Details

sample83.0ms

Algorithm

intervals

Results

20.0ms	30×	body	1280	valid
14.0ms	35×	body	2560	valid
12.0ms	179×	body	80	valid
5.0ms	76×	body	80	nan
4.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down` `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` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 76

Calls

4 calls:

70.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
27.0ms	(* (* 3.0 a) c)
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
21.0ms	(* (* 3.0 a) c)
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
78.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Counts: 88 → 88

prune233.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.5b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite191.0ms

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:

24.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
88.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
58.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
157.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
200.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
77.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify103.0ms

Counts: 166 → 166

prune428.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
0.3b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
114×	`*-un-lft-identity`
63×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
26×	`distribute-lft-out`
19×	`associate-/l*`
14×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-rgt-neg-in`
10×	`pow1`
8×	`add-log-exp`
5×	`div-inv`
3×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `sqrt-prod` `cbrt-unprod`
2×	`neg-sub0` `associate-+l-` `sqrt-div` `div-sub` `sum-log`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `neg-log` `clear-num` `*-commutative` `flip--` `flip-+` `associate-/l/`

Counts

4 → 143

Calls

4 calls:

72.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
17.0ms	(* (* 3.0 a) c)
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
20.0ms	(* (* 3.0 a) c)
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify68.0ms

Counts: 155 → 155

prune381.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down` `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` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 76

Calls

4 calls:

68.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
22.0ms	(* (* 3.0 a) c)
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
21.0ms	(* (* 3.0 a) c)
85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Counts: 88 → 88

prune173.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.3b

regimes522.0ms

Accuracy

83.1% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.0b

bsearch98.0ms

Steps

Iters	Range		Point
9	2.3136842542622443e-90	1.8034474160827886e-84	3.091361180800597e-86
6	-3.779251410483496e+105	-5.080294099506613e+104	-1.361733299857302e+105

simplify1.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

602.0ms	1022×	body	2560	valid
459.0ms	5865×	body	80	valid
203.0ms	907×	body	1280	valid
189.0ms	2913×	body	80	nan
108.0ms	442×	body	640	valid
101.0ms	127×	body	5120	valid
61.0ms	244×	body	320	valid
10.0ms	109×	body	160	valid