

106.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
60.0ms	(/ (* (- z t) y) (- a t))

simplify38.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	333	376
1	1377	346
2	5001	344

prune132.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.7b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.7b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
62.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
20.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (- a t))
148.0ms	(cbrt (- a t))
99.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
109.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	785	1736
1	3321	1577
2	5002	1498

prune468.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.7b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
15.8b	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 119

Calls

4 calls:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
64.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
2.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (- a t))
147.0ms	(cbrt (- a t))
95.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
80.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	657	1524
1	2791	1373
2	5001	1294

prune454.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
18.5b	(- y (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 45

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(cbrt y)
0.0ms	(cbrt y)
2.0ms	(- y (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

series664.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt y)
174.0ms	(cbrt y)
177.0ms	(cbrt y)
132.0ms	(- y (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

simplify28.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	145	631
1	562	537
2	5001	497

prune241.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.2b

regimes429.0ms

Accuracy

20.6% (5.7b remaining)

Error of 9.7b against oracle of 4.0b and baseline of 11.2b

bsearch234.0ms

Steps

Iters	Range		Point
7	4.696352832161571e-49	1.7422855315474825e-47	2.966911009458564e-48
10	1.7739239693314067e-180	3.2588129838122794e-162	2.475987323717541e-180
9	3.1779091062353683e-279	1.7067799222738254e-272	1.674500911629895e-272
8	-7.644900317317414e-142	-2.1415923759450418e-144	-5.089206195382601e-142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	73
1	56	73

end0.0ms

sample1.1s

Algorithm

intervals

Results

476.0ms	7297×	body	80	valid
120.0ms	468×	body	640	valid
75.0ms	413×	body	320	valid
72.0ms	229×	body	1280	valid
32.0ms	263×	body	160	valid
6.0ms	17×	body	2560	valid