Details

sample142.0ms

Algorithm

intervals

Results

15.0ms	38×	body	1280	valid
14.0ms	188×	body	80	valid
14.0ms	27×	body	2560	valid
8.0ms	87×	body	80	nan
5.0ms	19×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify82.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

82.0ms

(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize25.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

Slowest

129.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
61.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series666.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

356.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
167.0ms	(sqrt (- (* b_2 b_2) (* a c)))
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
48.0ms	(- (* b_2 b_2) (* a c))

simplify3.9s

Counts

73 → 100

Calls

73 calls:

Slowest

366.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
270.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
270.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
244.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
239.0ms	(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize38.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

Slowest

149.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
33.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(- (* b_2 b_2) (* a c))

series326.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms	(- (* b_2 b_2) (* a c))

simplify5.0s

Counts

62 → 101

Calls

62 calls:

Slowest

484.0ms	(* (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
457.0ms	(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)
406.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) 1)
299.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
254.0ms	(* (+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (+ (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)

prune973.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
13.5b	(/ (- 0 (* a c)) a)
1.6b	(- (* b_2 b_2) (* a c))
1.0b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `sqrt-prod` `flip--` `associate-/l`
2×	`sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-sub` `div-exp` `distribute-frac-neg` `flip-+` `div-inv` `distribute-lft-out` `sub0-neg`

Counts

4 → 74

Calls

4 calls:

Slowest

46.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms	(/ (- 0 (* a c)) a)
14.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))
64.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ (- 0 (* a c)) a)

simplify4.3s

Counts

50 → 86

Calls

50 calls:

Slowest

1.4s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
275.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
273.0ms	(- (pow 0 3) (pow (* a c) 3))
262.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
232.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune852.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

localize24.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.6b	(- (* b_2 b_2) (* a c))
1.0b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
40×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`distribute-lft-out`
10×	`associate-/l*`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `neg-mul-1`
4×	`associate-/r*` `insert-posit16`
3×	`sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `distribute-frac-neg` `div-inv`

Counts

4 → 113

Calls

4 calls:

Slowest

39.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series459.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

243.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
88.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))
48.0ms	(- (* b_2 b_2) (* a c))

simplify5.0s

Counts

119 → 125

Calls

119 calls:

Slowest

310.0ms	(+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (- (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2)))
281.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
263.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
244.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
203.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.6b

regimes314.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.5b against oracle of 5.7b and baseline of 29.4b

bsearch316.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1089×	body	2560	valid
1.2s	5842×	body	80	valid
583.0ms	906×	body	1280	valid
320.0ms	2795×	body	80	nan
285.0ms	464×	body	640	valid
95.0ms	122×	body	5120	valid
69.0ms	205×	body	320	valid
26.0ms	111×	body	160	valid