Details

sample64.0ms

Algorithm

intervals

Results

21.0ms	35×	body	2560	valid
9.0ms	179×	body	80	valid
7.0ms	30×	body	1280	valid
4.0ms	76×	body	80	nan
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-l` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 76

Calls

4 calls:

17.0ms	(* 4.0 (* a c))
82.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* 4.0 (* a c))
118.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
86.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Counts: 88 → 88

prune245.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.5b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

24.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
87.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
164.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
201.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
79.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Counts: 166 → 166

prune456.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.3b	(/ (* 2.0 a) (* 4.0 (* a c)))
25.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

283×	`add-exp-log`
136×	`div-exp`
121×	`prod-exp`
109×	`add-cbrt-cube`
42×	`cbrt-undiv`
41×	`cbrt-unprod`
40×	`1-exp`
32×	`times-frac`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
16×	`rec-exp`
14×	`associate-/l*`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
4×	`flip3--` `sqrt-prod` `flip--` `div-inv`
2×	`frac-times` `frac-2neg` `sqrt-div` `diff-log` `associate-r/` `clear-num` `associate-/r` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `neg-log` `associate-*l/` `associate-/l/`

Counts

4 → 173

Calls

4 calls:

82.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
28.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
83.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
82.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Counts: 185 → 185

prune303.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
0.3b	(/ (/ (/ 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)))))
25.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

20548×	`times-frac`
9817×	`add-sqr-sqrt`
9816×	`*-un-lft-identity`
7500×	`add-cube-cbrt`
1158×	`distribute-lft-out--` `difference-of-squares`
879×	`div-inv`
621×	`associate-/l*`
582×	`sqrt-prod`
579×	`distribute-rgt-neg-in`
200×	`add-exp-log`
169×	`div-exp`
129×	`associate-/r/`
54×	`add-cbrt-cube`
37×	`cbrt-undiv`
30×	`rec-exp` `1-exp`
20×	`associate-/r*`
8×	`add-log-exp`
5×	`pow1`
3×	`flip3--` `flip--`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 5380

Calls

4 calls:

40.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
245.0ms	(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
29.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
195.0ms	(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
85.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
88.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts: 5392 → 5392

prune16.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes186.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.8b

bsearch204.0ms

Steps

Iters	Range	Point
8	1.538525478595148e+72	6.402915924844171e+74	6.326287366549383e+74
9	-7.006116511457938e-281	-2.476656944921405e-289	-3.3203606567416007e-289
6	-3.779251410483496e+105	-5.080294099506613e+104	-1.361733299857302e+105

Iters

Range

Point

1.538525478595148e+72

6.402915924844171e+74

6.326287366549383e+74

-7.006116511457938e-281

-2.476656944921405e-289

-3.3203606567416007e-289

-3.779251410483496e+105

-5.080294099506613e+104

-1.361733299857302e+105

simplify1.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

571.0ms	2914×	body	80	nan
472.0ms	5866×	body	80	valid
384.0ms	442×	body	640	valid
368.0ms	906×	body	1280	valid
310.0ms	1023×	body	2560	valid
51.0ms	127×	body	5120	valid
35.0ms	244×	body	320	valid
13.0ms	109×	body	160	valid