Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	250×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	7×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	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: 26.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.0b	(+ x (/ (* (- y x) (- z t)) (- a t)))
19.0b	(/ (* (- y x) (- z t)) (- a t))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
7.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
12.0ms	(/ (* (- y x) (- z t)) (- a t))

series311.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (- y x) (- z t))
162.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
113.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify59.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune248.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 4.0b

Counts

91 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.0b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.6b	(* (- y x) (/ (- z t) (- a t)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 119

Calls

3 calls:

8.0ms	(/ (- z t) (- a t))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
20.0ms	(* (- y x) (/ (- z t) (- a t)))

series313.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (- z t) (- a t))
154.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
112.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify63.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	476	869
1	2018	820
2	5001	820

prune306.0ms

Filtered

128 candidates to 84 candidates (65.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	125	14	139

Merged error: 3.9b

Counts

139 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ z (- a t))
0.0b	(- (/ z (- a t)) (/ t (- a t)))
2.0b	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))
2.6b	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

6.0ms	(/ z (- a t))
28.0ms	(- (/ z (- a t)) (/ t (- a t)))
7.0ms	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))
39.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ z (- a t))
64.0ms	(- (/ z (- a t)) (/ t (- a t)))
159.0ms	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))
112.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))

simplify70.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	550	1126
1	2366	1072
2	5002	1072

prune433.0ms

Filtered

146 candidates to 109 candidates (74.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	5	8	13
Picked	0	1	1
Done	0	0	0
Total	145	15	160

Merged error: 3.9b

Counts

160 → 15

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.0b	(+ x (/ (- y x) (/ (- a t) (- z t))))
3.0b	(/ (- y x) (/ (- a t) (- z t)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

13.0ms	(/ (- a t) (- z t))
73.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
27.0ms	(/ (- y x) (/ (- a t) (- z t)))

series390.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (- a t) (- z t))
148.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
197.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify106.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1030	3053
1	4263	2984
2	5003	2984

prune592.0ms

Filtered

283 candidates to 172 candidates (60.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	278	5	283
Fresh	6	7	13
Picked	1	0	1
Done	1	0	1
Total	286	12	298

Merged error: 3.9b

Counts

298 → 12

regimes299.0ms

Accuracy

-0.3% (7.4b remaining)

Error of 11.7b against oracle of 4.3b and baseline of 11.7b

bsearch189.0ms

Steps

Iters	Range		Point
9	1.9908101505403098e-192	1.5032745506547678e-187	2.5021366598236835e-191
9	-2.0939008728128375e-165	-5.754752544746523e-173	-3.4260995767552516e-167
7	-2.3670312174782002e-57	-1.0708116427781383e-58	-4.819571159715696e-58
9	-0.0011167250079306748	-1.394695875033139e-08	-1.4065350202544076e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	34
1	43	34

end0.0ms

sample743.0ms

Algorithm

intervals

Results

280.0ms	7757×	body	80	valid
69.0ms	501×	body	640	valid
50.0ms	291×	body	1280	valid
38.0ms	391×	body	320	valid
16.0ms	246×	body	160	valid
3.0ms	16×	body	2560	valid