Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	55×	body	640	valid
4.0ms	139×	body	80	valid
3.0ms	23×	body	1280	valid
2.0ms	27×	body	320	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: 10.8b

localize11.0ms

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))
2.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite334.0ms

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:

11.0ms	(/ 1.0 (- x 1.0))
10.0ms	(/ 1.0 (+ x 1.0))
55.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
254.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1.0 (+ x 1.0))
46.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
211.0ms	(+ (- (/ 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 (37.0ms)

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

prune243.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1 (/ (+ x 1.0) 1.0))
0.0b	(- (/ 1 (/ (+ x 1.0) 1.0)) (/ 2.0 x))
2.9b	(+ (- (/ 1 (/ (+ x 1.0) 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite561.0ms

Algorithm

rewrite-expression-head

Rules

136×	`times-frac`
126×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
21×	`associate-/r*`
17×	`add-exp-log` `distribute-lft-out`
14×	`difference-of-squares`
12×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-log-exp`
8×	`div-exp` `div-inv`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
3×	`flip3--` `frac-add` `associate-/r/` `flip--`
2×	`sub-neg` `rec-exp` `associate-+l+` `frac-2neg` `diff-log` `1-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-` `pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 174

Calls

4 calls:

10.0ms	(/ 1.0 (- x 1.0))
16.0ms	(/ 1 (/ (+ x 1.0) 1.0))
90.0ms	(- (/ 1 (/ (+ x 1.0) 1.0)) (/ 2.0 x))
438.0ms	(+ (- (/ 1 (/ (+ x 1.0) 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1 (/ (+ x 1.0) 1.0))
41.0ms	(- (/ 1 (/ (+ x 1.0) 1.0)) (/ 2.0 x))
215.0ms	(+ (- (/ 1 (/ (+ x 1.0) 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	744	1509
1	3280	1300
2	5002	1292

prune273.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) 1.0) x) 1.0)) (* (* (/ (+ x 1.0) 1.0) x) (- x 1.0)))
0.0b	(- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0))
0.1b	(* (* (/ (+ x 1.0) 1.0) x) (- x 1.0))
13.8b	(+ (* (- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) 1.0) x) 1.0))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*l/`
27×	`add-exp-log` `add-cbrt-cube`
17×	`flip3--` `flip--`
16×	`frac-add`
12×	`frac-times`
10×	`prod-exp` `cbrt-unprod` `associate-/l/`
9×	`pow1` `add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-*r/` `add-log-exp`
7×	`add-cube-cbrt`
6×	`cbrt-undiv` `div-exp`
5×	`sub-neg` `associate-r` `associate-/r/`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
3×	`times-frac` `pow-prod-down` `associate-/l*`
2×	`flip3-+` `flip-+`
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 → 106

Calls

4 calls:

98.0ms	(/ (+ (* (- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) 1.0) x) 1.0)) (* (* (/ (+ x 1.0) 1.0) x) (- x 1.0)))
7.0ms	(- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0))
50.0ms	(* (* (/ (+ x 1.0) 1.0) x) (- x 1.0))
29.0ms	(+ (* (- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) 1.0) x) 1.0))

series256.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (* (- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) 1.0) x) 1.0)) (* (* (/ (+ x 1.0) 1.0) x) (- x 1.0)))
43.0ms	(- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0))
121.0ms	(* (* (/ (+ x 1.0) 1.0) x) (- x 1.0))
2.0ms	(+ (* (- (* 1 x) (* (/ (+ x 1.0) 1.0) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) 1.0) x) 1.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	780	1950
1	4343	1662
2	5002	1662

prune284.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (+ x 1.0) 1.0) x)
0.1b	(* (* (/ (+ x 1.0) 1.0) x) (- x 1.0))
0.1b	(/ 2.0 (* (* (/ (+ x 1.0) 1.0) x) (- x 1.0)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 96

Calls

3 calls:

27.0ms	(* (/ (+ x 1.0) 1.0) x)
51.0ms	(* (* (/ (+ x 1.0) 1.0) x) (- x 1.0))
47.0ms	(/ 2.0 (* (* (/ (+ x 1.0) 1.0) x) (- x 1.0)))

series279.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* (/ (+ x 1.0) 1.0) x)
129.0ms	(* (* (/ (+ x 1.0) 1.0) x) (- x 1.0))
88.0ms	(/ 2.0 (* (* (/ (+ x 1.0) 1.0) x) (- x 1.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	495	731
1	2511	606
2	5001	606

prune158.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes15.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	6
1	11	6

end0.0ms

sample603.0ms

Algorithm

intervals

Results

202.0ms	1912×	body	640	valid
112.0ms	4144×	body	80	valid
71.0ms	962×	body	320	valid
67.0ms	538×	body	1280	valid
25.0ms	445×	body	160	valid