Details

sample425.0ms

Algorithm

intervals

Results

43.0ms	120×	body	320	valid
32.0ms	276×	body	80	nan
32.0ms	15×	body	640	valid
28.0ms	532×	pre	80	true
20.0ms	84×	body	160	valid
4.0ms	37×	body	80	valid

simplify137.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

137.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.1b

localize29.0ms

Local error

Found 4 expressions with local error:

24.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b	(fma c (* -4 a) (* b b))
0.0b	(sqrt (fma c (* -4 a) (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

Slowest

17.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
9.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))
0.0ms	(fma c (* -4 a) (* b b))

series397.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(sqrt (fma c (* -4 a) (* b b)))
103.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
90.0ms	(fma c (* -4 a) (* b b))
87.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

simplify14.8s

Counts

225 → 191

Calls

225 calls:

Slowest

493.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) 1) (sqrt a))
432.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
263.0ms	(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))
202.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
191.0ms	(/ (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.4s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 48.9b

localize36.0ms

Local error

Found 4 expressions with local error:

51.5b	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.1b	(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.1b	(fma c (* -4 a) (* b b))
0.1b	(fma c (* -4 a) (* b b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
46×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/l*`
9×	`add-cbrt-cube` `add-exp-log`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `div-exp` `fma-udef`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 106

Calls

4 calls:

Slowest

8.0ms	(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.0ms	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms	(fma c (* -4 a) (* b b))
0.0ms	(fma c (* -4 a) (* b b))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

573.0ms	(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
434.0ms	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
86.0ms	(fma c (* -4 a) (* b b))
68.0ms	(fma c (* -4 a) (* b b))

simplify9.5s

Counts

109 → 118

Calls

109 calls:

Slowest

462.0ms	(/ (/ (* (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
377.0ms	(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
343.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
300.0ms	(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
227.0ms	(/ (/ (* (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune1.4s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 48.7b

localize85.0ms

Local error

Found 4 expressions with local error:

51.5b	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
51.5b	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
51.5b	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.4b	(cbrt (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
43×	`cbrt-prod`
39×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`fma-udef`
1×	`cbrt-div` `pow1/3`

Counts

4 → 88

Calls

4 calls:

Slowest

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

series1.8s

Counts

4 → 12

Calls

4 calls:

Slowest

588.0ms	(cbrt (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a))
439.0ms	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
403.0ms	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
375.0ms	(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify7.2s

Counts

56 → 100

Calls

56 calls:

Slowest

652.0ms	(- (+ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))) (cbrt -1/2)) (* 5/216 (/ (* (exp (* 1/3 (+ (* 4 (log (/ -1 a))) (* 2 (log (/ -1 b)))))) (* (cbrt -1/2) (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 6))) c))) (* 1/3 (/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))) (* (cbrt -1/2) (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2))) b)))
555.0ms	(- (* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b)))))) (+ (* 5/216 (/ (* (cbrt 1/2) (* (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 6) (exp (* 1/3 (+ (* 2 (log (/ 1 b))) (* 4 (log (/ 1 a)))))))) c)) (* 1/3 (/ (* (cbrt 1/2) (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2))) b))))
434.0ms	(cbrt (/ (/ (* (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a))))
377.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
373.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.4s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 48.3b

localize59.0ms

Local error

Found 4 expressions with local error:

51.5b	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.6b	(cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))))
0.5b	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
0.3b	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r`
5×	`fma-udef`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 87

Calls

4 calls:

Slowest

15.0ms	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))
11.0ms	(cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))))
6.0ms	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
0.0ms	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series772.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

417.0ms	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
192.0ms	(* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))
91.0ms	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
72.0ms	(cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))))

simplify6.6s

Counts

63 → 99

Calls

63 calls:

Slowest

1.0s	(* (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))) (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b))))
362.0ms	(- (+ (pow b 4) (* 16 (* (pow a 2) (pow c 2)))) (* 8 (* a (* (pow b 2) c))))
328.0ms	(+ (log (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))) (log (fma c (* -4 a) (* b b))))
312.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
299.0ms	(- (+ (pow b 4) (* 16 (* (pow a 2) (pow c 2)))) (* 8 (* a (* (pow b 2) c))))

prune1.5s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 48.3b

regimes683.0ms

Accuracy

0% (3.1b remaining)

Error of 52.0b against oracle of 48.9b and baseline of 52.0b

bsearch5.0ms

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.4s	3662×	body	320	valid
1.3s	8153×	body	80	nan
1.1s	16153×	pre	80	true
952.0ms	2958×	body	160	valid
294.0ms	497×	body	640	valid
192.0ms	883×	body	80	valid