Details

sample116.0ms

Algorithm

intervals

Results

28.0ms	111×	body	320	valid
24.0ms	220×	body	80	nan
22.0ms	476×	pre	80	true
19.0ms	107×	body	160	valid
5.0ms	14×	body	640	valid
2.0ms	24×	body	80	valid

simplify98.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize24.0ms

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))
29.5b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite44.0ms

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:

2.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
31.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
7.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series407.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (fma -3 (* c a) (* b b)))
79.0ms	(fma -3 (* c a) (* b b))
110.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
108.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify727.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	2000
2	940
1	347
0	152

prune609.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 50.5b

localize30.0ms

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))
52.9b	(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))
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.1s

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma -3 (* c a) (* b b))
75.0ms	(fma -3 (* c a) (* b b))
590.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
399.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify835.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	2001
2	672
1	231
0	112

prune601.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 50.5b

localize36.0ms

Local error

Found 4 expressions with local error:

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)) (/ 1/3 a))
0.4b	(/ 1/3 a)
52.9b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma -3 (* c a) (* b b))
9.0ms	(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1/3 a))
13.0ms	(/ 1/3 a)
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.1s

Counts

4 → 12

Calls

4 calls:

80.0ms	(fma -3 (* c a) (* b b))
559.0ms	(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1/3 a))
31.0ms	(/ 1/3 a)
409.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	2003
2	1039
1	320
0	152

prune755.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 50.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1/3 a)
0.4b	(/ 1/3 a)
0.5b	(* (sqrt (/ 1/3 a)) (sqrt (/ 1/3 a)))
52.9b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
66×	`sqrt-prod`
60×	`times-frac`
52×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow1`
18×	`swap-sqr`
16×	`associate-r` `associate-l`
10×	`add-cbrt-cube` `add-exp-log`
9×	`unswap-sqr`
8×	`sqrt-pow1` `pow1/2`
6×	`associate-/r` `div-inv` `associate-/l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 161

Calls

4 calls:

4.0ms	(/ 1/3 a)
4.0ms	(/ 1/3 a)
26.0ms	(* (sqrt (/ 1/3 a)) (sqrt (/ 1/3 a)))
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series559.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1/3 a)
24.0ms	(/ 1/3 a)
78.0ms	(* (sqrt (/ 1/3 a)) (sqrt (/ 1/3 a)))
439.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify762.0ms

Counts

173 → 173

Iterations

Iter	Nodes
done	2001
2	928
1	422
0	219

prune989.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 50.2b

regimes976.0ms

Accuracy

0% (2.7b remaining)

Error of 51.6b against oracle of 48.9b and baseline of 51.6b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample6.1s

Algorithm

intervals

Results

1.6s	3533×	body	320	valid
1.3s	8200×	body	80	nan
1.2s	3046×	body	160	valid
1.1s	16200×	pre	80	true
307.0ms	493×	body	640	valid
135.0ms	928×	body	80	valid