Details

sample29.0ms

Algorithm

intervals

Results

14.0ms	89×	body	1280	valid
4.0ms	138×	body	80	valid
2.0ms	20×	body	640	valid
0.0ms	6×	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: 11.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
1.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

10.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(/ 1.0 (hypot 1.0 x))
87.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2325	463
3	5001	463

prune166.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 11.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 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))
0.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite14.0ms

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:

2.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
38.0ms	(- (* 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 (31.0ms)

Iter	Nodes	Cost
0	306	616
1	1080	568
2	4851	560
3	5001	560

prune258.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
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)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.6b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
23.0ms	(/ (* 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)))
2.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
63.0ms	(/ (* 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)))
6.0ms	(/ 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)))

simplify81.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	625	1165
1	3259	984
2	5001	984

prune351.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
0.2b	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
0.6b	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

173×	`associate-*r/`
48×	`frac-sub`
44×	`add-exp-log` `add-cbrt-cube`
43×	`pow1`
41×	`frac-times`
39×	`flip3--` `flip--`
29×	`associate-*l/`
26×	`associate-/l/`
21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac` `prod-exp` `cbrt-unprod`
17×	`pow-prod-down`
8×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate--l+`
7×	`associate-/l*`
6×	`associate-/r*` `add-log-exp`
5×	`sub-neg` `difference-of-squares`
4×	`associate-/r/` `pow-sqr` `pow-prod-up`
2×	`frac-2neg` `pow-plus` `frac-add` `clear-num` `div-inv`
1×	`pow2` `flip3-+` `diff-log` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 181

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
80.0ms	(/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
19.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
34.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
103.0ms	(/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
24.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
59.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	933	3000
1	5002	2730

prune563.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.9b

regimes404.0ms

Accuracy

0% (0.3b remaining)

Error of 14.7b against oracle of 14.4b and baseline of 14.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	42
1	55	42
2	55	42

end0.0ms

sample788.0ms

Algorithm

intervals

Results

452.0ms	2835×	body	1280	valid
115.0ms	4065×	body	80	valid
83.0ms	647×	body	640	valid
26.0ms	305×	body	320	valid
8.0ms	148×	body	160	valid