Details

sample28.0ms

Algorithm

intervals

Results

11.0ms	68×	body	640	valid
4.0ms	125×	body	80	valid
3.0ms	19×	body	1280	valid
3.0ms	29×	body	320	valid
1.0ms	15×	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: 12.1b

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))
2.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

75.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
10.0ms	(/ 1.0 (+ x 1.0))
12.0ms	(/ 1.0 (- x 1.0))
332.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
22.0ms	(/ 1.0 (+ x 1.0))
24.0ms	(/ 1.0 (- x 1.0))
193.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify160.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.2b	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.6b	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
12.4b	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

1572×	`*-un-lft-identity`
1497×	`times-frac`
1096×	`add-sqr-sqrt`
985×	`add-cube-cbrt`
937×	`prod-diff`
472×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
172×	`distribute-lft-out`
150×	`frac-sub`
129×	`div-inv`
117×	`associate-/r/`
101×	`distribute-lft-out--`
94×	`frac-times`
64×	`flip3--` `flip--`
52×	`flip3-+` `associate-r/` `associate-l/` `flip-+`
51×	`difference-of-squares`
47×	`associate-/l/`
41×	`swap-sqr`
31×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`pow1`
11×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `sub-neg` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`frac-2neg` `fma-neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 1298

Calls

4 calls:

55.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
372.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
227.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
796.0ms	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

series937.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
56.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
211.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
629.0ms	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

simplify344.0ms

Algorithm

egg-herbie

Counts

1310 → 1310

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2992	36267
1	5001	33666

prune11.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- (* 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	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
32.4b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

36.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
50.0ms	(* (* (+ x 1.0) x) (- x 1.0))
0.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series557.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
39.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
87.0ms	(* (* (+ x 1.0) x) (- x 1.0))
163.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	637	1498
1	3082	1198
2	5001	1198

prune684.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 108

Calls

3 calls:

19.0ms	(* (+ x 1.0) x)
45.0ms	(* (* (+ x 1.0) x) (- x 1.0))
34.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (+ x 1.0) x)
84.0ms	(* (* (+ x 1.0) x) (- x 1.0))
76.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	565	948
1	2962	739
2	5001	737

prune221.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes15.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample621.0ms

Algorithm

intervals

Results

208.0ms	1833×	body	640	valid
129.0ms	4162×	body	80	valid
88.0ms	594×	body	1280	valid
80.0ms	958×	body	320	valid
26.0ms	457×	body	160	valid