Details

sample134.0ms

Algorithm

intervals

Results

44.0ms	194×	body	80	valid
27.0ms	32×	body	2560	valid
18.0ms	27×	body	1280	valid
14.0ms	95×	body	80	nan
5.0ms	5×	body	5120	valid
5.0ms	8×	body	640	valid
2.0ms	7×	body	320	valid
2.0ms	7×	body	160	valid

simplify195.0ms

Calls

1 calls:

Slowest

195.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize23.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (fma b b (* (* a c) -4)))
2.4b	(- (sqrt (fma b b (* (* a c) -4))) b)
1.3b	(fma b b (* (* a c) -4))
0.1b	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite27.0ms

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

18.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
6.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series245.0ms

Calls

4 calls:

Slowest

72.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
70.0ms	(sqrt (fma b b (* (* a c) -4)))
62.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
40.0ms	(fma b b (* (* a c) -4))

simplify1.2s

Calls

26 calls:

Slowest

234.0ms	(- b (* 2 (/ (* a c) b)))
114.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
96.0ms	(* -2 (/ (* a c) b))
82.0ms	(- (pow b 2) (* 4 (* a c)))
79.0ms	(- (* 2 (/ (* a c) b)) b)

prune928.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize6.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (fma b b (* (* a c) -4)))
2.4b	(- (sqrt (fma b b (* (* a c) -4))) b)
1.3b	(fma b b (* (* a c) -4))
0.2b	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))

rewrite29.0ms

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/` `un-div-inv` `*-commutative` `cbrt-unprod` `fma-udef` `flip--`

Calls

4 calls:

Slowest

20.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
6.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series227.0ms

Calls

4 calls:

Slowest

73.0ms	(sqrt (fma b b (* (* a c) -4)))
64.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
63.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
27.0ms	(fma b b (* (* a c) -4))

simplify2.1s

Calls

34 calls:

Slowest

344.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
209.0ms	(- b (* 2 (/ (* a c) b)))
199.0ms	(+ (log (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (log (/ 1 a)))
193.0ms	(* (* (* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
119.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

localize7.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (fma b b (* (* a c) -4)))
2.4b	(- (sqrt (fma b b (* (* a c) -4))) b)
1.3b	(fma b b (* (* a c) -4))
0.2b	(/ 1 (/ a (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))

rewrite16.0ms

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

series246.0ms

Calls

4 calls:

Slowest

90.0ms	(/ 1 (/ a (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))
68.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
55.0ms	(sqrt (fma b b (* (* a c) -4)))
33.0ms	(fma b b (* (* a c) -4))

simplify1.2s

Calls

27 calls:

Slowest

247.0ms	(- b (* 2 (/ (* a c) b)))
96.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
95.0ms	(- (* 2 (/ (* a c) b)) b)
84.0ms	(* -2 (/ (* a c) b))
63.0ms	(- (pow b 2) (* 4 (* a c)))

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize23.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (fma -4 (* a c) (* b b)))
2.4b	(- (sqrt (fma -4 (* a c) (* b b))) b)
1.0b	(fma -4 (* a c) (* b b))
0.2b	(/ (/ 1 a) (/ 2 (- (sqrt (fma -4 (* a c) (* b b))) b)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

12.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
11.0ms	(/ (/ 1 a) (/ 2 (- (sqrt (fma -4 (* a c) (* b b))) b)))
2.0ms	(sqrt (fma -4 (* a c) (* b b)))
1.0ms	(fma -4 (* a c) (* b b))

series227.0ms

Calls

4 calls:

Slowest

94.0ms	(/ (/ 1 a) (/ 2 (- (sqrt (fma -4 (* a c) (* b b))) b)))
53.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
46.0ms	(sqrt (fma -4 (* a c) (* b b)))
34.0ms	(fma -4 (* a c) (* b b))

simplify7.4s

Calls

80 calls:

Slowest

556.0ms	(/ 1 (/ 2 (- (* (sqrt (fma -4 (* a c) (* b b))) (sqrt (fma -4 (* a c) (* b b)))) (* b b))))
479.0ms	(/ 1 (/ 2 (- (* (sqrt (fma -4 (* a c) (* b b))) (sqrt (fma -4 (* a c) (* b b)))) (* b b))))
431.0ms	(/ (/ 1 a) (/ 2 (- (sqrt (fma -4 (* a c) (* b b))) b)))
425.0ms	(/ (/ 1 a) (/ 2 (- (sqrt (fma -4 (* a c) (* b b))) b)))
346.0ms	(/ (sqrt (/ 1 a)) (/ 2 (- (pow (sqrt (fma -4 (* a c) (* b b))) 3) (pow b 3))))

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.4b

regimes420.0ms

Accuracy

83.8% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 33.8b

bsearch216.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.8s	1116×	body	2560	valid
905.0ms	5803×	body	80	valid
667.0ms	878×	body	1280	valid
476.0ms	2895×	body	80	nan
275.0ms	470×	body	640	valid
171.0ms	117×	body	5120	valid
118.0ms	216×	body	320	valid
32.0ms	128×	body	160	valid