Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

305×

body

valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	5
1	29	5
2	45	5
3	56	5
4	74	5
5	86	5
6	120	5
7	136	5
8	146	5
9	150	5
10	160	5
11	446	5
12	2695	5
13	5001	5

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: 9.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (+ (/ x y) 1.0))
9.0b	(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
4×	`pow1` `times-frac` `associate-r/` `associate-r` `associate-/r`
3×	`flip3-+` `associate-l` `flip-+` `distribute-lft-out`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

2 → 54

Calls

2 calls:

8.0ms	(* x (+ (/ x y) 1.0))
11.0ms	(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

series68.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* x (+ (/ x y) 1.0))
44.0ms	(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	306	352
1	1568	305
2	5001	304

prune110.0ms

Filtered

60 candidates to 42 candidates (70.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	6	61

Merged error: 0b

Counts

61 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ (/ x y) 1.0))
0.2b	(cbrt (+ (/ x y) 1.0))
0.2b	(* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))
9.0b	(/ (* (* x (* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))) (cbrt (+ (/ x y) 1.0))) (+ x 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-div`
38×	`*-un-lft-identity`
36×	`flip3-+` `flip-+`
34×	`associate-*r/`
32×	`cbrt-prod` `frac-times`
26×	`associate-/l/`
24×	`add-sqr-sqrt`
20×	`add-exp-log`
16×	`add-cube-cbrt` `associate-*l/`
13×	`add-cbrt-cube`
11×	`pow1`
10×	`distribute-lft-out`
9×	`swap-sqr`
8×	`pow1/3`
7×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `times-frac` `div-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-/r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 144

Calls

4 calls:

6.0ms	(cbrt (+ (/ x y) 1.0))
6.0ms	(cbrt (+ (/ x y) 1.0))
16.0ms	(* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))
30.0ms	(/ (* (* x (* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))) (cbrt (+ (/ x y) 1.0))) (+ x 1.0))

series762.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(cbrt (+ (/ x y) 1.0))
229.0ms	(cbrt (+ (/ x y) 1.0))
255.0ms	(* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))
42.0ms	(/ (* (* x (* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))) (cbrt (+ (/ x y) 1.0))) (+ x 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	530	1764
1	2466	1525
2	5001	1415

prune412.0ms

Filtered

156 candidates to 114 candidates (73.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	156	6	162

Merged error: 0b

Counts

162 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (+ (/ x y) 1.0))
0.1b	(* (/ (* x (+ (/ x y) 1.0)) (- (* x x) (* 1.0 1.0))) (- x 1.0))
13.1b	(/ (* x (+ (/ x y) 1.0)) (- (* x x) (* 1.0 1.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`add-exp-log` `add-cbrt-cube`
18×	`prod-diff`
13×	`associate-l`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-r`
8×	`times-frac`
7×	`pow1`
6×	`associate-*r/` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `associate-/r/` `flip--` `difference-of-squares`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `sub-neg` `flip3-+` `pow-prod-down` `*-commutative` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `associate-l/` `clear-num` `distribute-lft-out` `associate-/l` `distribute-lft-out--`

Counts

3 → 114

Calls

3 calls:

12.0ms	(* x (+ (/ x y) 1.0))
17.0ms	(* (/ (* x (+ (/ x y) 1.0)) (- (* x x) (* 1.0 1.0))) (- x 1.0))
11.0ms	(/ (* x (+ (/ x y) 1.0)) (- (* x x) (* 1.0 1.0)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* x (+ (/ x y) 1.0))
75.0ms	(* (/ (* x (+ (/ x y) 1.0)) (- (* x x) (* 1.0 1.0))) (- x 1.0))
68.0ms	(/ (* x (+ (/ x y) 1.0)) (- (* x x) (* 1.0 1.0)))

simplify112.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	669	1467
1	4180	1206
2	5001	1206

prune264.0ms

Filtered

123 candidates to 76 candidates (61.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	123	6	129

Merged error: 0b

Counts

129 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x y) (/ x y))
0.8b	(* x (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
5.7b	(/ (* x (- (* (/ x y) (/ x y)) (* 1.0 1.0))) (- (/ x y) 1.0))
9.0b	(/ (/ (* x (- (* (/ x y) (/ x y)) (* 1.0 1.0))) (- (/ x y) 1.0)) (+ x 1.0))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

131×	`times-frac`
108×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
59×	`add-cube-cbrt`
32×	`add-exp-log` `add-cbrt-cube`
17×	`associate-r`
16×	`associate-l`
15×	`difference-of-squares`
14×	`associate-/r/`
13×	`pow1` `swap-sqr` `distribute-lft-out` `associate-/l*`
11×	`cbrt-undiv` `div-exp` `div-inv`
10×	`associate-/r*`
8×	`flip3--` `flip--`
7×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
5×	`associate-*r/` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-diff` `pow-prod-down` `clear-num` `*-commutative`
1×	`pow2` `frac-times` `flip3-+` `pow-plus` `associate-*l/` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 216

Calls

4 calls:

9.0ms	(* (/ x y) (/ x y))
9.0ms	(* x (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
18.0ms	(/ (* x (- (* (/ x y) (/ x y)) (* 1.0 1.0))) (- (/ x y) 1.0))
17.0ms	(/ (/ (* x (- (* (/ x y) (/ x y)) (* 1.0 1.0))) (- (/ x y) 1.0)) (+ x 1.0))

series255.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (/ x y) (/ x y))
64.0ms	(* x (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
83.0ms	(/ (* x (- (* (/ x y) (/ x y)) (* 1.0 1.0))) (- (/ x y) 1.0))
83.0ms	(/ (/ (* x (- (* (/ x y) (/ x y)) (* 1.0 1.0))) (- (/ x y) 1.0)) (+ x 1.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	963	2541
1	5001	2259

prune468.0ms

Filtered

228 candidates to 155 candidates (68.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	228	6	234

Merged error: 0b

Counts

234 → 6

regimes68.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.3b

bsearch82.0ms

Steps

Iters	Range		Point
10	1774840.6331059302	13141120828988944.0	125769773969809.8
9	-44727168880022856.0	-17812255955.75335	-28471394463391.582

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	33	14
2	33	14

end0.0ms

sample399.0ms

Algorithm

intervals

Results

248.0ms

9217×

body

valid