Details

sample140.0ms

Algorithm

intervals

Results

14.0ms	195×	body	80	valid
10.0ms	30×	body	1280	valid
10.0ms	24×	body	2560	valid
9.0ms	100×	body	80	nan
4.0ms	14×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify67.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

67.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize18.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.6b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

Slowest

99.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
53.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series382.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
117.0ms	(sqrt (- (* b_2 b_2) (* a c)))
88.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms	(- (* b_2 b_2) (* a c))

simplify11.0s

Counts

182 → 134

Calls

182 calls:

Slowest

656.0ms	(+ (* (* b_2 b_2) (* b_2 b_2)) (+ (* (* a c) (* a c)) (* (* b_2 b_2) (* a c))))
441.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
416.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
376.0ms	(- (pow (* b_2 b_2) 3) (pow (* a c) 3))
341.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize32.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b_2 b_2) (* a c)))
11.2b	(/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
2.8b	(/ (/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
0.9b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac`
158×	`*-un-lft-identity`
95×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
36×	`associate-/l*`
32×	`distribute-lft-out`
21×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `distribute-frac-neg`
2×	`neg-sub0` `clear-num` `frac-2neg` `sqrt-div`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3--` `pow1/2` `flip--` `associate-/l/`

Counts

4 → 235

Calls

4 calls:

Slowest

76.0ms	(/ (/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
39.0ms	(/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
35.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series698.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

287.0ms	(/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
210.0ms	(/ (/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
101.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.2s

Counts

363 → 247

Calls

363 calls:

Slowest

755.0ms	(/ (/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (+ (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))
651.0ms	(* (* (/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
644.0ms	(log (/ (/ (- (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
542.0ms	(+ (* (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)))
521.0ms	(/ a (/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))

prune2.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize38.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.9b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `associate-/l*`
2×	`flip3-+` `flip3--` `sqrt-div` `associate-/r/` `flip-+` `flip--`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `div-inv`

Counts

4 → 89

Calls

4 calls:

Slowest

45.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
15.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series474.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

235.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
43.0ms	(- (* b_2 b_2) (* a c))

simplify9.5s

Counts

118 → 101

Calls

118 calls:

Slowest

991.0ms	(/ c (- (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c))))))
890.0ms	(- (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))))
466.0ms	(* (* (/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) (/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
396.0ms	(+ (* b_2 b_2) (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 (sqrt (- (* b_2 b_2) (* a c))))))
393.0ms	(- (pow (* b_2 b_2) 3) (pow (* a c) 3))

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.7b

localize34.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.6b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `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 → 123

Calls

4 calls:

Slowest

146.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
38.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(- (* b_2 b_2) (* a c))

series395.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))
54.0ms	(- (* b_2 b_2) (* a c))

simplify15.3s

Counts

166 → 135

Calls

166 calls:

Slowest

989.0ms	(* (* (* (- (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)))
426.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
391.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
388.0ms	(exp (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a)))
377.0ms	(- (pow (* b_2 b_2) 3) (pow (* a c) 3))

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.7b

regimes332.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 28.9b

bsearch195.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

920.0ms	1051×	body	2560	valid
875.0ms	2921×	body	80	nan
851.0ms	5842×	body	80	valid
546.0ms	888×	body	1280	valid
239.0ms	489×	body	640	valid
118.0ms	108×	body	5120	valid
69.0ms	222×	body	320	valid
24.0ms	116×	body	160	valid