Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	194×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	76×	body	80	nan
1.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
3×	`associate-r` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `flip--` `associate-/l/`
1×	`neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-sub` `associate-l` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv`

Counts

4 → 73

Calls

4 calls:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
19.0ms	(* (* 3.0 a) c)
48.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	403	683
1	1865	595
2	5002	592

prune231.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms	(* (* 3.0 a) c)
2.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune191.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

25.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.0ms	(* (* 3.0 a) c)
48.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	368	654
1	1833	565
2	5001	559

prune215.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(* (* 3.0 a) c)
2.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
19.0ms	(* (* 3.0 a) c)
49.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	307	470
1	1303	428
2	5001	417

prune173.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.6b

regimes494.0ms

Accuracy

89.5% (3.0b remaining)

Error of 8.8b against oracle of 5.8b and baseline of 34.3b

bsearch195.0ms

Steps

Iters	Range	Point
8	1.5276508475467709e+44	4.1560730947117816e+46	6.827923207407828e+44
9	9.738150321786022e-203	8.653734362945753e-196	2.5319914608763346e-199
11	-1.829086240692416e+154	-2.187052964502477e+134	-8.555281377770497e+140

Iters

Range

Point

1.5276508475467709e+44

4.1560730947117816e+46

6.827923207407828e+44

9.738150321786022e-203

8.653734362945753e-196

2.5319914608763346e-199

-1.829086240692416e+154

-2.187052964502477e+134

-8.555281377770497e+140

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	30
1	53	30
2	53	30

end0.0ms

sample1.1s

Algorithm

intervals

Results

239.0ms	1105×	body	2560	valid
225.0ms	5867×	body	80	valid
164.0ms	909×	body	1280	valid
106.0ms	2861×	body	80	nan
63.0ms	422×	body	640	valid
26.0ms	96×	body	5120	valid
23.0ms	214×	body	320	valid
8.0ms	119×	body	160	valid