Details

sample106.0ms

Algorithm

intervals

Results

25.0ms	183×	body	80	valid
22.0ms	31×	body	2560	valid
20.0ms	35×	body	1280	valid
10.0ms	18×	body	640	valid
8.0ms	64×	body	80	nan
2.0ms	6×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	160	valid

simplify142.0ms

Calls

1 calls:

Slowest

142.0ms

(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize40.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma b b (* (* a c) -4)))
1.3b	(fma b b (* (* a c) -4))
0.8b	(- (sqrt (fma b b (* (* a c) -4))) b)
0.1b	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

17.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
6.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series233.0ms

Calls

4 calls:

Slowest

73.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
67.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
49.0ms	(sqrt (fma b b (* (* a c) -4)))
44.0ms	(fma b b (* (* a c) -4))

simplify1.2s

Calls

26 calls:

Slowest

204.0ms	(- b (* 2 (/ (* a c) b)))
115.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
86.0ms	(* -2 (/ (* a c) b))
73.0ms	(- (pow b 2) (* 4 (* a c)))
73.0ms	(- (pow b 2) (* 4 (* a c)))

prune970.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize16.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma (* a c) -4 (* b b)))
1.0b	(fma (* a c) -4 (* b b))
0.8b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

19.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
6.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series262.0ms

Calls

4 calls:

Slowest

116.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
60.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
53.0ms	(sqrt (fma (* a c) -4 (* b b)))
33.0ms	(fma (* a c) -4 (* b b))

simplify864.0ms

Calls

26 calls:

Slowest

93.0ms	(- (pow b 2) (* 4 (* a c)))
72.0ms	(* (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
69.0ms	(- (pow b 2) (* 4 (* a c)))
60.0ms	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
59.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)

prune859.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma (* a c) -4 (* b b)))
1.0b	(fma (* a c) -4 (* b b))
0.8b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.2b	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

12.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
0.0ms	(fma (* a c) -4 (* b b))

series256.0ms

Calls

4 calls:

Slowest

92.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
69.0ms	(sqrt (fma (* a c) -4 (* b b)))
53.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
42.0ms	(fma (* a c) -4 (* b b))

simplify867.0ms

Calls

27 calls:

Slowest

95.0ms	(- (pow b 2) (* 4 (* a c)))
73.0ms	(/ 1 (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
72.0ms	(/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
68.0ms	(cbrt (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
66.0ms	(- (pow b 2) (* 4 (* a c)))

prune1.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

localize6.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma (* a c) -4 (* b b)))
1.0b	(fma (* a c) -4 (* b b))
0.8b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.2b	(* (/ 1 a) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

10.0ms	(* (/ 1 a) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
6.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series256.0ms

Calls

4 calls:

Slowest

103.0ms	(* (/ 1 a) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
65.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
54.0ms	(sqrt (fma (* a c) -4 (* b b)))
33.0ms	(fma (* a c) -4 (* b b))

simplify1.8s

Calls

33 calls:

Slowest

362.0ms	(* (/ 1 a) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
234.0ms	(+ (log (/ 1 a)) (log (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
186.0ms	(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
163.0ms	(* 1 (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
86.0ms	(- (pow b 2) (* 4 (* a c)))

prune897.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

regimes570.0ms

Accuracy

84.7% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.6b

bsearch226.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.1s	924×	body	1280	valid
1.1s	1086×	body	2560	valid
855.0ms	5809×	body	80	valid
394.0ms	2848×	body	80	nan
257.0ms	460×	body	640	valid
122.0ms	96×	body	5120	valid
111.0ms	222×	body	320	valid
28.0ms	108×	body	160	valid