Details

sample116.0ms

Algorithm

intervals

Results

27.0ms	519×	pre	80	true
22.0ms	152×	body	160	valid
18.0ms	263×	body	80	nan
9.0ms	45×	body	320	valid
4.0ms	59×	body	80	valid

simplify106.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite215.0ms

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:

10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
124.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
71.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms	(- (* b b) (* (* 4.0 a) c))
140.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
125.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify667.0ms

Counts: 82 → 82

prune291.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* 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)))))

rewrite272.0ms

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:

45.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
121.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
77.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series757.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(- (* b b) (* (* 4.0 a) c))
234.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
326.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.8s

Counts: 163 → 163

prune681.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
114×	`times-frac`
66×	`distribute-lft-out`
44×	`add-sqr-sqrt` `add-cube-cbrt` `distribute-rgt-neg-in`
36×	`associate-/l*`
22×	`distribute-lft-neg-in` `neg-mul-1`
18×	`add-exp-log` `add-cbrt-cube`
14×	`add-log-exp`
10×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3-+` `flip-+`
4×	`pow1` `neg-log` `sum-log` `div-inv`
3×	`associate-/l/`
2×	`neg-sub0` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `associate-+l-` `associate-+r-` `sub-neg` `distribute-neg-out` `flip3--` `diff-log` `unsub-neg` `flip--`

Counts

4 → 178

Calls

4 calls:

57.0ms	(+ (- b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
192.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (+ (- b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
134.0ms	(/ (+ 0 (* 4.0 (* a c))) (+ (- b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (- b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
87.0ms	(- (* b b) (* (* 4.0 a) c))
210.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (+ (- b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
302.0ms	(/ (+ 0 (* 4.0 (* a c))) (+ (- b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify2.0s

Counts: 190 → 190

prune767.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b	(/ (/ 1 (- 1)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(* (/ (* 2.0 a) (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

214×	`add-exp-log`
138×	`add-cbrt-cube`
96×	`times-frac`
89×	`prod-exp`
84×	`div-exp`
57×	`cbrt-unprod`
48×	`cbrt-undiv` `add-sqr-sqrt` `*-un-lft-identity`
46×	`add-cube-cbrt`
35×	`associate-/l*`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`rec-exp` `1-exp`
6×	`pow1` `neg-mul-1` `add-log-exp`
5×	`associate-l` `associate-/r/` `div-inv`
4×	`frac-times` `flip3-+` `associate-r/` `associate-r*` `flip-+`
2×	`frac-2neg` `associate-l/` `clear-num` `associate-/r`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `pow-prod-down` `*-commutative` `flip--` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

4 → 210

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
31.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
136.0ms	(/ (/ 1 (- 1)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
191.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
244.0ms	(/ (/ 1 (- 1)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
123.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify793.0ms

Counts: 222 → 222

prune764.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes207.0ms

Accuracy

67.8% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify807.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	4874×	body	160	valid
786.0ms	8191×	body	80	nan
757.0ms	16191×	pre	80	true
280.0ms	1349×	body	320	valid
124.0ms	1777×	body	80	valid