Details

sample31.0ms

Algorithm

intervals

Results

5.0ms	46×	body	1280	valid
5.0ms	264×	body	80	nan
5.0ms	56×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	10×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 19.2b

localize10.0ms

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

rewrite199.0ms

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))
88.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1.0))
68.0ms	(/ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ 1.0 (sqrt x))
130.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify233.0ms

Algorithm

egg-herbie

Counts

770 → 770

Iterations

Useful iterations: 2 (83.0ms)

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

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 18.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.2b	(/ 1.0 (sqrt x))
0.3b	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
2.5b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

5936×	`sqrt-prod`
3335×	`times-frac`
2978×	`*-un-lft-identity`
2551×	`add-sqr-sqrt`
2453×	`add-cube-cbrt`
2250×	`prod-diff`
752×	`distribute-rgt-in` `distribute-lft-in`
246×	`distribute-lft-out`
174×	`div-inv`
168×	`sqrt-div`
150×	`associate-/r/`
79×	`flip3-+` `flip-+`
32×	`difference-of-squares`
31×	`associate-r`
25×	`fma-neg`
24×	`distribute-lft-out--`
15×	`associate-l`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`frac-times`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`flip3--` `frac-sub` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 2479

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt x))
6.0ms	(/ 1.0 (sqrt x))
687.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
117.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

series948.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (sqrt x))
41.0ms	(/ 1.0 (sqrt x))
587.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
283.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

simplify904.0ms

Algorithm

egg-herbie

Counts

2491 → 2491

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5002	136037

prune8.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3)
0.6b	(* (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))))
0.7b	(pow (sqrt (/ 1.0 (sqrt x))) 3)
2.5b	(- (pow (sqrt (/ 1.0 (sqrt x))) 3) (pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

9134×	`sqrt-prod`
5094×	`times-frac`
4613×	`*-un-lft-identity`
4151×	`add-sqr-sqrt`
3827×	`add-cube-cbrt`
3696×	`prod-diff`
3538×	`unpow-prod-down` `cube-prod`
354×	`distribute-lft-out`
262×	`div-inv`
236×	`sqrt-div`
228×	`associate-/r/`
145×	`sqr-pow`
125×	`cube-mult` `unpow3`
114×	`flip3-+` `flip-+`
100×	`difference-of-squares`
56×	`fma-neg`
49×	`distribute-lft-out--`
33×	`swap-sqr`
25×	`associate-r` `associate-l`
23×	`pow1`
16×	`unswap-sqr`
10×	`sqrt-pow1` `pow1/2`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow-unpow` `pow-pow` `add-log-exp`
5×	`pow-prod-up`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `pow-sqr`
2×	`pow-to-exp` `pow-exp` `sqrt-pow2` `rem-cube-cbrt`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `frac-sub` `flip--` `cbrt-unprod`

Counts

4 → 4202

Calls

4 calls:

18.0ms	(pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3)
45.0ms	(* (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))))
10.0ms	(pow (sqrt (/ 1.0 (sqrt x))) 3)
377.0ms	(- (pow (sqrt (/ 1.0 (sqrt x))) 3) (pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3))

series982.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3)
92.0ms	(* (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))))
269.0ms	(pow (sqrt (/ 1.0 (sqrt x))) 3)
367.0ms	(- (pow (sqrt (/ 1.0 (sqrt x))) 3) (pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3))

simplify1.4s

Algorithm

egg-herbie

Counts

4214 → 4214

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	3248	198312
1	5001	179660

prune3.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
2.5b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))
2.5b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))
2.5b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

10320×	`sqrt-prod`
5737×	`times-frac`
5036×	`*-un-lft-identity`
4701×	`add-sqr-sqrt`
4075×	`add-cube-cbrt`
3750×	`prod-diff`
752×	`distribute-rgt-in` `distribute-lft-in`
402×	`distribute-lft-out`
292×	`div-inv`
272×	`sqrt-div`
250×	`associate-/r/`
208×	`difference-of-squares`
125×	`flip3-+` `flip-+`
98×	`distribute-lft-out--`
87×	`swap-sqr`
75×	`fma-neg`
31×	`associate-r` `associate-l`
11×	`pow1` `flip3--` `frac-sub` `flip--`
10×	`add-log-exp`
9×	`frac-times`
6×	`add-exp-log` `add-cbrt-cube`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log` `associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 4140

Calls

4 calls:

670.0ms	(* (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
107.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))
107.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))
107.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

362.0ms	(* (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
267.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))
267.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))
500.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.3s

Algorithm

egg-herbie

Counts

4152 → 4152

Iterations

Useful iterations: 1 (60.0ms)

Iter	Nodes	Cost
0	3277	211435
1	5001	196004

prune7.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.6b

regimes123.0ms

Accuracy

97% (0.3b remaining)

Error of 10.8b against oracle of 10.5b and baseline of 20.0b

bsearch44.0ms

Steps

Iters	Range		Point
6	6031.575547282502	27711.216442224475	8090.6273311491805

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	85
1	75	85

end0.0ms

sample825.0ms

Algorithm

intervals

Results

161.0ms	7948×	body	80	nan
154.0ms	1795×	body	640	valid
132.0ms	1189×	body	1280	valid
98.0ms	4083×	body	80	valid
39.0ms	598×	body	320	valid
15.0ms	335×	body	160	valid