Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	321×	body	80	nan
7.0ms	47×	body	1280	valid
6.0ms	50×	body	640	valid
4.0ms	124×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	10×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
2.7b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `hypot-def`

Counts

4 → 758

Calls

4 calls:

8.0ms	(sqrt (+ x 1.0))
12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
92.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (+ x 1.0))
71.0ms	(/ 1.0 (sqrt (+ x 1.0)))
35.0ms	(/ 1.0 (sqrt x))
130.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify258.0ms

Algorithm

egg-herbie

Counts

770 → 770

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1538	25021
1	4278	18390
2	5001	18355

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1 (/ (sqrt (+ x 1.0)) 1.0))
0.2b	(/ 1.0 (sqrt x))
2.7b	(- (/ 1.0 (sqrt x)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))

rewrite474.0ms

Algorithm

rewrite-expression-head

Rules

4717×	`times-frac`
3089×	`*-un-lft-identity`
2731×	`add-sqr-sqrt`
2651×	`add-cube-cbrt`
1760×	`prod-diff`
1598×	`sqrt-prod`
211×	`distribute-lft-out`
176×	`div-inv`
31×	`associate-/r*`
23×	`associate-/r/`
22×	`fma-neg`
21×	`difference-of-squares`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `pow-flip` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `frac-sub` `flip--` `flip-+` `hypot-def` `inv-pow`

Counts

4 → 2007

Calls

4 calls:

8.0ms	(sqrt (+ x 1.0))
21.0ms	(/ 1 (/ (sqrt (+ x 1.0)) 1.0))
6.0ms	(/ 1.0 (sqrt x))
174.0ms	(- (/ 1.0 (sqrt x)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (+ x 1.0))
73.0ms	(/ 1 (/ (sqrt (+ x 1.0)) 1.0))
42.0ms	(/ 1.0 (sqrt x))
128.0ms	(- (/ 1.0 (sqrt x)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))

simplify699.0ms

Algorithm

egg-herbie

Counts

2019 → 2019

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3902	92156
1	5001	74735

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))
0.3b	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))) (fma (/ 1 (sqrt (+ x 1.0))) 1.0 (/ 1.0 (sqrt x))))
0.5b	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.7b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0))))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

944×	`times-frac`
663×	`add-sqr-sqrt`
559×	`*-un-lft-identity`
389×	`add-cube-cbrt`
274×	`sqrt-prod`
186×	`add-exp-log`
146×	`swap-sqr`
103×	`div-exp`
102×	`associate-r` `associate-l`
58×	`unswap-sqr`
54×	`add-cbrt-cube` `distribute-lft-out`
53×	`prod-exp`
28×	`rec-exp` `1-exp`
26×	`pow1`
24×	`frac-sub`
23×	`cbrt-undiv` `div-inv`
16×	`frac-times` `associate-r/` `associate-l/`
14×	`associate-/l/`
13×	`cbrt-unprod`
8×	`pow-flip` `inv-pow`
7×	`un-div-inv`
6×	`pow-prod-up` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r/` `pow-sqr` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*`
2×	`pow2` `flip3--` `pow-plus` `*-commutative` `flip--`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num`

Counts

4 → 596

Calls

4 calls:

183.0ms	(* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))
58.0ms	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))) (fma (/ 1 (sqrt (+ x 1.0))) 1.0 (/ 1.0 (sqrt x))))
39.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
20.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))
346.0ms	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0)))) (fma (/ 1 (sqrt (+ x 1.0))) 1.0 (/ 1.0 (sqrt x))))
26.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
65.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1 (/ (sqrt (+ x 1.0)) 1.0)) (/ 1 (/ (sqrt (+ x 1.0)) 1.0))))

simplify140.0ms

Algorithm

egg-herbie

Counts

608 → 608

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	2664	9802
1	5002	8396

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt (+ x 1.0)) 1.0) (/ (sqrt (+ x 1.0)) 1.0))
0.3b	(* (fma (/ 1 (sqrt (+ x 1.0))) 1.0 (/ 1.0 (sqrt x))) x)
0.5b	(* (sqrt x) (sqrt x))
2.2b	(- (* (* 1.0 1.0) (* (/ (sqrt (+ x 1.0)) 1.0) (/ (sqrt (+ x 1.0)) 1.0))) (* (* (sqrt x) (sqrt x)) (* 1 1)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt`
120×	`*-un-lft-identity` `times-frac`
90×	`sqrt-prod`
78×	`add-cube-cbrt`
45×	`swap-sqr`
34×	`associate-r` `associate-l`
28×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
18×	`distribute-lft-out`
14×	`unswap-sqr`
8×	`sqrt-pow1` `pow1/2`
6×	`prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
5×	`pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `pow-sqr` `log1p-expm1-u` `div-inv`
3×	`*-commutative`
2×	`pow2` `pow-plus`
1×	`frac-times` `sub-neg` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `associate-r/` `prod-diff` `associate-l/` `rem-square-sqrt` `flip--`

Counts

4 → 209

Calls

4 calls:

62.0ms	(* (/ (sqrt (+ x 1.0)) 1.0) (/ (sqrt (+ x 1.0)) 1.0))
7.0ms	(* (fma (/ 1 (sqrt (+ x 1.0))) 1.0 (/ 1.0 (sqrt x))) x)
13.0ms	(* (sqrt x) (sqrt x))
90.0ms	(- (* (* 1.0 1.0) (* (/ (sqrt (+ x 1.0)) 1.0) (/ (sqrt (+ x 1.0)) 1.0))) (* (* (sqrt x) (sqrt x)) (* 1 1)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (/ (sqrt (+ x 1.0)) 1.0) (/ (sqrt (+ x 1.0)) 1.0))
211.0ms	(* (fma (/ 1 (sqrt (+ x 1.0))) 1.0 (/ 1.0 (sqrt x))) x)
14.0ms	(* (sqrt x) (sqrt x))
16.0ms	(- (* (* 1.0 1.0) (* (/ (sqrt (+ x 1.0)) 1.0) (/ (sqrt (+ x 1.0)) 1.0))) (* (* (sqrt x) (sqrt x)) (* 1 1)))

simplify150.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	825	2038
1	4370	1667
2	5001	1662

prune527.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

regimes33.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	16
1	19	16

end0.0ms

sample1.0s

Algorithm

intervals

Results

216.0ms	1883×	body	640	valid
188.0ms	8004×	body	80	nan
171.0ms	1198×	body	1280	valid
115.0ms	3968×	body	80	valid
52.0ms	624×	body	320	valid
23.0ms	327×	body	160	valid