Details

sample61.0ms

Algorithm

intervals

Results

13.0ms	43×	body	2560	valid
10.0ms	185×	body	80	valid
6.0ms	25×	body	1280	valid
6.0ms	119×	body	80	nan
2.0ms	10×	body	640	valid
2.0ms	5×	body	5120	valid
2.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify86.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite156.0ms

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:

77.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify687.0ms

Counts: 82 → 82

prune296.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite245.0ms

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))))
92.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
106.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series638.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
231.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
215.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts: 166 → 166

prune542.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.9b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
11.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite230.0ms

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:

24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
64.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
174.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
208.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
87.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts: 161 → 161

prune478.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.5b	(/ (* 4.0 (* a c)) (* 2.0 a))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
29.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b b) (* (* 4.0 a) c))
92.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify809.0ms

Counts: 82 → 82

prune240.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

regimes179.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.7b

bsearch242.0ms

Steps

Iters	Range	Point
8	1.890514070312107e+96	2.5656331724562416e+99	2.521192511657276e+99
9	-1.8468183666089936e-283	-2.8481806021794936e-290	-4.193871707188483e-287
9	-1.3204298692890892e+123	-1.196267803426671e+118	-1.8440038131758226e+119

Iters

Range

Point

1.890514070312107e+96

2.5656331724562416e+99

2.521192511657276e+99

-1.8468183666089936e-283

-2.8481806021794936e-290

-4.193871707188483e-287

-1.3204298692890892e+123

-1.196267803426671e+118

-1.8440038131758226e+119

simplify382.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

728.0ms	1144×	body	2560	valid
526.0ms	5799×	body	80	valid
293.0ms	3016×	body	80	nan
281.0ms	859×	body	1280	valid
94.0ms	438×	body	640	valid
83.0ms	126×	body	5120	valid
39.0ms	243×	body	320	valid
11.0ms	111×	body	160	valid