Details

sample59.0ms

Algorithm

intervals

Results

11.0ms	193×	body	80	valid
10.0ms	32×	body	2560	valid
7.0ms	28×	body	1280	valid
5.0ms	87×	body	80	nan
4.0ms	20×	body	640	valid
2.0ms	12×	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: 34.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite118.0ms

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:

73.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
88.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms	(- (* b b) (* 4.0 (* a c)))
85.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Counts: 82 → 82

prune272.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.5b

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite208.0ms

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:

28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
94.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
62.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
170.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
207.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
81.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify96.0ms

Counts: 166 → 166

prune477.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
1.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.5b	(/ (* 2.0 a) (* 4.0 (* a c)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

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:

11.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* b b) (* 4.0 (* a c)))
85.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
81.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Counts: 82 → 82

prune247.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

95.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
17.0ms	(- (* b b) (* 4.0 (* a c)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
56.0ms	(- (* b b) (* 4.0 (* a c)))
92.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Counts: 101 → 101

prune271.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.4b

regimes252.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.4b against oracle of 5.3b and baseline of 30.1b

bsearch176.0ms

Steps

Iters	Range	Point
4	9.012561940608131e+125	1.467599966670541e+126	1.0763848226380752e+126
7	-4.532619757041417e-294	-8.312848984102269e-296	-1.3101258183672603e-294
9	-1.5317926616566243e+132	-2.1622394106188112e+123	-5.523069478976328e+123

Iters

Range

Point

9.012561940608131e+125

1.467599966670541e+126

1.0763848226380752e+126

-4.532619757041417e-294

-8.312848984102269e-296

-1.3101258183672603e-294

-1.5317926616566243e+132

-2.1622394106188112e+123

-5.523069478976328e+123

simplify1.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

771.0ms	1114×	body	2560	valid
476.0ms	5791×	body	80	valid
299.0ms	900×	body	1280	valid
292.0ms	2916×	body	80	nan
97.0ms	236×	body	320	valid
95.0ms	460×	body	640	valid
39.0ms	103×	body	5120	valid
11.0ms	103×	body	160	valid