Details

sample169.0ms

Algorithm

intervals

Results

23.0ms	200×	body	80	valid
22.0ms	34×	body	1280	valid
14.0ms	22×	body	2560	valid
10.0ms	104×	body	80	nan
4.0ms	11×	body	640	valid
2.0ms	2×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify95.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

94.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize30.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b_2 b_2) (* a c)))
1.4b	(- (* b_2 b_2) (* a c))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite137.0ms

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

71.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(- (* b_2 b_2) (* a c))

series578.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

164.0ms	(- (* b_2 b_2) (* a c))
160.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
135.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
118.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.8s

Counts

116 → 134

Calls

116 calls:

Slowest

497.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
350.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
288.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
286.0ms	(/ (* (* (- (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))
249.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize27.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b_2 b_2) (* a c)))
1.4b	(- (* b_2 b_2) (* a c))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite201.0ms

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

126.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
49.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))
36.0ms	(- (* b_2 b_2) (* a c))

simplify6.8s

Counts

105 → 135

Calls

105 calls:

Slowest

838.0ms	(* (+ (* (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)
577.0ms	(* (* (* (- (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)))
352.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
280.0ms	(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)
269.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize21.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b_2 b_2) (* a c)))
14.4b	(/ (- 0 (* a c)) a)
1.4b	(- (* b_2 b_2) (* a c))
0.7b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite91.0ms

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`

Counts

4 → 90

Calls

4 calls:

Slowest

49.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ (- 0 (* a c)) a)

series253.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

95.0ms	(sqrt (- (* b_2 b_2) (* a c)))
78.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (- 0 (* a c)) a)

simplify5.2s

Counts

57 → 102

Calls

57 calls:

Slowest

1.6s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
355.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
324.0ms	(- (pow 0 3) (pow (* a c) 3))
262.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
224.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize33.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b_2 b_2) (* a c)))
1.4b	(- (* b_2 b_2) (* a c))
0.7b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.3b	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite90.0ms

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`

Counts

4 → 129

Calls

4 calls:

Slowest

37.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
28.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series516.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

261.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
107.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))
64.0ms	(- (* b_2 b_2) (* a c))

simplify5.6s

Counts

126 → 141

Calls

126 calls:

Slowest

418.0ms	(+ (* (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)))
338.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
315.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
276.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
225.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

regimes313.0ms

Accuracy

80.8% (4.5b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 29.1b

bsearch209.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

834.0ms	5763×	body	80	valid
744.0ms	1113×	body	2560	valid
636.0ms	885×	body	1280	valid
632.0ms	485×	body	640	valid
409.0ms	2953×	body	80	nan
122.0ms	115×	body	5120	valid
67.0ms	229×	body	320	valid
22.0ms	117×	body	160	valid