Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	65×	body	640	valid
4.0ms	132×	body	80	valid
3.0ms	32×	body	320	valid
2.0ms	12×	body	1280	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: 9.0b

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))
2.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite354.0ms

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))
53.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
237.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (- x 1.0))
29.0ms	(/ 1.0 (+ x 1.0))
40.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
211.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify155.0ms

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: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1.0 (+ x 1.0)))
0.0b	(sqrt (/ 1.0 (+ x 1.0)))
0.1b	(fma (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))) (- (* (/ 1 x) 2.0)))
8.9b	(+ (fma (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

36×	`sqrt-prod`
35×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`add-cube-cbrt`
7×	`distribute-lft-out`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `flip-+` `fma-udef`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`
1×	`+-commutative` `associate-+l+` `associate-+r+` `sum-log`

Counts

4 → 93

Calls

4 calls:

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

series618.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt (/ 1.0 (+ x 1.0)))
89.0ms	(sqrt (/ 1.0 (+ x 1.0)))
185.0ms	(fma (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))) (- (* (/ 1 x) 2.0)))
247.0ms	(+ (fma (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

simplify43.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	380	1083
1	1248	962
2	5001	862

prune338.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

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))
31.2b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite49.0ms

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:

3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
20.0ms	(/ (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)))
21.0ms	(* (* (+ 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))

series604.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
292.0ms	(/ (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)))
93.0ms	(* (* (+ x 1.0) x) (- x 1.0))
177.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (16.0ms)

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

prune266.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

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)
16.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
22.0ms	(* (* (+ x 1.0) x) (- x 1.0))

series225.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (+ x 1.0) x)
87.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
98.0ms	(* (* (+ x 1.0) x) (- x 1.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (63.0ms)

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

prune181.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes17.0ms

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

sample584.0ms

Algorithm

intervals

Results

203.0ms	1914×	body	640	valid
120.0ms	4128×	body	80	valid
76.0ms	942×	body	320	valid
72.0ms	550×	body	1280	valid
25.0ms	469×	body	160	valid