Details

sample27.0ms

Algorithm

intervals

Results

10.0ms	237×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	12×	body	160	valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.9b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.4b	(/ (* (- z t) y) (- a t))

rewrite25.0ms

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:

6.0ms	(* (- z t) y)
9.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
8.0ms	(/ (* (- z t) y) (- a t))

series221.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* (- z t) y)
132.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
62.0ms	(/ (* (- z t) y) (- a t))

simplify53.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

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

prune198.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	67	12	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	12	80

Merged error: 4.0b

Counts

80 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.9b	(- (+ x y) (* (- z t) (/ y (- a t))))
9.5b	(* (- z t) (/ y (- a t)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 107

Calls

3 calls:

5.0ms	(/ y (- a t))
6.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
15.0ms	(* (- z t) (/ y (- a t)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ y (- a t))
108.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
64.0ms	(* (- z t) (/ y (- a t)))

simplify65.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	559	844
1	2676	803
2	5001	803

prune471.0ms

Filtered

116 candidates to 85 candidates (73.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	7	4	11
Picked	0	1	1
Done	0	0	0
Total	118	10	128

Merged error: 4.0b

Counts

128 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
3.3b	(* (- z t) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
9.5b	(- (+ x y) (* (* (- z t) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
22.0ms	(* (- z t) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
8.0ms	(- (+ x y) (* (* (- z t) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))))

series794.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt y)
204.0ms	(cbrt y)
222.0ms	(* (- z t) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
162.0ms	(- (+ x y) (* (* (- z t) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))))

simplify137.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	998	2016
1	4502	1702
2	5002	1671

prune504.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	114	10	124

Merged error: 4.0b

Counts

124 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

4.0b	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
4.0b	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
4.0b	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
9.7b	(- (+ x y) (* (* (* (- z t) (* (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))))) (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (- a t)))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

183×	`cbrt-div`
174×	`frac-times`
136×	`associate-*l/`
94×	`frac-sub`
60×	`associate-*r/`
51×	`flip3--` `flip--`
47×	`flip3-+` `flip-+`
39×	`cbrt-prod`
24×	`associate-/r/`
9×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`times-frac` `pow1/3` `div-inv`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 174

Calls

4 calls:

13.0ms	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
13.0ms	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
13.0ms	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
16.0ms	(- (+ x y) (* (* (* (- z t) (* (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))))) (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (- a t)))))

series914.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
245.0ms	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
243.0ms	(cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
182.0ms	(- (+ x y) (* (* (* (- z t) (* (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))))) (cbrt (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (- a t)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1689	8640
1	5001	8268

prune849.0ms

Filtered

186 candidates to 132 candidates (71.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	181	5	186
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	184	12	196

Merged error: 4.0b

Counts

196 → 12

regimes370.0ms

Accuracy

7.8% (6.4b remaining)

Error of 10.2b against oracle of 3.8b and baseline of 10.8b

bsearch59.0ms

Steps

Iters	Range		Point
10	-1.5581990694171068e+89	-3.976674738576283e+76	-1.53218274451368e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	46
1	40	46

end0.0ms

sample661.0ms

Algorithm

intervals

Results

251.0ms	7381×	body	80	valid
59.0ms	488×	body	640	valid
38.0ms	234×	body	1280	valid
34.0ms	353×	body	320	valid
15.0ms	254×	body	160	valid
4.0ms	23×	body	2560	valid