Details

sample43.0ms

Algorithm

intervals

Results

21.0ms	93×	body	1280	valid
5.0ms	132×	body	80	valid
4.0ms	20×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	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: 15.1b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series90.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/ 1.0 (hypot 1.0 x))
80.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	157	308
1	484	286
2	1409	284
3	5001	284

prune98.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize15.0ms

Local error

Found 4 expressions with local error:

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)))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.8b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite74.0ms

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:

45.0ms	(/ (- (* 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)))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
16.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (- (* 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)))))))
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 (/ 1.0 (hypot 1.0 x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (39.0ms)

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

prune320.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.8b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
42×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`add-exp-log` `add-cbrt-cube`
14×	`associate-*l/`
12×	`associate-/r/`
10×	`cbrt-undiv` `div-exp` `associate-/l*`
9×	`flip3-+` `flip-+` `distribute-lft-out`
8×	`add-log-exp`
7×	`associate-/r*` `div-inv`
4×	`pow1` `associate-*r/` `prod-exp` `frac-sub` `cbrt-unprod`
3×	`flip3--` `flip--`
2×	`frac-2neg` `clear-num` `associate--r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `sum-log` `associate-/l/`

Counts

4 → 119

Calls

4 calls:

40.0ms	(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
25.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
81.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify116.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	782	2521
1	4246	2222
2	5001	2222

prune414.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.8b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))
1.6b	(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

94×	`associate-*r/`
62×	`sqrt-div`
57×	`pow1`
33×	`flip3-+` `flip-+`
30×	`sqrt-pow1`
21×	`pow-prod-down`
20×	`frac-sub`
13×	`add-sqr-sqrt`
12×	`frac-times` `associate-*l/`
11×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
10×	`pow-prod-up`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-prod` `pow-sqr`
4×	`unpow-prod-down` `flip3--` `pow-pow` `cube-prod` `swap-sqr` `associate-r` `associate-l` `flip--` `sub-div`
3×	`pow-unpow`
2×	`cube-div` `sub-neg` `diff-log` `associate--r+`
1×	`pow2` `distribute-rgt-in` `cube-mult` `pow-to-exp` `distribute-rgt-out--` `distribute-lft-in` `pow-plus` `sqrt-unprod` `unpow3` `pow-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 139

Calls

4 calls:

94.0ms	(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
15.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
25.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))
114.0ms	(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
136.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
30.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))
265.0ms	(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify156.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (129.0ms)

Iter	Nodes	Cost
0	778	2336
1	4088	1998
2	5003	1985

prune572.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.5b

regimes63.0ms

Accuracy

0% (0.0b remaining)

Error of 15.1b against oracle of 15.1b and baseline of 15.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	52
1	54	52
2	54	52

end0.0ms

sample825.0ms

Algorithm

intervals

Results

457.0ms	2858×	body	1280	valid
113.0ms	4057×	body	80	valid
80.0ms	626×	body	640	valid
27.0ms	318×	body	320	valid
8.0ms	141×	body	160	valid