Details

sample79.0ms

Algorithm

intervals

Results

20.0ms	120×	body	320	valid
11.0ms	488×	pre	80	true
10.0ms	232×	body	80	nan
8.0ms	93×	body	160	valid
3.0ms	18×	body	640	valid
1.0ms	25×	body	80	valid

simplify94.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	120
5	120
4	112
3	83
2	42
1	22
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (* 3.0 a) (- c) (* b b)))
0.1b	(fma (* 3.0 a) (- c) (* b b))
0.2b	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
28.3b	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

2.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))
0.0ms	(fma (* 3.0 a) (- c) (* b b))
50.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
17.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

series514.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))
85.0ms	(fma (* 3.0 a) (- c) (* b b))
200.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
109.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

simplify773.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1258
1	342
0	148

prune586.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* c a) (- 3.0) (* b b))
0.3b	(fma (- (* c a)) 3.0 0)
0.3b	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
0.4b	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
49×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
18×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-lft-out`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`associate-/l/`

Counts

4 → 113

Calls

4 calls:

0.0ms	(fma (* c a) (- 3.0) (* b b))
1.0ms	(fma (- (* c a)) 3.0 0)
17.0ms	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
36.0ms	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

series724.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(fma (* c a) (- 3.0) (* b b))
50.0ms	(fma (- (* c a)) 3.0 0)
278.0ms	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
288.0ms	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

simplify1.1s

Counts

125 → 125

Iterations

Iter	Nodes
done	5001
2	2235
1	487
0	197

prune917.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ b (sqrt (fma (* (- 3.0) a) c (pow b 2))))
0.1b	(/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)
0.1b	(fma (* (- 3.0) a) c (pow b 2))
0.3b	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

366×	`add-exp-log`
213×	`div-exp`
126×	`prod-exp`
123×	`add-cbrt-cube`
60×	`cbrt-undiv`
55×	`1-exp`
43×	`times-frac`
38×	`*-un-lft-identity`
36×	`cbrt-unprod`
28×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`rec-exp`
17×	`associate-/l*`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-/r/` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`frac-times` `+-commutative` `sum-log` `associate-l/` `associate-r/` `fma-udef`

Counts

4 → 204

Calls

4 calls:

11.0ms	(+ b (sqrt (fma (* (- 3.0) a) c (pow b 2))))
34.0ms	(/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)
1.0ms	(fma (* (- 3.0) a) c (pow b 2))
55.0ms	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ b (sqrt (fma (* (- 3.0) a) c (pow b 2))))
137.0ms	(/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)
82.0ms	(fma (* (- 3.0) a) c (pow b 2))
230.0ms	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)))

simplify805.0ms

Counts

216 → 216

Iterations

Iter	Nodes
done	5000
1	1401
0	369

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- 3.0) a) c)
0.3b	(/ 1 (* a 3.0))
0.3b	(/ (/ 1 (* a 3.0)) (+ (sqrt (fma c (* (- 3.0) a) (pow b 2))) b))
0.3b	(* (/ (/ 1 (* a 3.0)) (+ (sqrt (fma c (* (- 3.0) a) (pow b 2))) b)) (* (* (- 3.0) a) c))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-exp-log`
86×	`times-frac`
77×	`add-cbrt-cube`
71×	`*-un-lft-identity`
66×	`prod-exp`
48×	`div-exp`
41×	`add-sqr-sqrt` `add-cube-cbrt`
35×	`associate-l`
32×	`cbrt-unprod`
22×	`cbrt-undiv`
21×	`pow1`
15×	`distribute-lft-out`
12×	`div-inv`
10×	`rec-exp` `1-exp` `pow-prod-down` `associate-/l*`
5×	`associate-/r*`
4×	`distribute-lft-neg-out` `expm1-log1p-u` `associate-r` `associate-/r/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `*-commutative` `flip-+` `pow-flip`
1×	`associate-*l/` `distribute-rgt-neg-out` `inv-pow` `associate-/l/`

Counts

4 → 201

Calls

4 calls:

17.0ms	(* (* (- 3.0) a) c)
9.0ms	(/ 1 (* a 3.0))
36.0ms	(/ (/ 1 (* a 3.0)) (+ (sqrt (fma c (* (- 3.0) a) (pow b 2))) b))
118.0ms	(* (/ (/ 1 (* a 3.0)) (+ (sqrt (fma c (* (- 3.0) a) (pow b 2))) b)) (* (* (- 3.0) a) c))

series550.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (* (- 3.0) a) c)
23.0ms	(/ 1 (* a 3.0))
228.0ms	(/ (/ 1 (* a 3.0)) (+ (sqrt (fma c (* (- 3.0) a) (pow b 2))) b))
272.0ms	(* (/ (/ 1 (* a 3.0)) (+ (sqrt (fma c (* (- 3.0) a) (pow b 2))) b)) (* (* (- 3.0) a) c))

simplify471.0ms

Counts

213 → 213

Iterations

Iter	Nodes
done	5000
1	894
0	283

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes345.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
2	28
1	25
0	18

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.1s	15953×	pre	80	true
1.0s	7953×	body	80	nan
861.0ms	3668×	body	320	valid
567.0ms	2896×	body	160	valid
263.0ms	505×	body	640	valid
64.0ms	931×	body	80	valid