Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	239×	body	80	valid
2.0ms	21×	body	320	valid
2.0ms	15×	body	640	valid
1.0ms	4×	body	1280	valid
0.0ms	6×	body	160	valid

simplify110.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.9b	(- (+ x y) (/ (* (- z t) y) (- a t)))
8.1b	(/ (* (- z t) y) (- a t))

rewrite49.0ms

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))

series195.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(* (- z t) y)
106.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
61.0ms	(/ (* (- z t) y) (- a t))

simplify44.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (10.0ms)

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

prune215.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.1b	(- (+ x y) (* (- z t) (/ y (- a t))))
12.2b	(* (- z t) (/ y (- a t)))

rewrite55.0ms

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))
22.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
23.0ms	(* (- z t) (/ y (- a t)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ y (- a t))
112.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
59.0ms	(* (- 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

prune287.0ms

Filtered

116 candidates to 83 candidates (71.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
4.1b	(- (+ x y) (* (- z t) (* y (/ 1 (- a t)))))
12.2b	(* (- z t) (* y (/ 1 (- a t))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 147

Calls

4 calls:

6.0ms	(/ 1 (- a t))
16.0ms	(* y (/ 1 (- a t)))
24.0ms	(- (+ x y) (* (- z t) (* y (/ 1 (- a t)))))
25.0ms	(* (- z t) (* y (/ 1 (- a t))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (- a t))
26.0ms	(* y (/ 1 (- a t)))
106.0ms	(- (+ x y) (* (- z t) (* y (/ 1 (- a t)))))
61.0ms	(* (- z t) (* y (/ 1 (- a t))))

simplify76.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	676	1151
1	3060	1040
2	5002	991

prune339.0ms

Filtered

159 candidates to 91 candidates (57.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
5.6b	(* (cbrt (- z t)) (/ y (- a t)))
6.6b	(* (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- z t)) (/ y (- a t))))
8.9b	(- (+ x y) (* (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- z t)) (/ y (- a t)))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

330×	`cbrt-div`
248×	`frac-times`
167×	`flip3--` `flip--`
116×	`associate-*l/`
106×	`frac-sub`
79×	`associate-*r/`
53×	`flip3-+` `flip-+`
36×	`add-sqr-sqrt`
30×	`add-exp-log`
26×	`*-un-lft-identity`
22×	`associate-r`
18×	`pow1` `add-cbrt-cube`
17×	`times-frac`
16×	`add-cube-cbrt`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-prod`
9×	`associate-l` `pow-prod-down` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`diff-log` `associate-/r/` `*-commutative`
1×	`sub-neg` `pow1/3` `associate--l+` `sum-log` `div-inv`

Counts

4 → 265

Calls

4 calls:

2.0ms	(cbrt (- z t))
25.0ms	(* (cbrt (- z t)) (/ y (- a t)))
53.0ms	(* (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- z t)) (/ y (- a t))))
43.0ms	(- (+ x y) (* (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- z t)) (/ y (- a t)))))

series604.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (- z t))
293.0ms	(* (cbrt (- z t)) (/ y (- a t)))
61.0ms	(* (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- z t)) (/ y (- a t))))
109.0ms	(- (+ x y) (* (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- z t)) (/ y (- a t)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1928	7329
1	5001	7172

prune965.0ms

Filtered

277 candidates to 184 candidates (66.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.3b

regimes236.0ms

Accuracy

10.5% (7.1b remaining)

Error of 11.3b against oracle of 4.2b and baseline of 12.1b

bsearch45.0ms

Steps

Iters	Range		Point
9	3.215110474696283e+106	1.9127830697436207e+113	8.337227270352703e+106

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample655.0ms

Algorithm

intervals

Results

241.0ms	7354×	body	80	valid
53.0ms	462×	body	640	valid
38.0ms	412×	body	320	valid
37.0ms	236×	body	1280	valid
15.0ms	261×	body	160	valid
3.0ms	18×	body	2560	valid