Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	64×	body	640	valid
6.0ms	259×	body	80	nan
3.0ms	130×	body	80	valid
3.0ms	25×	body	1280	valid
2.0ms	23×	body	320	valid
1.0ms	14×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 20.3b

Counts

2 → 1

localize7.0ms

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 913

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
56.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
76.0ms	(/ 1.0 (sqrt (+ x 1.0)))
41.0ms	(/ 1.0 (sqrt x))
140.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify255.0ms

Algorithm

egg-herbie

Counts

925 → 925

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2596	27798
1	5001	23121

prune1.5s

Filtered

925 candidates to 468 candidates (50.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	911	14	925
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	912	14	926

Merged error: 19.6b

Counts

926 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (- (- (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))))
0.3b	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0)))
3.4b	(- (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))

rewrite6.3s

Algorithm

rewrite-expression-head

Rules

99796×	`add-sqr-sqrt`
43150×	`times-frac`
40202×	`unswap-sqr`
24889×	`cbrt-prod`
23726×	`sqrt-prod`
16758×	`difference-of-squares`
16069×	`associate-r`
15710×	`*-un-lft-identity`
10989×	`add-cube-cbrt`
10406×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5614×	`associate-l`
4118×	`swap-sqr`
3304×	`prod-diff`
2454×	`*-commutative`
1845×	`distribute-lft-out`
735×	`distribute-lft-out--`
323×	`neg-mul-1`
308×	`div-inv`
264×	`associate-/l*`
84×	`associate-/r*`
59×	`fma-neg`
36×	`associate-*r/`
23×	`add-cbrt-cube`
20×	`associate-/r/`
18×	`add-exp-log`
8×	`cbrt-undiv`
7×	`pow1`
6×	`sqrt-div` `cbrt-unprod` `associate-/l/` `add-log-exp`
5×	`div-exp` `clear-num`
4×	`expm1-log1p-u` `prod-exp` `un-div-inv` `log1p-expm1-u`
3×	`frac-2neg` `flip3-+` `flip-+`
2×	`flip3--` `flip--` `distribute-neg-frac`
1×	`distribute-lft-neg-out` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `distribute-frac-neg` `pow-prod-down` `hypot-def`

Counts

4 → 21838

Calls

4 calls:

28.0ms	(sqrt (+ x 1.0))
831.0ms	(/ (- (- (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))))
26.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0)))
213.0ms	(- (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
670.0ms	(/ (- (- (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))))
160.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0)))
302.0ms	(- (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))

simplify8.0s

Algorithm

egg-herbie

Counts

21850 → 21850

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	8426	1006195

prune27.8s

Filtered

21850 candidates to 5642 candidates (25.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	21836	14	21850
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	21844	20	21864

Merged error: 19.5b

Counts

21864 → 20

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.5s

Algorithm

rewrite-expression-head

Rules

988737×	`add-sqr-sqrt`
591609×	`unswap-sqr`
282344×	`cbrt-prod`
240688×	`sqrt-prod`
222532×	`associate-r`
197166×	`times-frac`
150969×	`swap-sqr`
145824×	`prod-diff`
145012×	`*-un-lft-identity`
90880×	`add-cube-cbrt`
71029×	`associate-l`
34579×	`*-commutative`
21289×	`distribute-lft-out`
20825×	`difference-of-squares`
2361×	`div-inv`
794×	`associate-*r/`
400×	`frac-times`
344×	`associate-/l*`
258×	`associate-/r*`
248×	`fma-neg`
207×	`add-cbrt-cube`
187×	`cbrt-unprod`
159×	`pow1`
86×	`sqrt-div` `clear-num` `un-div-inv` `associate-/l/`
84×	`pow-prod-down`
81×	`add-exp-log`
50×	`prod-exp`
43×	`frac-2neg` `flip3-+` `flip-+`
27×	`distribute-lft-out--`
20×	`associate-*l/`
18×	`cbrt-undiv`
13×	`pow-sqr` `pow-prod-up`
7×	`div-exp`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-log-exp`
5×	`pow-plus`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow2`
1×	`distribute-lft-neg-out` `neg-mul-1` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 168444

Calls

4 calls:

27.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0)))
93.0ms	(* (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))))
86.0ms	(* (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))
7.3s	(- (* (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0)))) (* (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0)))))

series704.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0)))
142.0ms	(* (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))))
92.0ms	(* (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))
315.0ms	(- (* (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0)))) (* (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0)))))

simplify2.3m

Algorithm

egg-herbie

Counts

168456 → 168456

Iterations

Useful iterations: 0 (2.4s)

Iter	Nodes	Cost
0	26995	17037370

prune3.1m

Filtered

168456 candidates to 24006 candidates (14.3%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	168433	23	168456
Fresh	9	10	19
Picked	1	0	1
Done	0	0	0
Total	168443	33	168476

Merged error: 19.0b

Counts

168476 → 33

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0)))))
0.1b	(/ (- (- (+ (* 1.0 (/ x (pow (cbrt 1.0) 2))) (* 1.0 (/ 1 (pow (cbrt 1.0) 2)))) (* x (pow (cbrt 1.0) 4)))) (* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))))
0.3b	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0)))
2.7b	(- (+ (* 1.0 (/ x (pow (cbrt 1.0) 2))) (* 1.0 (/ 1 (pow (cbrt 1.0) 2)))) (* x (pow (cbrt 1.0) 4)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

9093×	`*-un-lft-identity`
6601×	`associate-l`
6361×	`times-frac`
6265×	`add-sqr-sqrt`
3465×	`associate-r`
2415×	`distribute-lft-out`
2208×	`add-cube-cbrt`
1914×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
1850×	`distribute-lft-out--`
1560×	`cbrt-prod`
1537×	`unswap-sqr`
1488×	`sqrt-prod`
932×	`unpow-prod-down`
925×	`difference-of-squares`
660×	`prod-diff`
291×	`sqr-pow`
228×	`div-inv`
203×	`*-commutative`
161×	`distribute-rgt-out`
135×	`neg-mul-1`
133×	`associate-/r*`
130×	`associate-*r/`
96×	`associate-/l*`
80×	`frac-times`
62×	`associate-/r/`
49×	`flip3-+` `flip-+`
46×	`unpow2`
41×	`add-cbrt-cube`
40×	`associate-*l/`
32×	`add-exp-log`
30×	`fma-neg`
17×	`cbrt-unprod`
16×	`associate-/l/`
15×	`clear-num`
14×	`sqrt-div` `un-div-inv`
12×	`prod-exp`
11×	`pow1` `cbrt-undiv`
9×	`add-log-exp`
8×	`frac-2neg`
7×	`div-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`+-commutative` `distribute-lft-neg-out`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `diff-log` `associate--l+` `flip--` `distribute-neg-frac`
1×	`neg-sub0` `sub-neg` `div-sub` `distribute-frac-neg` `sum-log`

Counts

4 → 4856

Calls

4 calls:

176.0ms	(* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0)))))
493.0ms	(/ (- (- (+ (* 1.0 (/ x (pow (cbrt 1.0) 2))) (* 1.0 (/ 1 (pow (cbrt 1.0) 2)))) (* x (pow (cbrt 1.0) 4)))) (* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))))
24.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0)))
198.0ms	(- (+ (* 1.0 (/ x (pow (cbrt 1.0) 2))) (* 1.0 (/ 1 (pow (cbrt 1.0) 2)))) (* x (pow (cbrt 1.0) 4)))

series3.6s

Counts

4 → 12

Calls

4 calls:

965.0ms	(* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0)))))
2.2s	(/ (- (- (+ (* 1.0 (/ x (pow (cbrt 1.0) 2))) (* 1.0 (/ 1 (pow (cbrt 1.0) 2)))) (* x (pow (cbrt 1.0) 4)))) (* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))))
150.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0)))
355.0ms	(- (+ (* 1.0 (/ x (pow (cbrt 1.0) 2))) (* 1.0 (/ 1 (pow (cbrt 1.0) 2)))) (* x (pow (cbrt 1.0) 4)))

simplify1.8s

Algorithm

egg-herbie

Counts

4868 → 4868

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5001	223979

prune12.4s

Filtered

4868 candidates to 2008 candidates (41.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	4860	8	4868
Fresh	29	3	32
Picked	1	0	1
Done	0	0	0
Total	4890	11	4901

Merged error: 0.7b

Counts

4901 → 11

regimes86.0ms

Accuracy

0% (0.1b remaining)

Error of 0.9b against oracle of 0.7b and baseline of 0.9b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	34
1	62	34
2	70	34
3	74	34
4	83	34
5	86	34
6	86	34

end0.0ms

sample776.0ms

Algorithm

intervals

Results

167.0ms	7818×	body	80	nan
160.0ms	1823×	body	640	valid
132.0ms	1134×	body	1280	valid
100.0ms	4113×	body	80	valid
42.0ms	606×	body	320	valid
14.0ms	324×	body	160	valid

Details

sample31.0ms

simplify6.0ms

prune2.0ms

localize7.0ms

rewrite148.0ms

series288.0ms

simplify255.0ms

prune1.5s

localize18.0ms

rewrite6.3s

series1.2s

simplify8.0s

prune27.8s

localize20.0ms

rewrite57.5s

series704.0ms

simplify2.3m

prune3.1m

localize24.0ms

rewrite1.5s

series3.6s

simplify1.8s

prune12.4s

regimes86.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample776.0ms

end2.5m