Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	186×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	82×	body	80	nan
2.0ms	8×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 33.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

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:

37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune216.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.7b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite94.0ms

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:

14.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
27.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
142.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
178.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	647	2692
1	3114	2439
2	5001	2426

prune406.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.7b	(* (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
8.7b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`sqrt-prod`
8×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod` `add-log-exp`
7×	`pow1` `associate-r` `associate-/r*`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(* (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
26.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series652.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
145.0ms	(* (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
363.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify137.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	739	2415
1	3893	2081
2	5001	2074

prune408.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize25.0ms

Local error

Found 4 expressions with local error:

8.7b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
21×	`times-frac`
19×	`add-cube-cbrt`
13×	`sqrt-prod`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `associate-/r*`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`flip3--` `distribute-rgt-neg-in` `flip--` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

31.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	346	1251
1	1713	1177
2	5001	1165

prune435.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

regimes353.0ms

Accuracy

81.8% (5.0b remaining)

Error of 10.4b against oracle of 5.4b and baseline of 32.6b

bsearch140.0ms

Steps

Iters	Range		Point
10	4.734590495924167e-35	7.237368999400794e-22	8.870690604736125e-35
11	-1.1860998636736231e+119	-1.6133553378404837e+99	-3.7171108546007633e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

237.0ms	1074×	body	2560	valid
225.0ms	5830×	body	80	valid
164.0ms	901×	body	1280	valid
114.0ms	2961×	body	80	nan
67.0ms	453×	body	640	valid
27.0ms	256×	body	320	valid
25.0ms	91×	body	5120	valid
9.0ms	121×	body	160	valid