Details

sample59.0ms

Algorithm

intervals

Results

13.0ms	193×	body	80	valid
9.0ms	32×	body	2560	valid
7.0ms	28×	body	1280	valid
4.0ms	87×	body	80	nan
4.0ms	20×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize15.0ms

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)))

rewrite139.0ms

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:

75.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify41.0ms

Counts: 82 → 82

prune253.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.5b

localize20.0ms

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)))

rewrite207.0ms

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:

25.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
95.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
69.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
168.0ms	(/ (/ (+ 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)))))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify106.0ms

Counts: 166 → 166

prune488.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

localize28.0ms

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))))) (/ 1 (* 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)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`sqrt-prod`
8×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod` `add-log-exp`
7×	`pow1` `associate-r` `associate-/r*`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

26.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
130.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
65.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
164.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
206.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify132.0ms

Counts: 161 → 161

prune543.0ms

Pruning

12 alts after pruning (11 fresh and 1 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))))
12.4b	(/ (* 4.0 (* a c)) (* 2.0 a))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

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:

9.0ms	(- (* b b) (* (* 4.0 a) c))
32.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* (* 4.0 a) c))
87.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Counts: 82 → 82

prune213.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

regimes285.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 29.9b

bsearch201.0ms

Steps

Iters	Range	Point
4	9.012561940608131e+125	1.467599966670541e+126	1.3720752601738524e+126
9	-8.312848984102269e-296	-1.0819843522862608e-301	-8.219482842591945e-296
9	-1.5317926616566243e+132	-2.1622394106188112e+123	-5.523069478976328e+123

Iters

Range

Point

9.012561940608131e+125

1.467599966670541e+126

1.3720752601738524e+126

-8.312848984102269e-296

-1.0819843522862608e-301

-8.219482842591945e-296

-1.5317926616566243e+132

-2.1622394106188112e+123

-5.523069478976328e+123

simplify1.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

514.0ms	5791×	body	80	valid
456.0ms	460×	body	640	valid
384.0ms	1114×	body	2560	valid
350.0ms	900×	body	1280	valid
181.0ms	2916×	body	80	nan
75.0ms	103×	body	5120	valid
35.0ms	236×	body	320	valid
11.0ms	103×	body	160	valid