Details

sample114.0ms

Algorithm

intervals

Results

24.0ms	116×	body	320	valid
18.0ms	256×	body	80	nan
17.0ms	512×	pre	80	true
14.0ms	97×	body	160	valid
4.0ms	16×	body	640	valid
2.0ms	27×	body	80	valid

simplify132.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.3b

localize23.0ms

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))
26.3b	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

rewrite37.0ms

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:

1.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))
1.0ms	(fma (* 3.0 a) (- c) (* b b))
24.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
9.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

series935.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))
92.0ms	(fma (* 3.0 a) (- c) (* b b))
225.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
486.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

simplify819.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1258
1	342
0	148

prune503.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* c a) (- 3.0) (* b b))
0.2b	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
0.3b	(fma (- (* c a)) 3.0 0)
0.4b	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

rewrite38.0ms

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))
12.0ms	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
0.0ms	(fma (- (* c a)) 3.0 0)
22.0ms	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

series757.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(fma (* c a) (- 3.0) (* b b))
328.0ms	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
50.0ms	(fma (- (* c a)) 3.0 0)
284.0ms	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

simplify1.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	2235
1	486
0	197

prune896.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

235×	`times-frac`
173×	`*-un-lft-identity`
145×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`associate-r`
55×	`add-exp-log`
37×	`add-cbrt-cube`
27×	`distribute-lft-out`
24×	`div-exp`
23×	`associate-l`
19×	`associate-/l*`
13×	`cbrt-undiv` `prod-exp` `div-inv`
11×	`pow1`
9×	`cbrt-unprod`
8×	`unswap-sqr`
7×	`distribute-lft-neg-in` `associate-/r*` `neg-mul-1` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `distribute-frac-neg` `*-commutative` `flip-+`
1×	`distribute-lft-neg-out` `neg-sub0` `frac-times` `div-sub` `associate-l/` `associate-r/` `associate-/l/`

Counts

4 → 272

Calls

4 calls:

8.0ms	(/ (- (* (* a c) 3.0)) 3.0)
26.0ms	(* (* a c) 3.0)
19.0ms	(/ (/ 1 a) (+ b (sqrt (fma (- (* a c)) 3.0 (* b b)))))
68.0ms	(* (/ (- (* (* a c) 3.0)) 3.0) (/ (/ 1 a) (+ b (sqrt (fma (- (* a c)) 3.0 (* b b))))))

series550.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- (* (* a c) 3.0)) 3.0)
33.0ms	(* (* a c) 3.0)
235.0ms	(/ (/ 1 a) (+ b (sqrt (fma (- (* a c)) 3.0 (* b b)))))
243.0ms	(* (/ (- (* (* a c) 3.0)) 3.0) (/ (/ 1 a) (+ b (sqrt (fma (- (* a c)) 3.0 (* b b))))))

simplify597.0ms

Counts

284 → 284

Iterations

Iter	Nodes
done	5000
1	1222
0	384

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (sqrt (fma (* (- a) c) 3.0 (* b b))) b)
0.1b	(/ (/ (* (* a c) 1) a) (+ (sqrt (fma (* (- a) c) 3.0 (* b b))) b))
0.1b	(fma (* (- a) c) 3.0 (* b b))
0.1b	(/ (* (* a c) 1) a)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
44×	`*-un-lft-identity`
39×	`add-exp-log`
27×	`add-cbrt-cube`
26×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`div-exp`
12×	`prod-exp`
10×	`cbrt-undiv`
9×	`distribute-lft-out`
8×	`associate-/l*`
7×	`associate-/r*` `div-inv`
6×	`fma-def` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `1-exp` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-/r/` `flip-+`
1×	`+-commutative` `sum-log` `fma-udef` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

13.0ms	(+ (sqrt (fma (* (- a) c) 3.0 (* b b))) b)
49.0ms	(/ (/ (* (* a c) 1) a) (+ (sqrt (fma (* (- a) c) 3.0 (* b b))) b))
1.0ms	(fma (* (- a) c) 3.0 (* b b))
39.0ms	(/ (* (* a c) 1) a)

series471.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(+ (sqrt (fma (* (- a) c) 3.0 (* b b))) b)
200.0ms	(/ (/ (* (* a c) 1) a) (+ (sqrt (fma (* (- a) c) 3.0 (* b b))) b))
89.0ms	(fma (* (- a) c) 3.0 (* b b))
14.0ms	(/ (* (* a c) 1) a)

simplify2.5s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	4033
1	536
0	192

prune691.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes191.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	39
3	39
2	37
1	25
0	16

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.4s	3569×	body	320	valid
1.1s	16060×	pre	80	true
677.0ms	8060×	body	80	nan
629.0ms	3033×	body	160	valid
129.0ms	477×	body	640	valid
63.0ms	921×	body	80	valid