Details

sample224.0ms

Algorithm

intervals

Results

28.0ms	199×	body	80	valid
22.0ms	25×	body	2560	valid
18.0ms	26×	body	1280	valid
13.0ms	81×	body	80	nan
9.0ms	14×	body	640	valid
4.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	5120	valid

simplify128.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

127.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize50.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite133.0ms

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

73.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
33.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series329.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
90.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))
40.0ms	(- (* b_2 b_2) (* a c))

simplify4.1s

Counts

73 → 100

Calls

73 calls:

Slowest

412.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
308.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
305.0ms	(/ (* (* (- (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))
285.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
237.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize20.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite168.0ms

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

104.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
48.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))
50.0ms	(- (* b_2 b_2) (* a c))

simplify4.0s

Counts

73 → 100

Calls

73 calls:

Slowest

374.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
317.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
295.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
287.0ms	(/ (* (* (- (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))
202.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize27.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 166

Calls

4 calls:

Slowest

55.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(- (* b_2 b_2) (* a c))

series900.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

478.0ms	(- (* b_2 b_2) (* a c))
200.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
126.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify20.2s

Counts

204 → 178

Calls

204 calls:

Slowest

585.0ms	(/ (* (* 1 1) 1) (/ (* (* a a) a) (* (* (- (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))))
372.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))
365.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
353.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
347.0ms	(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

localize51.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
18.1b	(/ (- 0 (* a c)) a)
0.9b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))

rewrite77.0ms

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

36.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(/ (- 0 (* a c)) a)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series226.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

96.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))
42.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ (- 0 (* a c)) a)

simplify4.3s

Counts

50 → 86

Calls

50 calls:

Slowest

1.3s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
309.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
253.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
249.0ms	(- (pow 0 3) (pow (* a c) 3))
187.0ms	(/ (exp (* b_2 b_2)) (exp (* a c)))

prune878.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

regimes251.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.1b

bsearch347.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

917.0ms	1031×	body	2560	valid
774.0ms	5890×	body	80	valid
673.0ms	426×	body	640	valid
560.0ms	892×	body	1280	valid
422.0ms	2856×	body	80	nan
118.0ms	101×	body	5120	valid
115.0ms	227×	body	320	valid
25.0ms	114×	body	160	valid