Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	56×	body	640	valid
4.0ms	138×	body	80	valid
3.0ms	32×	body	320	valid
2.0ms	17×	body	1280	valid
1.0ms	13×	body	160	valid

simplify18.0ms

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)) (/ 2.0 x))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
1.6b	(+ (- (/ 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:

16.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
34.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
24.0ms	(/ 1.0 (+ x 1.0))
27.0ms	(/ 1.0 (- x 1.0))
218.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5001	816

prune250.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 (/ 1 (+ x 1.0))) (/ 2.0 x))
0.0b	(/ 1 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
1.6b	(+ (- (* 1.0 (/ 1 (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

12.0ms	(- (* 1.0 (/ 1 (+ x 1.0))) (/ 2.0 x))
5.0ms	(/ 1 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
17.0ms	(+ (- (* 1.0 (/ 1 (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* 1.0 (/ 1 (+ x 1.0))) (/ 2.0 x))
22.0ms	(/ 1 (+ x 1.0))
33.0ms	(/ 1.0 (- x 1.0))
214.0ms	(+ (- (* 1.0 (/ 1 (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	512	830
1	2076	775
2	5001	748

prune209.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

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)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
17.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite55.0ms

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:

22.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
9.0ms	(* (* (+ x 1.0) x) (- x 1.0))
3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
11.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series219.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
93.0ms	(* (* (+ x 1.0) x) (- x 1.0))
36.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129

prune610.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
0.1b	(/ 1 (pow x 5))
0.2b	(/ 1 (pow x 7))
0.5b	(/ 1 (pow x 3))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

90×	`*-un-lft-identity`
87×	`times-frac`
68×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
36×	`unpow-prod-down`
33×	`add-exp-log`
26×	`associate-/r*`
24×	`distribute-lft-out`
18×	`div-exp`
16×	`associate-r` `div-inv`
12×	`cube-prod` `add-cbrt-cube` `sqr-pow`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
6×	`pow1`
5×	`associate-*r/`
4×	`cube-mult` `unpow3` `frac-add` `add-log-exp`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `associate-l` `clear-num` `inv-pow`
2×	`flip3-+` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 217

Calls

4 calls:

63.0ms	(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 7))
5.0ms	(/ 1 (pow x 3))

series185.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
43.0ms	(/ 1 (pow x 5))
55.0ms	(/ 1 (pow x 7))
31.0ms	(/ 1 (pow x 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	652	1171
1	3945	952
2	5003	952

prune308.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 9.5b

bsearch82.0ms

Steps

Iters	Range		Point
6	145.42571904303156	1078.5849367128544	472.4265139213075
9	-4696503048995838.0	-66949431.36780037	-133365124.473443

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	24
1	49	24

end0.0ms

sample569.0ms

Algorithm

intervals

Results

190.0ms	1834×	body	640	valid
116.0ms	4196×	body	80	valid
77.0ms	574×	body	1280	valid
76.0ms	916×	body	320	valid
25.0ms	480×	body	160	valid