Details

sample83.0ms

Algorithm

intervals

Results

15.0ms	33×	body	2560	valid
13.0ms	35×	body	1280	valid
13.0ms	168×	body	80	valid
7.0ms	92×	body	80	nan
5.0ms	15×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	8×	body	160	valid

simplify4.0ms

Counts: 1 → 1

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b	(- (* b b) (* (* 4.0 a) c))
2.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite193.0ms

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:

125.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms	(- (* b b) (* (* 4.0 a) c))
36.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
86.0ms	(- (* b b) (* (* 4.0 a) c))
121.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Counts: 82 → 82

prune359.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize39.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

15.0ms	(- (* b b) (* (* 4.0 a) c))
146.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
96.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* b b) (* (* 4.0 a) c))
195.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
261.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify124.0ms

Counts: 160 → 160

prune674.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
16.5b	(/ (* 2.0 a) (* 4.0 (* a c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

32.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(- (* b b) (* (* 4.0 a) c))
20.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Counts: 82 → 82

prune285.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-exp-log`
166×	`div-exp`
119×	`prod-exp`
64×	`1-exp`
60×	`add-cbrt-cube`
34×	`rec-exp`
31×	`times-frac`
26×	`cbrt-undiv`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`cbrt-unprod`
14×	`associate-/r/`
13×	`associate-/l*`
11×	`frac-times`
10×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`associate-*l/`
5×	`pow1` `associate-*r/`
4×	`sqrt-prod`
3×	`diff-log` `un-div-inv` `div-inv`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

94.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
48.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
94.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
57.0ms	(- (* b b) (* (* 4.0 a) c))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Counts: 191 → 191

prune420.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.2b

regimes364.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.6b

bsearch246.0ms

Steps

Iters	Range	Point
5	3.1594096090812424e+104	8.241903478382293e+104	6.2080577970805e+104
8	-4.3193946104502796e-226	-4.381317687258745e-230	-7.892835993842436e-230
10	-3.742210988141449e+103	-1.1204690717208776e+87	-8.301687926884189e+98

Iters

Range

Point

3.1594096090812424e+104

8.241903478382293e+104

6.2080577970805e+104

-4.3193946104502796e-226

-4.381317687258745e-230

-7.892835993842436e-230

-3.742210988141449e+103

-1.1204690717208776e+87

-8.301687926884189e+98

simplify87.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

598.0ms	1051×	body	2560	valid
468.0ms	5870×	body	80	valid
423.0ms	218×	body	320	valid
411.0ms	893×	body	1280	valid
306.0ms	2845×	body	80	nan
152.0ms	480×	body	640	valid
46.0ms	98×	body	5120	valid
13.0ms	108×	body	160	valid