Details

sample84.0ms

Algorithm

intervals

Results

23.0ms	147×	body	160	valid
14.0ms	297×	body	80	nan
12.0ms	553×	pre	80	true
5.0ms	109×	body	80	valid

simplify61.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite143.0ms

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:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
56.0ms	(- (* b b) (* (* 4.0 a) c))
119.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify759.0ms

Counts: 82 → 82

prune266.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

11.0ms	(- (* b b) (* (* 4.0 a) c))
31.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
99.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b b) (* (* 4.0 a) c))
116.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
178.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
226.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.6s

Counts: 163 → 163

prune631.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.5b	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b	(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite459.0ms

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` `associate-/l/`
2×	`cube-mult` `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 → 209

Calls

4 calls:

240.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
170.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
11.0ms	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
12.0ms	(pow (- (* b b) (* (* 4.0 a) c)) 3)

series637.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
225.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
62.0ms	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
133.0ms	(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify2.4s

Counts: 221 → 221

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
89×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
32×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
17×	`distribute-lft-out`
14×	`div-inv`
12×	`associate-/r*`
8×	`neg-mul-1` `add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1`
3×	`prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `sum-log` `associate-/l/`

Counts

4 → 163

Calls

4 calls:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
137.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
260.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
60.0ms	(- (* b b) (* (* 4.0 a) c))
122.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.7s

Counts: 175 → 175

prune796.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes179.0ms

Accuracy

19.5% (0.2b remaining)

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

bsearch0.0ms

simplify562.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	4566×	body	160	valid
791.0ms	8511×	body	80	nan
553.0ms	16511×	pre	80	true
338.0ms	3434×	body	80	valid