Details

sample31.0ms

Algorithm

intervals

Results

16.0ms	98×	body	1280	valid
3.0ms	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize7.0ms

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))))))

rewrite19.0ms

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:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(/ 1.0 (hypot 1.0 x))
73.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
83.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (18.0ms)

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

prune167.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 18.4b

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 (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))))

rewrite15.0ms

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

series128.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
80.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify137.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (29.0ms)

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

prune252.0ms

Filtered

96 candidates to 69 candidates (71.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize20.0ms

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:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
81.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
35.0ms	(- (* (- (* 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 (11.0ms)

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

prune480.0ms

Filtered

82 candidates to 62 candidates (75.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt` `times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
59×	`sqrt-prod`
45×	`cbrt-prod`
40×	`associate-r`
32×	`add-exp-log`
22×	`add-cbrt-cube`
15×	`associate-*r/` `unswap-sqr`
12×	`associate-/r*`
10×	`cbrt-undiv` `div-exp` `associate-l`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-/l*`
6×	`pow1` `frac-sub` `add-log-exp`
4×	`flip3--` `associate--l+` `flip--` `div-inv`
3×	`frac-times` `sub-neg` `associate-*l/`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 198

Calls

4 calls:

4.0ms	(/ (cbrt 1.0) (sqrt (hypot 1.0 x)))
5.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (hypot 1.0 x)))
33.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (hypot 1.0 x))) (/ (cbrt 1.0) (sqrt (hypot 1.0 x))))
11.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (hypot 1.0 x))) (/ (cbrt 1.0) (sqrt (hypot 1.0 x))))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (cbrt 1.0) (sqrt (hypot 1.0 x)))
72.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (hypot 1.0 x)))
68.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (hypot 1.0 x))) (/ (cbrt 1.0) (sqrt (hypot 1.0 x))))
104.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (hypot 1.0 x))) (/ (cbrt 1.0) (sqrt (hypot 1.0 x))))))

simplify104.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	729	2643
1	3831	2428
2	5002	2268

prune624.0ms

Filtered

210 candidates to 130 candidates (61.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

regimes110.0ms

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	28	24
1	28	24

end0.0ms

sample803.0ms

Algorithm

intervals

Results

456.0ms	2796×	body	1280	valid
123.0ms	4124×	body	80	valid
77.0ms	610×	body	640	valid
29.0ms	309×	body	320	valid
9.0ms	161×	body	160	valid