Details

sample58.0ms

Algorithm

intervals

Results

14.0ms	37×	body	2560	valid
9.0ms	185×	body	80	valid
8.0ms	33×	body	1280	valid
5.0ms	81×	body	80	nan
4.0ms	20×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize14.0ms

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))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

17.0ms	(* 4.0 (* a c))
72.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* 4.0 (* a c))
105.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
90.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Counts: 95 → 95

prune266.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

76.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Counts: 74 → 74

prune198.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
30×	`add-exp-log`
29×	`add-cube-cbrt`
20×	`associate-/r*`
18×	`add-cbrt-cube`
14×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `flip--`
6×	`pow1` `div-inv`
4×	`prod-exp` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `neg-log` `inv-pow`

Counts

4 → 144

Calls

4 calls:

48.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
57.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* 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)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
120.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
86.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify68.0ms

Counts: 156 → 156

prune321.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 63

Calls

4 calls:

25.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify95.0ms

Counts: 75 → 75

prune327.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes224.0ms

Accuracy

86.3% (3.9b remaining)

Error of 9.5b against oracle of 5.6b and baseline of 34.0b

bsearch258.0ms

Steps

Iters	Range		Point
8	1.538525478595148e+72	6.402915924844171e+74	6.326287366549383e+74
9	-7.826064039423189e-132	-1.1138670077130767e-140	-5.358830408552925e-132
6	-3.4377365604695865e-95	-7.852755480555329e-96	-8.46693322491602e-96
7	-8.794280737794768e+42	-4.315177351158757e+40	-7.305451620439275e+42

simplify1.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

651.0ms	924×	body	1280	valid
514.0ms	5850×	body	80	valid
467.0ms	1054×	body	2560	valid
184.0ms	2933×	body	80	nan
124.0ms	502×	body	640	valid
45.0ms	110×	body	5120	valid
31.0ms	207×	body	320	valid
13.0ms	108×	body	160	valid