Details

sample111.0ms

Algorithm

intervals

Results

38.0ms	32×	body	1280	valid
21.0ms	197×	body	80	valid
17.0ms	29×	body	2560	valid
8.0ms	89×	body	80	nan
5.0ms	12×	body	640	valid
3.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify135.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

135.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize37.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b b) (* (* 3 a) c)))
1.0b	(- (* b b) (* (* 3 a) c))
0.5b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b	(* (* 3 a) c)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

Slowest

58.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.0ms	(- (* b b) (* (* 3 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
13.0ms	(* (* 3 a) c)

series348.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
115.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
77.0ms	(- (* b b) (* (* 3 a) c))
34.0ms	(* (* 3 a) c)

simplify3.5s

Counts

34 → 76

Calls

34 calls:

Slowest

504.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
409.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
399.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
269.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
230.0ms	(- b (* 3/2 (/ (* a c) b)))

prune888.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.2b

localize24.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (+ (* b b) (* (* c -3) a)))
1.0b	(+ (* b b) (* (* c -3) a))
0.5b	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
0.2b	(/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) (* 3 a))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`insert-posit16`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `div-exp` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 75

Calls

4 calls:

Slowest

60.0ms	(/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) (* 3 a))
28.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
14.0ms	(+ (* b b) (* (* c -3) a))
12.0ms	(sqrt (+ (* b b) (* (* c -3) a)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) (* 3 a))
119.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
95.0ms	(sqrt (+ (* b b) (* (* c -3) a)))
55.0ms	(+ (* b b) (* (* c -3) a))

simplify4.8s

Counts

49 → 87

Calls

49 calls:

Slowest

865.0ms	(- (* (sqrt (+ (* b b) (* (* c -3) a))) (sqrt (+ (* b b) (* (* c -3) a)))) (* b b))
408.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* c -3) a) (* (* c -3) a))))
343.0ms	(- (pow (sqrt (+ (* b b) (* (* c -3) a))) 3) (pow b 3))
319.0ms	(/ (* (* (- (sqrt (+ (* b b) (* (* c -3) a))) b) (- (sqrt (+ (* b b) (* (* c -3) a))) b)) (- (sqrt (+ (* b b) (* (* c -3) a))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
257.0ms	(* (exp (* b b)) (exp (* (* c -3) a)))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (+ (* b b) (* (* c -3) a)))
1.0b	(+ (* b b) (* (* c -3) a))
0.5b	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
0.2b	(* (* c -3) a)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

Slowest

38.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
27.0ms	(* (* c -3) a)
12.0ms	(sqrt (+ (* b b) (* (* c -3) a)))
10.0ms	(+ (* b b) (* (* c -3) a))

series295.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

97.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
96.0ms	(sqrt (+ (* b b) (* (* c -3) a)))
65.0ms	(+ (* b b) (* (* c -3) a))
37.0ms	(* (* c -3) a)

simplify2.9s

Counts

34 → 75

Calls

34 calls:

Slowest

458.0ms	(* (* (* (* c -3) (* c -3)) (* c -3)) (* (* a a) a))
359.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* c -3) a) (* (* c -3) a))))
355.0ms	(* (* (* (* c c) c) (* (* -3 -3) -3)) (* (* a a) a))
285.0ms	(* (exp (* b b)) (exp (* (* c -3) a)))
272.0ms	(- b (* 3/2 (/ (* a c) b)))

prune983.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize30.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (+ (* b b) (* -3 (* a c))))
1.0b	(+ (* b b) (* -3 (* a c)))
0.5b	(- (sqrt (+ (* b b) (* -3 (* a c)))) b)
0.2b	(* -3 (* a c))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-r` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

Slowest

39.0ms	(- (sqrt (+ (* b b) (* -3 (* a c)))) b)
27.0ms	(* -3 (* a c))
9.0ms	(sqrt (+ (* b b) (* -3 (* a c))))
8.0ms	(+ (* b b) (* -3 (* a c)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

137.0ms	(- (sqrt (+ (* b b) (* -3 (* a c)))) b)
78.0ms	(sqrt (+ (* b b) (* -3 (* a c))))
73.0ms	(+ (* b b) (* -3 (* a c)))
36.0ms	(* -3 (* a c))

simplify3.9s

Counts

34 → 75

Calls

34 calls:

Slowest

718.0ms	(sqrt (- (* (* b b) (* b b)) (* (* -3 (* a c)) (* -3 (* a c)))))
650.0ms	(* (* (* -3 -3) -3) (* (* (* a c) (* a c)) (* a c)))
559.0ms	(sqrt (+ (pow (* b b) 3) (pow (* -3 (* a c)) 3)))
333.0ms	(* (* (* -3 -3) -3) (* (* (* a a) a) (* (* c c) c)))
271.0ms	(* (exp (* b b)) (exp (* -3 (* a c))))

prune791.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

regimes509.0ms

Accuracy

82.5% (4.9b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 33.1b

bsearch126.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.2s	5894×	body	80	valid
1.0s	1022×	body	2560	valid
665.0ms	929×	body	1280	valid
425.0ms	2822×	body	80	nan
217.0ms	460×	body	640	valid
107.0ms	239×	body	320	valid
92.0ms	103×	body	5120	valid
26.0ms	112×	body	160	valid