Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	204×	body	80	valid
6.0ms	28×	body	2560	valid
5.0ms	25×	body	1280	valid
3.0ms	91×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune239.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

57.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	481	920
1	2189	790
2	5001	777

prune240.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
45×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 114

Calls

4 calls:

30.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	525	1588
1	2570	1375
2	5001	1308

prune259.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (* b b) (* (* 4.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
47.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
257.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	149	476
1	576	446
2	2486	444
3	5001	440

prune223.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.1b

regimes230.0ms

Accuracy

82.9% (5.0b remaining)

Error of 10.7b against oracle of 5.7b and baseline of 34.9b

bsearch90.0ms

Steps

Iters	Range		Point
8	1.0581952271802821e-68	3.094434386839899e-66	1.92049775718538e-66
5	-4.678225599872262e+33	-1.2984931902309085e+33	-4.6051414178616705e+33

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

259.0ms	1099×	body	2560	valid
223.0ms	5785×	body	80	valid
168.0ms	897×	body	1280	valid
101.0ms	2794×	body	80	nan
73.0ms	483×	body	640	valid
33.0ms	108×	body	5120	valid
27.0ms	232×	body	320	valid
11.0ms	118×	body	160	valid