Details

sample89.0ms

Algorithm

intervals

Results

33.0ms	210×	body	80	valid
13.0ms	23×	body	2560	valid
13.0ms	25×	body	1280	valid
7.0ms	84×	body	80	nan
3.0ms	8×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
20.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

54.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
16.0ms	(- (* b b) (* (* 3 a) c))
29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
70.0ms	(- (* b b) (* (* 3 a) c))
103.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.5s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1430
1	442
0	170

prune671.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (fma b b (* c (* -3 a)))) b) 3)
1.0b	(- (sqrt (fma b b (* c (* -3 a)))) b)
1.0b	(fma b b (* c (* -3 a)))
20.8b	(sqrt (fma b b (* c (* -3 a))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

20.0ms	(/ (- (sqrt (fma b b (* c (* -3 a)))) b) 3)
15.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
0.0ms	(fma b b (* c (* -3 a)))
2.0ms	(sqrt (fma b b (* c (* -3 a))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (sqrt (fma b b (* c (* -3 a)))) b) 3)
120.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
78.0ms	(fma b b (* c (* -3 a)))
109.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify2.7s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
3	3214
2	934
1	399
0	176

prune603.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* c (* -3 a))
1.0b	(- (/ (sqrt (fma b b (* c (* -3 a)))) 3) (/ b 3))
1.0b	(fma b b (* c (* -3 a)))
20.8b	(sqrt (fma b b (* c (* -3 a))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

463×	`times-frac`
364×	`add-sqr-sqrt`
352×	`*-un-lft-identity`
344×	`add-cube-cbrt`
286×	`prod-diff`
131×	`sqrt-prod`
38×	`div-inv`
22×	`fma-neg`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `distribute-rgt-out--` `pow1/2` `diff-log` `associate-r` `*-commutative` `frac-sub` `fma-udef` `flip--` `sub-div`

Counts

4 → 384

Calls

4 calls:

13.0ms	(* c (* -3 a))
22.0ms	(- (/ (sqrt (fma b b (* c (* -3 a)))) 3) (/ b 3))
0.0ms	(fma b b (* c (* -3 a)))
1.0ms	(sqrt (fma b b (* c (* -3 a))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* c (* -3 a))
156.0ms	(- (/ (sqrt (fma b b (* c (* -3 a)))) 3) (/ b 3))
75.0ms	(fma b b (* c (* -3 a)))
82.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify1.8s

Counts

396 → 396

Iterations

Iter	Nodes
done	5002
2	2446
1	1075
0	486

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* 1/3 (- (sqrt (fma b b (* c (* -3 a)))) b))
1.0b	(- (sqrt (fma b b (* c (* -3 a)))) b)
1.0b	(fma b b (* c (* -3 a)))
20.8b	(sqrt (fma b b (* c (* -3 a))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
54×	`prod-diff`
49×	`*-un-lft-identity`
45×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
7×	`pow1`
6×	`add-cbrt-cube` `fma-neg` `associate-r` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-l`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

25.0ms	(* 1/3 (- (sqrt (fma b b (* c (* -3 a)))) b))
7.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
0.0ms	(fma b b (* c (* -3 a)))
1.0ms	(sqrt (fma b b (* c (* -3 a))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* 1/3 (- (sqrt (fma b b (* c (* -3 a)))) b))
92.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
49.0ms	(fma b b (* c (* -3 a)))
90.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify2.3s

Counts

147 → 147

Iterations

Iter	Nodes
done	5001
3	3151
2	922
1	391
0	189

prune486.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.5b

regimes540.0ms

Accuracy

82.5% (4.8b remaining)

Error of 10.5b against oracle of 5.7b and baseline of 33.1b

bsearch393.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	3.5051690294214705e-69
7	6.366271362828677e-80	2.0474353944207673e-78	4.020455841328689e-79
8	1.9015403840268286e-125	4.787339246176752e-121	3.7535994007355634e-122
7	-6.914140684613533e+154	-2.006932639140506e+153	-1.2620519469386174e+154

simplify15.0ms

Iterations

Iter	Nodes
done	50
1	50
0	42

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5867×	body	80	valid
805.0ms	1084×	body	2560	valid
637.0ms	908×	body	1280	valid
397.0ms	3007×	body	80	nan
276.0ms	446×	body	640	valid
109.0ms	101×	body	5120	valid
97.0ms	236×	body	320	valid
22.0ms	108×	body	160	valid