Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	52×	body	640	valid
4.0ms	145×	body	80	valid
2.0ms	30×	body	320	valid
2.0ms	15×	body	1280	valid
1.0ms	14×	body	160	valid

simplify17.0ms

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: 7.4b

localize8.0ms

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))
2.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite64.0ms

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)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
29.0ms	(/ 1.0 (+ x 1.0))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
219.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

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

prune286.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
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))
17.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

88×	`associate-*l/`
32×	`frac-add`
31×	`flip3--` `flip--`
24×	`frac-times` `flip3-+` `flip-+`
18×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
12×	`associate-*r/`
9×	`pow1` `add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
7×	`add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
5×	`sub-neg` `associate-r`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
3×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
1×	`+-commutative` `frac-2neg` `diff-log` `associate-l` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 124

Calls

4 calls:

3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
26.0ms	(/ (+ (* (- (* 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))

series230.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
90.0ms	(/ (+ (* (- (* 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))

simplify46.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129

prune414.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
0.0b	(/ 1 (pow x 7))
0.1b	(/ 1 (pow x 5))
0.4b	(/ 1 (pow x 3))

rewrite67.0ms

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:

45.0ms	(+ (/ 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))

series225.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
57.0ms	(/ 1 (pow x 7))
46.0ms	(/ 1 (pow x 5))
31.0ms	(/ 1 (pow x 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (13.0ms)

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

prune285.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (pow x (- 3)))))
0.0b	(+ (/ 1 (pow x 5)) (pow x (- 3)))
0.0b	(/ 1 (pow x 7))
0.1b	(/ 1 (pow x 5))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
24×	`add-exp-log` `unpow-prod-down`
14×	`associate-/r*`
12×	`div-exp` `distribute-lft-out`
10×	`add-cbrt-cube`
9×	`associate-r`
8×	`frac-add` `div-inv` `sqr-pow`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `associate-r/` `pow-exp` `associate-/l` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+`
2×	`cbrt-undiv` `neg-sub0` `pow-neg` `pow-flip` `frac-2neg` `clear-num` `inv-pow` `pow-sub`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

32.0ms	(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (pow x (- 3)))))
15.0ms	(+ (/ 1 (pow x 5)) (pow x (- 3)))
5.0ms	(/ 1 (pow x 7))
5.0ms	(/ 1 (pow x 5))

series282.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (pow x (- 3)))))
111.0ms	(+ (/ 1 (pow x 5)) (pow x (- 3)))
52.0ms	(/ 1 (pow x 7))
47.0ms	(/ 1 (pow x 5))

simplify68.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	556	991
1	2903	850
2	5001	850

prune279.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample611.0ms

Algorithm

intervals

Results

201.0ms	1860×	body	640	valid
120.0ms	4139×	body	80	valid
81.0ms	974×	body	320	valid
79.0ms	565×	body	1280	valid
31.0ms	466×	body	160	valid