Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	75×	body	1280	valid
4.0ms	141×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	4×	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: 14.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 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))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

0.0ms	(hypot 1.0 x)
10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
31.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(/ 1.0 (hypot 1.0 x))
85.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	204	408
1	643	378
2	1992	376
3	5001	375

prune146.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.3b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

9.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
39.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify143.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	288	547
1	1035	512
2	4960	506
3	5001	506

prune249.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.7b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*r/`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`times-frac`
8×	`associate-*l/` `frac-sub`
6×	`pow1` `flip3--` `flip3-+` `flip--` `flip-+` `associate-/l/` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/r` `associate-/l`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r/` `div-inv` `associate--r+`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

117.0ms	(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
4.0ms	(/ 1.0 (hypot 1.0 x))
36.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
57.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
7.0ms	(/ 1.0 (hypot 1.0 x))
21.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
40.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	642	1587
1	3997	1325
2	5002	1325

prune460.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.3b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (log (exp (/ 1.0 (hypot 1.0 x))))))
3.6b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
14×	`log-pow`
13×	`exp-prod`
9×	`log-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l` `associate--r+` `add-log-exp`
5×	`pow1` `distribute-rgt-in` `distribute-lft-in`
4×	`associate--l+`
3×	`sub-neg` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 101

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
21.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (log (exp (/ 1.0 (hypot 1.0 x))))))
7.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (log (exp (/ 1.0 (hypot 1.0 x))))))
8.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

simplify88.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	252	652
1	700	594
2	2806	581
3	5001	581

prune328.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.7b

regimes147.0ms

Accuracy

0% (0.0b remaining)

Error of 14.5b against oracle of 14.4b and baseline of 14.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	22
1	23	22

end0.0ms

sample834.0ms

Algorithm

intervals

Results

467.0ms	2927×	body	1280	valid
119.0ms	4043×	body	80	valid
75.0ms	601×	body	640	valid
23.0ms	278×	body	320	valid
8.0ms	151×	body	160	valid