Details

sample117.0ms

Algorithm

intervals

Results

31.0ms	45×	body	2560	valid
22.0ms	177×	body	80	valid
19.0ms	30×	body	1280	valid
10.0ms	84×	body	80	nan
7.0ms	7×	body	5120	valid
6.0ms	14×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	5×	body	160	valid

simplify142.0ms

Calls

1 calls:

Slowest

142.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize31.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.5b	(* (* 3 a) c)
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

44.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
5.0ms	(* (* 3 a) c)

series186.0ms

Calls

4 calls:

Slowest

67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
60.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
42.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
17.0ms	(* (* 3 a) c)

simplify3.8s

Calls

37 calls:

Slowest

546.0ms	(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
517.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))
285.0ms	(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
266.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
213.0ms	(- b (* 3/2 (/ (* a c) b)))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize17.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma -3 (* c a) (* b b)))
1.2b	(- (sqrt (fma -3 (* c a) (* b b))) b)
0.2b	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
0.1b	(fma -3 (* c a) (* b b))

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` `associate-r` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `pow1/2` `associate-r/` `-commutative` `fma-udef` `div-inv` `flip--`

Calls

4 calls:

Slowest

12.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
12.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
2.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))

series200.0ms

Calls

4 calls:

Slowest

58.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
50.0ms	(sqrt (fma -3 (* c a) (* b b)))
46.0ms	(fma -3 (* c a) (* b b))
45.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify654.0ms

Calls

25 calls:

Slowest

100.0ms	(- (pow b 2) (* 3 (* a c)))
88.0ms	(- (pow b 2) (* 3 (* a c)))
61.0ms	(- (pow b 2) (* 3 (* a c)))
59.0ms	(cbrt (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
52.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)

prune971.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.5b	(* (* 3 a) c)
0.1b	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) 3) a)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

26.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) 3) a)
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
3.0ms	(* (* 3 a) c)

series237.0ms

Calls

4 calls:

Slowest

91.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) 3) a)
67.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
60.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
18.0ms	(* (* 3 a) c)

simplify2.3s

Calls

27 calls:

Slowest

535.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))
271.0ms	(- b (* 3/2 (/ (* a c) b)))
230.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
152.0ms	(* (exp (- b)) (exp (sqrt (- (* b b) (* (* 3 a) c)))))
131.0ms	(sqrt (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) 3))

prune981.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.7b

localize25.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma -3 (* c a) (* b b)))
25.3b	(sqrt (fma -3 (* c a) (* b b)))
13.2b	(- (* (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b))))) b)
0.5b	(* (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `associate-r` `associate-l`
6×	`add-cbrt-cube` `pow1/2` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `pow-prod-down` `pow-prod-up`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `fma-neg` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip--`

Calls

4 calls:

Slowest

12.0ms	(* (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))))
11.0ms	(- (* (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b))))) b)
2.0ms	(sqrt (fma -3 (* c a) (* b b)))
2.0ms	(sqrt (fma -3 (* c a) (* b b)))

series194.0ms

Calls

4 calls:

Slowest

65.0ms	(- (* (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b))))) b)
49.0ms	(sqrt (fma -3 (* c a) (* b b)))
41.0ms	(* (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))))
39.0ms	(sqrt (fma -3 (* c a) (* b b)))

simplify1.2s

Calls

49 calls:

Slowest

136.0ms	(* (* (* (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b))))) (sqrt (sqrt (fma -3 (* c a) (* b b))))) (* (* (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b))))) (sqrt (sqrt (fma -3 (* c a) (* b b))))))
44.0ms	(sqrt (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b)))))
44.0ms	(sqrt (sqrt (cbrt (fma -3 (* c a) (* b b)))))
42.0ms	(sqrt (fma -3 (* c a) (* b b)))
42.0ms	(sqrt (sqrt (fma -3 (* c a) (* b b))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.7b

regimes619.0ms

Accuracy

84.5% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 33.4b

bsearch230.0ms

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.3s	5911×	body	80	valid
1.1s	875×	body	1280	valid
1.0s	1075×	body	2560	valid
403.0ms	2824×	body	80	nan
229.0ms	468×	body	640	valid
129.0ms	107×	body	5120	valid
85.0ms	231×	body	320	valid
27.0ms	116×	body	160	valid