Details

sample93.0ms

Algorithm

intervals

Results

24.0ms	268×	body	80	nan
22.0ms	148×	body	160	valid
19.0ms	524×	pre	80	true
9.0ms	108×	body	80	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: 29.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
29.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite59.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(* (* 3.0 a) c)
34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(* (* 3.0 a) c)
103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (49.0ms)

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

prune173.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

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) c)))))
0.3b	(* 3.0 (* a c))
0.3b	(* (* 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))

rewrite375.0ms

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:

169.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms	(* 3.0 (* a c))
6.0ms	(* (* 3.0 a) c)
187.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series325.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms	(* 3.0 (* a c))
22.0ms	(* (* 3.0 a) c)
123.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify114.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	684	3100
1	3296	2567
2	5002	2533

prune428.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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) c)))))
0.3b	(* (* 3.0 a) c)
0.3b	(* (* 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))

rewrite376.0ms

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×	`associate-r` `pow-prod-down` `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 → 159

Calls

4 calls:

169.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
8.0ms	(* (* 3.0 a) c)
6.0ms	(* (* 3.0 a) c)
186.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series325.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms	(* (* 3.0 a) c)
19.0ms	(* (* 3.0 a) c)
126.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify110.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	627	3101
1	3139	2568
2	5001	2534

prune405.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(* (* 3.0 a) c)
0.4b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c))))))) (* 3.0 a))
0.5b	(* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

141×	`pow1`
77×	`pow-prod-down`
69×	`times-frac`
60×	`sqrt-pow1`
58×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
32×	`add-cube-cbrt`
28×	`add-exp-log` `add-cbrt-cube`
27×	`associate-/l*`
17×	`pow-prod-up`
12×	`pow1/2` `distribute-lft-out--` `difference-of-squares`
11×	`pow-sqr`
10×	`associate-r` `sqrt-prod`
9×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `distribute-rgt-neg-in` `div-exp` `associate-l`
4×	`swap-sqr` `associate-/r/` `add-log-exp`
3×	`*-commutative` `div-inv`
2×	`flip3--` `div-sub` `flip--`
1×	`pow2` `associate-+l-` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r*` `rem-square-sqrt` `associate-/l/` `unswap-sqr`

Counts

4 → 177

Calls

4 calls:

7.0ms	(* (* 3.0 a) c)
7.0ms	(* (* 3.0 a) c)
187.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c))))))) (* 3.0 a))
38.0ms	(* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
19.0ms	(* (* 3.0 a) c)
403.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c))))))) (* 3.0 a))
77.0ms	(* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))

simplify133.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	610	2763
1	3645	2306
2	5003	2260

prune379.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes187.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	21
1	22	21

end0.0ms

sample2.7s

Algorithm

intervals

Results

713.0ms	8575×	body	80	nan
665.0ms	4398×	body	160	valid
610.0ms	16575×	pre	80	true
324.0ms	3602×	body	80	valid