Details

sample387.0ms

Algorithm

intervals

Results

65.0ms	38×	body	2560	valid
54.0ms	178×	body	80	valid
48.0ms	5×	body	320	valid
39.0ms	20×	body	640	valid
21.0ms	28×	body	1280	valid
14.0ms	97×	body	80	nan
3.0ms	2×	body	5120	valid
2.0ms	6×	body	160	valid

simplify114.0ms

Calls

1 calls:

Slowest

113.0ms

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize36.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b_2 b_2) (* a c)))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
0.3b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite249.0ms

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`

Calls

4 calls:

Slowest

118.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
87.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(- (* b_2 b_2) (* a c))

series419.0ms

Calls

4 calls:

Slowest

158.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))
101.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms	(- (* b_2 b_2) (* a c))

simplify6.0s

Calls

116 calls:

Slowest

521.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
371.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
361.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
331.0ms	(/ (* (* (- (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))
262.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.4b

localize18.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b_2 b_2) (* a c)))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
0.5b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite199.0ms

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`

Calls

4 calls:

Slowest

127.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
53.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series404.0ms

Calls

4 calls:

Slowest

148.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
121.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))
36.0ms	(- (* b_2 b_2) (* a c))

simplify6.6s

Calls

105 calls:

Slowest

512.0ms	(* (* (* (- (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)))
344.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
307.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
306.0ms	(* (+ (* (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)
266.0ms	(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) (/ 1 a))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.4b

localize446.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b_2 b_2) (* a c)))
18.5b	(/ (- 0 (* a c)) a)
0.8b	(- (* b_2 b_2) (* a c))
0.5b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `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` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `distribute-frac-neg` `flip-+` `div-inv` `distribute-lft-out` `sub0-neg`

Calls

4 calls:

Slowest

27.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(/ (- 0 (* a c)) a)
8.0ms	(- (* b_2 b_2) (* a c))

series280.0ms

Calls

4 calls:

Slowest

108.0ms	(sqrt (- (* b_2 b_2) (* a c)))
99.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ (- 0 (* a c)) a)

simplify4.9s

Calls

57 calls:

Slowest

1.6s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
334.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
246.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
239.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
228.0ms	(- (pow 0 3) (pow (* a c) 3))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.4b

localize32.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b_2 b_2) (* a c)))
0.8b	(- (* b_2 b_2) (* a c))
0.5b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
40×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`distribute-lft-out`
10×	`associate-/l*`
8×	`add-log-exp`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod`
5×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `distribute-frac-neg` `div-inv`

Calls

4 calls:

Slowest

58.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
47.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series520.0ms

Calls

4 calls:

Slowest

243.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
121.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))
64.0ms	(- (* b_2 b_2) (* a c))

simplify5.5s

Calls

126 calls:

Slowest

496.0ms	(+ (* (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)))
325.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
250.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
227.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
223.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.3b

regimes343.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.4b

bsearch214.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5800×	body	80	valid
906.0ms	1095×	body	2560	valid
595.0ms	920×	body	1280	valid
338.0ms	2941×	body	80	nan
253.0ms	451×	body	640	valid
145.0ms	243×	body	320	valid
86.0ms	110×	body	5120	valid
22.0ms	116×	body	160	valid