Details

sample123.0ms

Algorithm

intervals

Results

42.0ms	471×	pre	80	true
27.0ms	121×	body	320	valid
15.0ms	215×	body	80	nan
14.0ms	93×	body	160	valid
4.0ms	13×	body	640	valid
2.0ms	29×	body	80	valid

simplify114.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma -3 (* c a) (* b b)))
0.1b	(fma -3 (* c a) (* b b))
0.2b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
25.6b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite92.0ms

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` `insert-posit16` `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 → 102

Calls

4 calls:

3.0ms	(sqrt (fma -3 (* c a) (* b b)))
1.0ms	(fma -3 (* c a) (* b b))
63.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
22.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series402.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (fma -3 (* c a) (* b b)))
76.0ms	(fma -3 (* c a) (* b b))
95.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
96.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.7s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	3990
2	940
1	347
0	152

prune617.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 48.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma -3 (* c a) (* b b))
0.1b	(fma -3 (* c a) (* b b))
0.2b	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
51.6b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

0.0ms	(fma -3 (* c a) (* b b))
0.0ms	(fma -3 (* c a) (* b b))
8.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.6s

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma -3 (* c a) (* b b))
57.0ms	(fma -3 (* c a) (* b b))
674.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
789.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify2.9s

Counts

69 → 69

Iterations

Iter	Nodes
done	5002
3	2382
2	672
1	231
0	112

prune613.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 48.9b

localize88.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma -3 (* c a) (* b b))
0.2b	(/ (fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.3b	(* (* a -3) c)
51.6b	(fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `pow-prod-down` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `fma-udef`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-l` `-commutative` `div-inv`

Counts

4 → 67

Calls

4 calls:

1.0ms	(fma -3 (* c a) (* b b))
16.0ms	(/ (fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
34.0ms	(* (* a -3) c)
1.0ms	(fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series470.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma -3 (* c a) (* b b))
230.0ms	(/ (fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
21.0ms	(* (* a -3) c)
164.0ms	(fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify3.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4843
2	975
1	306
0	135

prune841.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 48.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1/3 a))
0.3b	(* (* a -3) c)
0.4b	(/ 1/3 a)
51.6b	(fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
16×	`add-cbrt-cube` `associate-r` `add-exp-log`
11×	`pow1`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*r/` `fma-udef`

Counts

4 → 97

Calls

4 calls:

33.0ms	(* (fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1/3 a))
35.0ms	(* (* a -3) c)
9.0ms	(/ 1/3 a)
1.0ms	(fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series438.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(* (fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1/3 a))
23.0ms	(* (* a -3) c)
24.0ms	(/ 1/3 a)
152.0ms	(fma (sqrt (sqrt (fma b b (* (* a -3) c)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5004
2	1308
1	373
0	163

prune687.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 48.7b

regimes998.0ms

Accuracy

0% (2.7b remaining)

Error of 51.5b against oracle of 48.8b and baseline of 51.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	8014×	body	80	nan
905.0ms	3654×	body	320	valid
785.0ms	16014×	pre	80	true
453.0ms	2914×	body	160	valid
162.0ms	948×	body	80	valid
129.0ms	484×	body	640	valid