Details

sample144.0ms

Algorithm

intervals

Results

57.0ms	38×	body	2560	valid
23.0ms	178×	body	80	valid
20.0ms	28×	body	1280	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

simplify488.0ms

Calls

1 calls:

Slowest

488.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize28.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma b b (* (* a c) -4)))
1.5b	(- (sqrt (fma b b (* (* a c) -4))) b)
1.0b	(fma b b (* (* a c) -4))
0.2b	(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)

rewrite29.0ms

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` `add-log-exp`
3×	`associate-/l*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `pow1/2` `div-sub` `fma-udef` `div-inv`

Calls

4 calls:

Slowest

16.0ms	(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)
11.0ms	(- (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))

series422.0ms

Calls

4 calls:

Slowest

126.0ms	(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)
118.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
104.0ms	(sqrt (fma b b (* (* a c) -4)))
73.0ms	(fma b b (* (* a c) -4))

simplify1.9s

Calls

26 calls:

Slowest

465.0ms	(- (* (sqrt (fma b b (* (* a c) -4))) (sqrt (fma b b (* (* a c) -4)))) (* b b))
169.0ms	(- (pow (sqrt (fma b b (* (* a c) -4))) 3) (pow b 3))
164.0ms	(- b (* 2 (/ (* a c) b)))
140.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
128.0ms	(* -1 (/ (* a c) b))

prune894.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize36.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma b b (* (* a c) -4)))
13.2b	(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
3.4b	(/ (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
1.0b	(fma b b (* (* a c) -4))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

18.0ms	(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
18.0ms	(/ (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
2.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series639.0ms

Calls

4 calls:

Slowest

256.0ms	(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
219.0ms	(/ (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
101.0ms	(sqrt (fma b b (* (* a c) -4)))
63.0ms	(fma b b (* (* a c) -4))

simplify4.0s

Calls

31 calls:

Slowest

1.3s	(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* 2 (+ (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))))
452.0ms	(sqrt (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
346.0ms	(+ (* (sqrt (fma b b (* (* a c) -4))) (sqrt (fma b b (* (* a c) -4)))) (- (* b b) (* (sqrt (fma b b (* (* a c) -4))) b)))
324.0ms	(* (cbrt (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))) (cbrt (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))))
281.0ms	(- (log (* (* a -4) c)) (log (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.3b

localize26.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma b b (* (* a c) -4)))
3.4b	(/ (* (/ a -1/2) (/ c (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
1.5b	(* (/ a -1/2) (/ c (+ (sqrt (fma b b (* (* a c) -4))) b)))
1.0b	(fma b b (* (* a c) -4))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

15.0ms	(/ (* (/ a -1/2) (/ c (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
9.0ms	(* (/ a -1/2) (/ c (+ (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))

series694.0ms

Calls

4 calls:

Slowest

299.0ms	(* (/ a -1/2) (/ c (+ (sqrt (fma b b (* (* a c) -4))) b)))
213.0ms	(/ (* (/ a -1/2) (/ c (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
103.0ms	(sqrt (fma b b (* (* a c) -4)))
79.0ms	(fma b b (* (* a c) -4))

simplify1.9s

Calls

35 calls:

Slowest

356.0ms	(+ (* (sqrt (fma b b (* (* a c) -4))) (sqrt (fma b b (* (* a c) -4)))) (- (* b b) (* (sqrt (fma b b (* (* a c) -4))) b)))
271.0ms	(- b (* 2 (/ (* a c) b)))
242.0ms	(+ (log (/ a -1/2)) (log (/ c (+ (sqrt (fma b b (* (* a c) -4))) b))))
143.0ms	(* (* (* (/ a -1/2) (/ a -1/2)) (/ a -1/2)) (* (* (/ c (+ (sqrt (fma b b (* (* a c) -4))) b)) (/ c (+ (sqrt (fma b b (* (* a c) -4))) b))) (/ c (+ (sqrt (fma b b (* (* a c) -4))) b))))
111.0ms	(* (/ a -1/2) (/ c (+ (sqrt (fma b b (* (* a c) -4))) b)))

prune959.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma b b (* (* a c) -4)))
13.2b	(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
3.4b	(/ a (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
1.0b	(fma b b (* (* a c) -4))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

14.0ms	(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
2.0ms	(sqrt (fma b b (* (* a c) -4)))
1.0ms	(/ a (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
0.0ms	(fma b b (* (* a c) -4))

series611.0ms

Calls

4 calls:

Slowest

303.0ms	(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
129.0ms	(/ a (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
104.0ms	(sqrt (fma b b (* (* a c) -4)))
74.0ms	(fma b b (* (* a c) -4))

simplify4.2s

Calls

32 calls:

Slowest

1.2s	(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* 2 (+ (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))))
387.0ms	(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
379.0ms	(+ (* (sqrt (fma b b (* (* a c) -4))) (sqrt (fma b b (* (* a c) -4)))) (- (* b b) (* (sqrt (fma b b (* (* a c) -4))) b)))
366.0ms	(cbrt (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
336.0ms	(- (log (* (* a -4) c)) (log (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))

prune985.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.6b

regimes376.0ms

Accuracy

83.4% (4.4b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 32.4b

bsearch233.0ms

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.4s	1093×	body	2560	valid
991.0ms	2941×	body	80	nan
978.0ms	5797×	body	80	valid
753.0ms	916×	body	1280	valid
276.0ms	453×	body	640	valid
118.0ms	240×	body	320	valid
115.0ms	110×	body	5120	valid
33.0ms	120×	body	160	valid