Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	189×	body	80	valid
5.0ms	27×	body	1280	valid
4.0ms	101×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	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: 33.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

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:

33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms	(+ (- 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)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
74.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

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

prune217.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
141.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
173.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune409.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

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:

50.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
13.0ms	(+ (- 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)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	481	921
1	2189	790
2	5001	777

prune216.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

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:

27.0ms	(/ 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)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(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

prune227.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 5.5b

regimes270.0ms

Accuracy

82% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 32.4b

bsearch115.0ms

Steps

Iters	Range		Point
10	2.922623675251237e-45	3.998186072825638e-35	8.679707852111266e-40
8	-2.75227652547193e+57	-2.8729039666377685e+54	-2.237522594933402e+57

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

236.0ms	1039×	body	2560	valid
221.0ms	5877×	body	80	valid
168.0ms	910×	body	1280	valid
107.0ms	2874×	body	80	nan
67.0ms	463×	body	640	valid
33.0ms	112×	body	5120	valid
24.0ms	230×	body	320	valid
7.0ms	103×	body	160	valid