Details

sample103.0ms

Algorithm

intervals

Results

29.0ms	91×	body	80	nan
20.0ms	197×	body	80	valid
18.0ms	28×	body	2560	valid
10.0ms	20×	body	1280	valid
7.0ms	19×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify123.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

123.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize19.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (- (* b b) (* (* 3 a) c)))
1.0b	(- (* b b) (* (* 3 a) c))
0.5b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))

rewrite179.0ms

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

95.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
49.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
20.0ms	(- (* b b) (* (* 3 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
114.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
90.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
75.0ms	(- (* b b) (* (* 3 a) c))

simplify5.3s

Counts

49 → 88

Calls

49 calls:

Slowest

548.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
392.0ms	(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
339.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
297.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
239.0ms	(/ (* (* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (* (* (* 3 3) 3) (* (* a a) a)))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

localize45.0ms

Local error

Found 4 expressions with local error:

22.1b	(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)

rewrite93.0ms

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

41.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.0ms	(* (* 3 a) c)
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
13.0ms	(- (* b b) (* (* 3 a) c))

series283.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

96.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
92.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
69.0ms	(- (* b b) (* (* 3 a) c))
25.0ms	(* (* 3 a) c)

simplify3.3s

Counts

34 → 76

Calls

34 calls:

Slowest

489.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
427.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
306.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
300.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
201.0ms	(- b (* 3/2 (/ (* a c) b)))

prune971.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.5b

localize51.0ms

Local error

Found 4 expressions with local error:

22.1b	(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))

rewrite203.0ms

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

118.0ms	(/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) (* 3 a))
56.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
15.0ms	(+ (* b b) (* (* c -3) a))
12.0ms	(sqrt (+ (* b b) (* (* c -3) a)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

133.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
125.0ms	(/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) (* 3 a))
124.0ms	(sqrt (+ (* b b) (* (* c -3) a)))
81.0ms	(+ (* b b) (* (* c -3) a))

simplify4.6s

Counts

49 → 87

Calls

49 calls:

Slowest

793.0ms	(- (* (sqrt (+ (* b b) (* (* c -3) a))) (sqrt (+ (* b b) (* (* c -3) a)))) (* b b))
409.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* c -3) a) (* (* c -3) a))))
277.0ms	(- (pow (sqrt (+ (* b b) (* (* c -3) a))) 3) (pow b 3))
264.0ms	(* (exp (* b b)) (exp (* (* c -3) a)))
243.0ms	(- b (* 3/2 (/ (* a c) b)))

prune988.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.5b

localize22.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (+ (* b b) (* (* c -3) a)))
1.0b	(+ (* b b) (* (* c -3) a))
0.5b	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
0.3b	(* 1/3 (/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) a))

rewrite169.0ms

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×	`associate-l`
2×	`flip3-+` `sqrt-div` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--`

Counts

4 → 86

Calls

4 calls:

Slowest

81.0ms	(* 1/3 (/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) a))
55.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
20.0ms	(+ (* b b) (* (* c -3) a))
10.0ms	(sqrt (+ (* b b) (* (* c -3) a)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

163.0ms	(* 1/3 (/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) a))
120.0ms	(sqrt (+ (* b b) (* (* c -3) a)))
101.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
52.0ms	(+ (* b b) (* (* c -3) a))

simplify3.9s

Counts

59 → 98

Calls

59 calls:

Slowest

332.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* c -3) a) (* (* c -3) a))))
244.0ms	(* (exp (* b b)) (exp (* (* c -3) a)))
231.0ms	(* (* (* 1/3 1/3) 1/3) (/ (* (* (- (sqrt (+ (* b b) (* (* c -3) a))) b) (- (sqrt (+ (* b b) (* (* c -3) a))) b)) (- (sqrt (+ (* b b) (* (* c -3) a))) b)) (* (* a a) a)))
222.0ms	(- b (* 3/2 (/ (* a c) b)))
175.0ms	(* (* (* 1/3 1/3) 1/3) (* (* (/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) a) (/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) a)) (/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) a)))

prune1.2s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 6.5b

regimes960.0ms

Accuracy

82.9% (4.8b remaining)

Error of 10.1b against oracle of 5.3b and baseline of 33.2b

bsearch248.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.4s	1009×	body	2560	valid
1.1s	889×	body	1280	valid
837.0ms	5885×	body	80	valid
417.0ms	2893×	body	80	nan
277.0ms	469×	body	640	valid
119.0ms	259×	body	320	valid
85.0ms	99×	body	5120	valid
25.0ms	109×	body	160	valid