Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	67×	body	640	valid
4.0ms	125×	body	80	valid
3.0ms	19×	body	1280	valid
3.0ms	31×	body	320	valid
1.0ms	14×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 9.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

688×	`*-un-lft-identity`
676×	`times-frac`
495×	`add-sqr-sqrt`
471×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
91×	`distribute-lft-out`
63×	`div-inv`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
18×	`fma-neg`
13×	`distribute-lft-out--`
10×	`fma-def`
9×	`add-log-exp`
8×	`difference-of-squares`
3×	`frac-add`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`+-commutative` `associate-+l-`

Counts

2 → 544

Calls

2 calls:

78.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
342.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series394.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
352.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify144.0ms

Algorithm

egg-herbie

Counts

550 → 550

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	1001	10566
1	2918	7914
2	5001	6472

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
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)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
32.2b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite95.0ms

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:

8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
35.0ms	(/ (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)))
47.0ms	(* (* (+ 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))

series585.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
282.0ms	(/ (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)))
97.0ms	(* (* (+ x 1.0) x) (- x 1.0))
170.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify92.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (17.0ms)

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

prune280.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite110.0ms

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:

20.0ms	(* (+ x 1.0) x)
37.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
49.0ms	(* (* (+ x 1.0) x) (- x 1.0))

series223.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* (+ x 1.0) x)
86.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
92.0ms	(* (* (+ x 1.0) x) (- x 1.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	565	948
1	2961	739
2	5002	737

prune203.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (pow x 3) (* 1.0 x))
0.1b	(/ 2.0 (- (pow x 3) (* 1.0 x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac` `fma-neg` `prod-diff`
7×	`unpow3`
6×	`unpow-prod-down` `cube-prod`
5×	`distribute-rgt-out--`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `cube-mult` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `sqr-pow`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 74

Calls

2 calls:

21.0ms	(- (pow x 3) (* 1.0 x))
24.0ms	(/ 2.0 (- (pow x 3) (* 1.0 x)))

series144.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (pow x 3) (* 1.0 x))
67.0ms	(/ 2.0 (- (pow x 3) (* 1.0 x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	294	484
1	1279	440
2	5001	434

prune155.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample681.0ms

Algorithm

intervals

Results

221.0ms	1845×	body	640	valid
128.0ms	4078×	body	80	valid
90.0ms	608×	body	1280	valid
83.0ms	973×	body	320	valid
29.0ms	497×	body	160	valid