Details

sample78.0ms

Algorithm

intervals

Results

16.0ms	34×	body	2560	valid
15.0ms	187×	body	80	valid
14.0ms	35×	body	1280	valid
8.0ms	115×	body	80	nan
6.0ms	18×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	5×	body	160	valid

simplify104.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

104.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize37.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b	(- (* b b) (* (* 3 a) c))
0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))

rewrite142.0ms

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×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

Slowest

64.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
57.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
14.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms	(- (* b b) (* (* 3 a) c))

series492.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
130.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
109.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
74.0ms	(- (* b b) (* (* 3 a) c))

simplify5.3s

Counts

49 → 88

Calls

49 calls:

Slowest

614.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
326.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
321.0ms	(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
258.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
256.0ms	(/ (* (* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize27.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b	(- (* b b) (* (* 3 a) c))
0.2b	(* (* 3 a) c)

rewrite76.0ms

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

40.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
19.0ms	(* (* 3 a) c)
9.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
102.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
54.0ms	(- (* b b) (* (* 3 a) c))
25.0ms	(* (* 3 a) c)

simplify3.3s

Counts

34 → 76

Calls

34 calls:

Slowest

431.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
429.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
354.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
269.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
225.0ms	(- b (* 3/2 (/ (* a c) b)))

prune895.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize32.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (- (* b b) (* 3 (* a c))))
1.2b	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
0.4b	(- (* b b) (* 3 (* a c)))
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×	`flip3--` `associate-l` `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-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

Slowest

50.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 3 (* a c))))
12.0ms	(* 3 (* a c))
8.0ms	(- (* b b) (* 3 (* a c)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

103.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
87.0ms	(sqrt (- (* b b) (* 3 (* a c))))
63.0ms	(- (* b b) (* 3 (* a c)))
25.0ms	(* 3 (* a c))

simplify3.3s

Counts

34 → 76

Calls

34 calls:

Slowest

593.0ms	(* (* (* 3 3) 3) (* (* (* a c) (* a c)) (* a c)))
384.0ms	(* (* (* 3 3) 3) (* (* (* a a) a) (* (* c c) c)))
312.0ms	(/ (exp (* b b)) (exp (* 3 (* a c))))
297.0ms	(sqrt (- (* (* b b) (* b b)) (* (* 3 (* a c)) (* 3 (* a c)))))
240.0ms	(- b (* 3/2 (/ (* a c) b)))

prune891.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize26.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b	(- (* b b) (* (* 3 a) c))
0.3b	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`associate-r`
19×	`times-frac`
16×	`add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
4×	`insert-posit16` `distribute-lft-out--`
3×	`flip3--` `associate-l` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

74.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
40.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
16.0ms	(- (* b b) (* (* 3 a) c))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
117.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
104.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
78.0ms	(- (* b b) (* (* 3 a) c))

simplify5.7s

Counts

59 → 99

Calls

59 calls:

Slowest

365.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
296.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
287.0ms	(* (* (* 1/3 1/3) 1/3) (/ (* (* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (* (* a a) a)))
217.0ms	(- b (* 3/2 (/ (* a c) b)))
191.0ms	(+ (log 1/3) (- (log (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (log a)))

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.5b

regimes636.0ms

Accuracy

83.6% (4.5b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 33.3b

bsearch148.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

997.0ms	1084×	body	2560	valid
972.0ms	865×	body	1280	valid
739.0ms	5877×	body	80	valid
443.0ms	2872×	body	80	nan
306.0ms	475×	body	640	valid
134.0ms	93×	body	5120	valid
81.0ms	239×	body	320	valid
24.0ms	101×	body	160	valid