Details

sample31.0ms

Algorithm

intervals

Results

16.0ms	97×	body	1280	valid
4.0ms	130×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

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: 14.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.1b	(- 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:

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

series198.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
76.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(/ 1.0 (hypot 1.0 x))
89.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (20.0ms)

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

prune167.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.0b

localize13.0ms

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

rewrite22.0ms

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:

10.0ms	(+ 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))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify176.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (35.0ms)

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

prune261.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.6b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
20.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
2.0ms	(/ 1.0 (hypot 1.0 x))
30.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
22.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
5.0ms	(/ 1.0 (hypot 1.0 x))
37.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify93.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	533	882
1	2698	815
2	5001	815

prune401.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 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)))

rewrite40.0ms

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:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
21.0ms	(/ (* 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)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
67.0ms	(/ (* 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))
34.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	606	1101
1	3189	929
2	5002	929

prune485.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.9b

regimes229.0ms

Accuracy

0% (0.0b remaining)

Error of 15.3b against oracle of 15.2b and baseline of 15.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	22
1	32	22
2	32	22

end0.0ms

sample849.0ms

Algorithm

intervals

Results

487.0ms	2859×	body	1280	valid
124.0ms	4020×	body	80	valid
85.0ms	647×	body	640	valid
29.0ms	322×	body	320	valid
10.0ms	152×	body	160	valid