Details

sample82.0ms

Algorithm

intervals

Results

22.0ms	534×	pre	80	true
14.0ms	278×	body	80	nan
12.0ms	122×	body	160	valid
6.0ms	134×	body	80	valid

simplify7.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite166.0ms

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)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(- (* b b) (* (* 4.0 a) c))
145.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
112.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify63.0ms

Counts: 82 → 82

prune289.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite300.0ms

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:

34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
136.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
108.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
59.0ms	(- (* b b) (* (* 4.0 a) c))
250.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
238.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify83.0ms

Counts: 163 → 163

prune744.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
0.4b	(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
0.5b	(* (* b b) (* b b))
0.8b	(pow (* (* 4.0 a) c) 3)

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

130×	`pow1`
49×	`add-sqr-sqrt`
36×	`pow-prod-up`
33×	`add-exp-log` `add-cbrt-cube`
32×	`pow-prod-down`
30×	`times-frac`
29×	`*-un-lft-identity`
24×	`difference-of-squares`
22×	`pow-sqr`
21×	`add-cube-cbrt` `sqr-pow`
18×	`pow-plus`
17×	`prod-exp` `cbrt-unprod`
13×	`pow2`
10×	`associate-/l*`
9×	`unpow-prod-down`
4×	`associate-r` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `pow-pow` `pow-exp` `associate-/r*` `rem-cube-cbrt`
2×	`flip3-+` `associate-r/` `associate-l` `associate-/r/` `-commutative` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `flip3--` `frac-2neg` `distribute-lft-in` `unpow3` `div-sub` `cube-prod` `swap-sqr` `div-exp` `clear-num` `flip--` `div-inv` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

241.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
168.0ms	(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
54.0ms	(* (* b b) (* b b))
32.0ms	(pow (* (* 4.0 a) c) 3)

series459.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
127.0ms	(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
58.0ms	(* (* b b) (* b b))
82.0ms	(pow (* (* 4.0 a) c) 3)

simplify154.0ms

Counts: 185 → 185

prune984.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
0.6b	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
0.6b	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
0.8b	(pow (* (* 4.0 a) c) 3)

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`cbrt-div` `associate-*r/`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`cbrt-prod` `pow-unpow` `pow-pow` `flip3-+` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 58

Calls

4 calls:

94.0ms	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
117.0ms	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
119.0ms	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
40.0ms	(pow (* (* 4.0 a) c) 3)

series1.6s

Counts

4 → 12

Calls

4 calls:

483.0ms	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
521.0ms	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
505.0ms	(cbrt (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))))
81.0ms	(pow (* (* 4.0 a) c) 3)

simplify56.0ms

Counts: 70 → 70

prune819.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

1.5% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify63.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

886.0ms	4450×	body	160	valid
823.0ms	16611×	pre	80	true
697.0ms	3550×	body	80	valid
682.0ms	8611×	body	80	nan