Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	55×	body	640	valid
3.0ms	130×	body	80	valid
3.0ms	34×	body	320	valid
2.0ms	18×	body	1280	valid
1.0ms	19×	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: 9.1b

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))
3.3b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite344.0ms

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:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
51.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
228.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1.0 (+ x 1.0))
44.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
212.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify153.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (75.0ms)

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

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ (sqrt 1.0) (+ x 1.0))
0.0b	(fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0)))
3.3b	(+ (fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
39×	`times-frac`
32×	`add-cube-cbrt`
15×	`sqrt-prod`
9×	`associate-/r` `associate-/l`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-def` `fma-udef`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l+` `associate-+r+` `flip3--` `sum-log` `flip--`

Counts

4 → 118

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
6.0ms	(/ (sqrt 1.0) (+ x 1.0))
0.0ms	(fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0)))
3.0ms	(+ (fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (- x 1.0))
52.0ms	(/ (sqrt 1.0) (+ x 1.0))
110.0ms	(fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0)))
171.0ms	(+ (fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	512	1149
1	2144	1050
2	5003	999

prune428.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
30.9b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

10.0ms	(* (+ x 1.0) x)
3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
24.0ms	(* (* (+ 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))

series372.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ x 1.0) x)
44.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
99.0ms	(* (* (+ x 1.0) x) (- x 1.0))
186.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	510	907
1	2772	711
2	5001	711

prune236.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite53.0ms

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:

10.0ms	(* (+ x 1.0) x)
22.0ms	(* (* (+ x 1.0) x) (- x 1.0))
17.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series238.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (+ x 1.0) x)
103.0ms	(* (* (+ x 1.0) x) (- x 1.0))
92.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (64.0ms)

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

prune189.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

regimes10.0ms

Accuracy

0% (0.0b 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	10	5
1	10	5

end0.0ms

sample588.0ms

Algorithm

intervals

Results

204.0ms	1926×	body	640	valid
112.0ms	4057×	body	80	valid
80.0ms	604×	body	1280	valid
72.0ms	944×	body	320	valid
31.0ms	471×	body	160	valid