Details

sample177.0ms

Algorithm

intervals

Results

53.0ms	38×	body	2560	valid
18.0ms	186×	body	80	valid
13.0ms	27×	body	1280	valid
12.0ms	92×	body	80	nan
7.0ms	13×	body	640	valid
3.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	160	valid

simplify68.0ms

Calls

1 calls:

Slowest

67.0ms

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize28.0ms

Local error

Found 4 expressions with local error:

21.1b	(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)

rewrite207.0ms

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

88.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
86.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series365.0ms

Calls

4 calls:

Slowest

114.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
110.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))
51.0ms	(- (* b_2 b_2) (* a c))

simplify6.5s

Calls

116 calls:

Slowest

564.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
404.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
364.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
338.0ms	(/ (* (* (- (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))
235.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize30.0ms

Local error

Found 4 expressions with local error:

21.1b	(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)

rewrite221.0ms

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

100.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
83.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(- (* b_2 b_2) (* a c))

series341.0ms

Calls

4 calls:

Slowest

102.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))
60.0ms	(- (* b_2 b_2) (* a c))

simplify6.4s

Calls

116 calls:

Slowest

599.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
341.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
321.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
303.0ms	(/ (* (* (- (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))
294.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite278.0ms

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

180.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(- (* b_2 b_2) (* a c))

series309.0ms

Calls

4 calls:

Slowest

109.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
36.0ms	(- (* b_2 b_2) (* a c))

simplify7.0s

Calls

105 calls:

Slowest

573.0ms	(* (* (* (- (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)))
414.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
396.0ms	(* (+ (* (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)
303.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
298.0ms	(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize46.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
14.2b	(/ (- 0 (* a c)) a)
1.1b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))

rewrite78.0ms

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

37.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ (- 0 (* a c)) a)

series258.0ms

Calls

4 calls:

Slowest

109.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (- 0 (* a c)) a)

simplify5.1s

Calls

57 calls:

Slowest

1.5s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
414.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
294.0ms	(- (pow 0 3) (pow (* a c) 3))
284.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
268.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.5b

regimes310.0ms

Accuracy

94.2% (1.4b remaining)

Error of 7.0b against oracle of 5.6b and baseline of 29.6b

bsearch321.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5881×	body	80	valid
864.0ms	1063×	body	2560	valid
617.0ms	913×	body	1280	valid
390.0ms	2865×	body	80	nan
245.0ms	413×	body	640	valid
132.0ms	123×	body	5120	valid
73.0ms	229×	body	320	valid
61.0ms	104×	body	160	valid