Details

sample318.0ms

Algorithm

intervals

Results

51.0ms	178×	body	80	valid
46.0ms	28×	body	1280	valid
38.0ms	38×	body	2560	valid
12.0ms	97×	body	80	nan
11.0ms	20×	body	640	valid
2.0ms	2×	body	5120	valid
2.0ms	5×	body	320	valid
2.0ms	6×	body	160	valid

simplify557.0ms

Calls

1 calls:

Slowest

556.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize95.0ms

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)

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`fma-neg`
6×	`sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `pow1/2` `diff-log` `div-sub` `prod-diff` `div-inv`

Calls

4 calls:

Slowest

128.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
39.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series327.0ms

Calls

4 calls:

Slowest

108.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
38.0ms	(- (* b_2 b_2) (* a c))

simplify2.1s

Calls

31 calls:

Slowest

444.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
276.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
176.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
161.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
131.0ms	(- (* 1/2 (/ (* a c) b_2)) b_2)

prune872.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.4b

localize6.0ms

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))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`fma-neg`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u`
3×	`associate-l`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*l/`
1×	`rem-sqrt-square` `pow1/2` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `associate-r/` `un-div-inv` `-commutative` `cbrt-unprod` `div-inv`

Calls

4 calls:

Slowest

38.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
16.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series367.0ms

Calls

4 calls:

Slowest

122.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
120.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))
39.0ms	(- (* b_2 b_2) (* a c))

simplify4.0s

Calls

41 calls:

Slowest

456.0ms	(* (* (* (- (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)))
395.0ms	(* (+ (* (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)
381.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) (/ 1 a))
380.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
351.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) 1)

prune924.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.4b

localize14.0ms

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)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`fma-def` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--` `associate-/l*`
2×	`sqrt-div` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `distribute-frac-neg` `flip-+` `div-inv` `sub0-neg`

Calls

4 calls:

Slowest

11.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(/ (- 0 (* a c)) a)
3.0ms	(- (* b_2 b_2) (* a c))

series316.0ms

Calls

4 calls:

Slowest

123.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))
64.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(/ (- 0 (* a c)) a)

simplify2.2s

Calls

32 calls:

Slowest

364.0ms	(- (pow 0 3) (pow (* a c) 3))
326.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
256.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
248.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
203.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune843.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.4b

localize11.0ms

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))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `neg-mul-1` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `distribute-frac-neg` `div-inv`

Calls

4 calls:

Slowest

28.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(- (* b_2 b_2) (* a c))

series506.0ms

Calls

4 calls:

Slowest

249.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
103.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(- (* b_2 b_2) (* a c))

simplify3.3s

Calls

61 calls:

Slowest

446.0ms	(+ (* (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)))
389.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
252.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
228.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
217.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune986.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.3b

regimes425.0ms

Accuracy

96.2% (0.9b remaining)

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

bsearch227.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

895.0ms	1095×	body	2560	valid
784.0ms	5800×	body	80	valid
586.0ms	920×	body	1280	valid
574.0ms	243×	body	320	valid
305.0ms	2941×	body	80	nan
261.0ms	451×	body	640	valid
185.0ms	110×	body	5120	valid
26.0ms	116×	body	160	valid