Details

sample62.0ms

Algorithm

intervals

Results

21.0ms	38×	body	2560	valid
8.0ms	175×	body	80	valid
6.0ms	28×	body	1280	valid
5.0ms	108×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify58.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite107.0ms

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:

62.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
27.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify500.0ms

Counts: 82 → 82

prune213.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.9b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite169.0ms

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:

22.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
54.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
142.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
179.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts: 166 → 166

prune379.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
10.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite197.0ms

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:

21.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
108.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
54.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series468.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
145.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
176.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts: 161 → 161

prune355.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

91.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
19.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify638.0ms

Counts: 92 → 92

prune203.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.5b

regimes166.0ms

Accuracy

83.8% (4.6b remaining)

Error of 9.8b against oracle of 5.2b and baseline of 33.3b

bsearch100.0ms

Steps

Iters	Range		Point
7	4.050286610423012e-56	1.1696740409864934e-54	5.251983820611911e-55
8	-1.967027894857281e+59	-1.0622106186949144e+55	-1.939122797387645e+59

simplify748.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

558.0ms	929×	body	1280	valid
455.0ms	1104×	body	2560	valid
319.0ms	5790×	body	80	valid
154.0ms	2846×	body	80	nan
121.0ms	415×	body	640	valid
68.0ms	114×	body	5120	valid
29.0ms	228×	body	320	valid
10.0ms	121×	body	160	valid