Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	72×	body	640	valid
3.0ms	120×	body	80	valid
3.0ms	38×	body	320	valid
1.0ms	11×	body	1280	valid
1.0ms	15×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
17.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
34.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
30.0ms	(/ 1.0 (+ x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
224.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5002	816

prune252.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
0.1b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 5))
0.3b	(/ 1 (pow x 3))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
73×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
31×	`add-exp-log`
26×	`associate-/r*`
18×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
7×	`div-inv` `distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `cube-mult` `unpow3`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+`

Counts

4 → 198

Calls

4 calls:

43.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
5.0ms	(/ 1 (pow x 7))
5.0ms	(/ 1 (pow x 5))
6.0ms	(/ 1 (pow x 3))

series228.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
59.0ms	(/ 1 (pow x 7))
46.0ms	(/ 1 (pow x 5))
32.0ms	(/ 1 (pow x 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	469	961
1	2563	767
2	5001	767

prune310.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (pow x (- 3))))
0.0b	(+ (/ 1 (pow x 5)) (pow x (- 3)))
0.1b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 5))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
42×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down`
22×	`add-exp-log`
14×	`associate-/r*`
12×	`div-exp` `distribute-lft-out`
11×	`add-log-exp`
8×	`frac-add` `add-cbrt-cube` `div-inv` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
4×	`pow1` `sum-log`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `+-commutative` `neg-sub0` `pow-neg` `pow-flip` `frac-2neg` `clear-num` `inv-pow` `pow-sub`
1×	`associate-+r+`

Counts

4 → 144

Calls

4 calls:

25.0ms	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (pow x (- 3))))
14.0ms	(+ (/ 1 (pow x 5)) (pow x (- 3)))
5.0ms	(/ 1 (pow x 7))
8.0ms	(/ 1 (pow x 5))

series275.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (pow x (- 3))))
109.0ms	(+ (/ 1 (pow x 5)) (pow x (- 3)))
57.0ms	(/ 1 (pow x 7))
46.0ms	(/ 1 (pow x 5))

simplify59.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	479	976
1	2361	858
2	5002	857

prune263.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
19.7b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

90×	`associate-*l/`
36×	`flip3--` `flip--`
32×	`frac-add`
28×	`frac-times`
24×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/l/`
15×	`add-sqr-sqrt`
14×	`associate-*r/`
13×	`*-un-lft-identity`
11×	`pow1`
10×	`associate-r`
9×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`prod-exp` `cbrt-unprod`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
4×	`associate-+l+` `associate-l` `pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

8.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
23.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
10.0ms	(* (* (+ x 1.0) x) (- x 1.0))
11.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series232.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
95.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
97.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1037	2507
1	5001	2360

prune677.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch83.0ms

Steps

Iters	Range		Point
6	24048332.968690775	157562194.2867214	43997267.71868038
8	-6278109458.210218	-4010492.3299602284	-24271205.09098764

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	24
1	49	24

end0.0ms

sample595.0ms

Algorithm

intervals

Results

204.0ms	1880×	body	640	valid
118.0ms	4114×	body	80	valid
82.0ms	607×	body	1280	valid
76.0ms	952×	body	320	valid
24.0ms	447×	body	160	valid