Details

sample48.0ms

Algorithm

intervals

Results

9.0ms	149×	body	160	valid
9.0ms	509×	pre	80	true
8.0ms	253×	body	80	nan
4.0ms	44×	body	320	valid
2.0ms	63×	body	80	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: 43.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (* 3.0 a) c)
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
38.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

2.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(* (* 3.0 a) c)
33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
26.0ms	(* (* 3.0 a) c)
110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	419	716
1	1930	613
2	5002	608

prune173.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(* 3.0 (* a c))
0.3b	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`prod-exp` `associate-/r*` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down` `associate-/r/`
4×	`associate-r` `associate-l` `div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `flip--` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 159

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
6.0ms	(* 3.0 (* a c))
158.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
176.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series333.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
24.0ms	(* 3.0 (* a c))
160.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
129.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify111.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	684	3100
1	3307	2567
2	5001	2533

prune426.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(* 3.0 (* a c))
0.4b	(/ (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log` `add-cbrt-cube`
27×	`prod-exp` `cbrt-unprod`
19×	`pow1`
11×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*`
9×	`cbrt-undiv` `div-exp` `pow-prod-down`
7×	`add-cube-cbrt`
5×	`associate-l`
4×	`associate-*r/` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-neg-in` `frac-2neg` `times-frac` `clear-num` `associate-/r` `sqrt-prod` `div-inv` `associate-/l`

Counts

4 → 97

Calls

4 calls:

9.0ms	(* (* 3.0 a) c)
34.0ms	(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms	(* 3.0 (* a c))
23.0ms	(/ (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 (* a c)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* 3.0 a) c)
108.0ms	(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms	(* 3.0 (* a c))
123.0ms	(/ (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 (* a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	514	1160
1	3684	822
2	5001	822

prune226.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (sqrt c)) (sqrt c))))))
0.4b	(* (* (* 3.0 a) (sqrt c)) (sqrt c))
0.4b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (sqrt c)) (sqrt c)))))) (* 3.0 a))
0.4b	(* (* 3.0 a) (sqrt c))

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
42×	`add-cube-cbrt`
32×	`add-exp-log` `add-cbrt-cube`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`pow1`
16×	`sqrt-prod`
12×	`associate-r`
11×	`prod-exp` `cbrt-unprod`
10×	`distribute-rgt-neg-in`
9×	`pow-prod-down`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
4×	`div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `flip--` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 168

Calls

4 calls:

160.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (sqrt c)) (sqrt c))))))
24.0ms	(* (* (* 3.0 a) (sqrt c)) (sqrt c))
177.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (sqrt c)) (sqrt c)))))) (* 3.0 a))
8.0ms	(* (* 3.0 a) (sqrt c))

series412.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (sqrt c)) (sqrt c))))))
41.0ms	(* (* (* 3.0 a) (sqrt c)) (sqrt c))
143.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (sqrt c)) (sqrt c)))))) (* 3.0 a))
64.0ms	(* (* 3.0 a) (sqrt c))

simplify138.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	799	3788
1	4102	3184
2	5003	3144

prune459.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes113.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	25	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

309.0ms	4856×	body	160	valid
293.0ms	16232×	pre	80	true
253.0ms	8232×	body	80	nan
131.0ms	1383×	body	320	valid
57.0ms	1761×	body	80	valid