Details

sample52.0ms

Algorithm

intervals

Results

10.0ms	35×	body	2560	valid
9.0ms	179×	body	80	valid
7.0ms	30×	body	1280	valid
4.0ms	76×	body	80	nan
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	10×	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: 36.5b

localize33.0ms

Local error

Found 3 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))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

70.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series273.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify38.0ms

Counts: 67 → 67

prune205.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.9b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite188.0ms

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:

23.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
86.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
63.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
158.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
194.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify100.0ms

Counts: 166 → 166

prune442.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b	(/ (* 4.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
3.5b	(/ (* 1 (/ (* 4.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))) (* 2.0 a))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-exp-log`
72×	`add-cbrt-cube`
68×	`times-frac`
56×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
52×	`div-exp`
41×	`prod-exp`
30×	`cbrt-undiv`
27×	`add-cube-cbrt`
26×	`associate-/r*`
22×	`cbrt-unprod`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`1-exp` `sqrt-prod`
8×	`add-log-exp`
7×	`distribute-rgt-neg-in`
5×	`pow1`
4×	`div-inv`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--` `associate-/l*`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `neg-log` `associate-/r/` `associate-/l/`

Counts

4 → 151

Calls

4 calls:

24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms	(/ (* 4.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
45.0ms	(/ (* 1 (/ (* 4.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))) (* 2.0 a))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
214.0ms	(/ (* 4.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
171.0ms	(/ (* 1 (/ (* 4.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))) (* 2.0 a))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Counts: 163 → 163

prune354.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
11.9b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite220.0ms

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:

23.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
61.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
160.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
194.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Counts: 161 → 161

prune409.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

regimes218.0ms

Accuracy

87.9% (3.3b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 32.7b

bsearch215.0ms

Steps

Iters	Range		Point
8	1.538525478595148e+72	6.402915924844171e+74	1.5059650565626715e+74
9	1.4802762572194915e-224	5.864956779345081e-215	6.89680782654711e-222
6	-3.779251410483496e+105	-5.080294099506613e+104	-1.361733299857302e+105

simplify1.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

652.0ms	1023×	body	2560	valid
532.0ms	5866×	body	80	valid
356.0ms	906×	body	1280	valid
215.0ms	2914×	body	80	nan
87.0ms	442×	body	640	valid
81.0ms	127×	body	5120	valid
36.0ms	244×	body	320	valid
11.0ms	109×	body	160	valid