Details

sample31.0ms

Algorithm

intervals

Results

15.0ms	94×	body	1280	valid
3.0ms	126×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
76.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
86.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	201	433
1	602	413
2	2000	411
3	5001	411

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.4b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-*r/`
6×	`add-log-exp`
4×	`pow1` `flip3--` `associate--l+` `frac-sub` `flip--` `associate-/l/` `distribute-lft-out`
3×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
1×	`flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 110

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
162.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify51.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	407	1275
1	1594	1181
2	5001	1177

prune328.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.4b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

1332×	`associate-*r/`
555×	`times-frac`
524×	`frac-add`
421×	`*-un-lft-identity`
372×	`associate-/r/`
354×	`flip3--` `flip--`
344×	`frac-times`
241×	`add-sqr-sqrt`
177×	`add-cube-cbrt`
131×	`associate-*l/`
106×	`distribute-lft-out`
105×	`associate-/l*`
88×	`flip3-+` `flip-+`
65×	`sqr-pow`
64×	`difference-of-squares`
24×	`add-exp-log` `add-cbrt-cube`
16×	`difference-cubes` `distribute-lft-out--`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`div-inv` `add-log-exp`
5×	`cbrt-undiv` `cube-div` `div-exp`
4×	`pow-prod-down` `associate-/r*`
3×	`pow-unpow` `associate-r` `pow-exp` `rem-cube-cbrt`
2×	`pow-pow` `div-sub` `frac-sub`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `cube-prod` `associate-l` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 623

Calls

4 calls:

49.0ms	(/ (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
5.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
9.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series504.0ms

Counts

4 → 12

Calls

4 calls:

336.0ms	(/ (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
58.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
33.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
77.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify369.0ms

Algorithm

egg-herbie

Counts

635 → 635

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	4089	35346
1	5003	35207

prune3.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.4b	(- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)))
9.9b	(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
9.9b	(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-prod`
21×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`sqr-pow`
9×	`difference-of-squares`
7×	`add-cube-cbrt`
6×	`cube-div` `sqrt-div` `associate-*r/` `add-log-exp`
4×	`pow1` `add-exp-log` `cbrt-prod` `rem-sqrt-square` `add-cbrt-cube`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `flip3--` `sqrt-pow1` `pow1/2` `unpow3` `cube-prod` `frac-sub` `flip--` `distribute-lft-out--`
1×	`sub-neg` `flip3-+` `pow1/3` `diff-log` `flip-+` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
12.0ms	(- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)))
2.0ms	(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
2.0ms	(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series550.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
147.0ms	(- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)))
84.0ms	(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
85.0ms	(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	313	977
1	919	940
2	5001	938

prune460.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.2b

regimes135.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.6b and baseline of 14.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	64
1	41	64

end0.0ms

sample804.0ms

Algorithm

intervals

Results

471.0ms	2965×	body	1280	valid
118.0ms	3992×	body	80	valid
78.0ms	606×	body	640	valid
26.0ms	299×	body	320	valid
8.0ms	138×	body	160	valid