Details

sample117.0ms

Algorithm

intervals

Results

38.0ms	42×	body	2560	valid
16.0ms	181×	body	80	valid
12.0ms	29×	body	1280	valid
8.0ms	97×	body	80	nan
5.0ms	14×	body	640	valid
5.0ms	7×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify11.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.3b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite185.0ms

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:

23.0ms	(* 4.0 (* a c))
119.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* 4.0 (* a c))
141.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
101.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Counts: 95 → 95

prune376.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.2b	(/ 1 (* 2.0 a))
0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

153.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
12.0ms	(/ 1 (* 2.0 a))
32.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
29.0ms	(/ 1 (* 2.0 a))
116.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Counts: 113 → 113

prune369.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite206.0ms

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:

81.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
34.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series635.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
255.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
124.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
86.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify86.0ms

Counts: 156 → 156

prune518.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.8b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts: 0 → 0

prune1.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 4.8b

regimes411.0ms

Accuracy

84.1% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.3b

bsearch163.0ms

Steps

Iters	Range		Point
8	6.830756908302209e+71	2.772849885831336e+75	1.112435874232008e+74
9	-1.285144198600061e-73	-1.928789297449181e-79	-1.5255092132011432e-76

simplify21.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	5906×	body	80	valid
615.0ms	1069×	body	2560	valid
458.0ms	928×	body	1280	valid
362.0ms	2898×	body	80	nan
178.0ms	444×	body	640	valid
98.0ms	108×	body	5120	valid
67.0ms	106×	body	160	valid
46.0ms	208×	body	320	valid