Details

sample91.0ms

Algorithm

intervals

Results

21.0ms	112×	body	80	valid
15.0ms	144×	body	160	valid
14.0ms	255×	body	80	nan
14.0ms	511×	pre	80	true

simplify67.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
28.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite208.0ms

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:

38.0ms	(* (* 3.0 a) c)
16.0ms	(- (* b b) (* (* 3.0 a) c))
116.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
36.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 3.0 a) c)
67.0ms	(- (* b b) (* (* 3.0 a) c))
178.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify987.0ms

Counts: 85 → 85

prune289.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite864.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

17.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(* 3.0 (* a c))
451.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
368.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* b b) (* (* 3.0 a) c))
30.0ms	(* 3.0 (* a c))
179.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
244.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify1.8s

Counts: 165 → 165

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3))))) (* 3.0 a))
0.4b	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3)))))
0.6b	(cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3))
0.7b	(pow (- (* b b) (* (* 3.0 a) c)) 3)

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
138×	`times-frac`
96×	`*-un-lft-identity`
60×	`difference-of-squares`
56×	`add-cube-cbrt`
52×	`cbrt-prod`
50×	`sqrt-prod`
42×	`associate-/l*`
20×	`distribute-lft-out--`
19×	`add-exp-log` `add-cbrt-cube`
16×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*` `sqr-pow`
10×	`distribute-rgt-neg-in`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`cube-div` `div-inv` `add-log-exp`
3×	`pow-unpow` `div-sub` `associate-/l/`
2×	`cube-mult` `associate-+l-` `cbrt-div` `frac-2neg` `unpow3` `prod-exp` `clear-num` `cbrt-unprod`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `pow-exp` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 211

Calls

4 calls:

542.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3))))) (* 3.0 a))
426.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3)))))
19.0ms	(cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3))
13.0ms	(pow (- (* b b) (* (* 3.0 a) c)) 3)

series647.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3))))) (* 3.0 a))
242.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3)))))
85.0ms	(cbrt (pow (- (* b b) (* (* 3.0 a) c)) 3))
151.0ms	(pow (- (* b b) (* (* 3.0 a) c)) 3)

simplify2.6s

Counts: 223 → 223

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ (* 3.0 a) (/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c))
0.4b	(/ (* 1 (/ (* 3.0 a) (/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c))) (* 3.0 a))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

149×	`times-frac`
115×	`add-exp-log`
113×	`*-un-lft-identity`
74×	`add-cbrt-cube`
73×	`add-sqr-sqrt` `add-cube-cbrt`
53×	`div-exp`
44×	`associate-/r*`
41×	`prod-exp`
40×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
31×	`cbrt-undiv`
22×	`cbrt-unprod`
20×	`distribute-lft-out`
14×	`associate-/l*`
10×	`neg-mul-1` `1-exp`
6×	`add-log-exp`
5×	`div-inv`
4×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`distribute-neg-frac`
1×	`neg-sub0` `sub-neg` `flip3--` `flip3-+` `diff-log` `div-sub` `associate-*r/` `distribute-frac-neg` `associate-/r/` `flip--` `flip-+`

Counts

4 → 227

Calls

4 calls:

137.0ms	(/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c)
8.0ms	(- (* b b) (* (* 3.0 a) c))
101.0ms	(/ (* 3.0 a) (/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c))
93.0ms	(/ (* 1 (/ (* 3.0 a) (/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c))) (* 3.0 a))

series810.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c)
85.0ms	(- (* b b) (* (* 3.0 a) c))
349.0ms	(/ (* 3.0 a) (/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c))
221.0ms	(/ (* 1 (/ (* 3.0 a) (/ (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) c))) (* 3.0 a))

simplify670.0ms

Counts: 239 → 239

prune833.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes330.0ms

Accuracy

30.7% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0s

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.0s	8506×	body	80	nan
707.0ms	16506×	pre	80	true
608.0ms	4451×	body	160	valid
378.0ms	3549×	body	80	valid