Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	98×	body	1280	valid
4.0ms	118×	body	80	valid
3.0ms	21×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	8×	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: 18.9b

localize8.0ms

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	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite20.0ms

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:

5.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
71.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
80.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2323	463
3	5001	463

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 18.4b

localize12.0ms

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

rewrite17.0ms

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:

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

series117.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
75.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
31.0ms	(- (* 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	306	616
1	1080	568
2	4851	560
3	5001	560

prune255.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize19.0ms

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 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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))))))
7.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
75.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
31.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	445	704
1	1765	663
2	5001	663

prune287.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (hypot 1.0 x)))
0.1b	(/ 1 (sqrt (hypot 1.0 x)))
0.3b	(* (/ 1 (sqrt (hypot 1.0 x))) (/ 1.0 (sqrt (hypot 1.0 x))))
2.0b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (/ 1 (sqrt (hypot 1.0 x))) (/ 1.0 (sqrt (hypot 1.0 x))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
94×	`times-frac`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`associate-*r/` `unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `frac-sub` `associate-/l*` `add-log-exp`
4×	`flip3--` `associate--l+` `flip--` `cbrt-unprod` `div-inv`
3×	`frac-times` `sub-neg` `rec-exp` `pow-flip` `1-exp` `associate-*l/`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 189

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
4.0ms	(/ 1 (sqrt (hypot 1.0 x)))
17.0ms	(* (/ 1 (sqrt (hypot 1.0 x))) (/ 1.0 (sqrt (hypot 1.0 x))))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (/ 1 (sqrt (hypot 1.0 x))) (/ 1.0 (sqrt (hypot 1.0 x))))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
14.0ms	(/ 1 (sqrt (hypot 1.0 x)))
6.0ms	(* (/ 1 (sqrt (hypot 1.0 x))) (/ 1.0 (sqrt (hypot 1.0 x))))
31.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (/ 1 (sqrt (hypot 1.0 x))) (/ 1.0 (sqrt (hypot 1.0 x))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	642	1857
1	3176	1641
2	5001	1524

prune436.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

regimes105.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	20
1	29	20

end0.0ms

sample826.0ms

Algorithm

intervals

Results

464.0ms	2796×	body	1280	valid
131.0ms	4124×	body	80	valid
81.0ms	610×	body	640	valid
28.0ms	309×	body	320	valid
12.0ms	161×	body	160	valid