Details

sample109.0ms

Algorithm

intervals

Results

73.0ms	277×	body	80	valid
16.0ms	82×	body	80	nan

simplify177.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	199
6	199
5	195
4	185
3	147
2	80
1	39
0	20

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize167.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (fma -4 (* a c) (* b b))) b)
1.0b	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
21.8b	(sqrt (fma -4 (* a c) (* b b)))
21.8b	(sqrt (fma -4 (* a c) (* b b)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

10.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
11.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
107.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
117.0ms	(sqrt (fma -4 (* a c) (* b b)))
101.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify2.8s

Counts

177 → 177

Iterations

Iter	Nodes
done	5001
2	1847
1	432
0	194

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.6b

localize114.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2 c) (- (sqrt (fma -4 (* a c) (* b b))) b))
0.4b	(fma -4 (* a c) (* b b))
0.9b	(- (sqrt (fma -4 (* a c) (* b b))) b)
21.8b	(sqrt (fma -4 (* a c) (* b b)))

rewrite43.0ms

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×	`associate-/r*` `times-frac` `fma-neg` `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` `associate-/r/` `flip--`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 101

Calls

4 calls:

28.0ms	(/ (* 2 c) (- (sqrt (fma -4 (* a c) (* b b))) b))
0.0ms	(fma -4 (* a c) (* b b))
12.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
1.0ms	(sqrt (fma -4 (* a c) (* b b)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ (* 2 c) (- (sqrt (fma -4 (* a c) (* b b))) b))
82.0ms	(fma -4 (* a c) (* b b))
103.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
96.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify1.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1489
1	376
0	159

prune672.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.6b

localize161.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (fma -4 (* a c) (* b b))) b)
0.9b	(- (sqrt (fma -4 (* a c) (* b b))) b)
21.8b	(sqrt (fma -4 (* a c) (* b b)))
21.8b	(sqrt (fma -4 (* a c) (* b b)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

24.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
15.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
2.0ms	(sqrt (fma -4 (* a c) (* b b)))
2.0ms	(sqrt (fma -4 (* a c) (* b b)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
113.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
126.0ms	(sqrt (fma -4 (* a c) (* b b)))
111.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify2.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
3	2028
2	427
1	174
0	86

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.6b

localize159.0ms

Local error

Found 4 expressions with local error:

21.8b	(sqrt (* (* (cbrt (fma -4 (* a c) (* b b))) (cbrt (fma -4 (* a c) (* b b)))) (cbrt (fma -4 (* a c) (* b b)))))
22.6b	(cbrt (fma -4 (* a c) (* b b)))
22.6b	(cbrt (fma -4 (* a c) (* b b)))
22.6b	(cbrt (fma -4 (* a c) (* b b)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 69

Calls

4 calls:

20.0ms	(sqrt (* (* (cbrt (fma -4 (* a c) (* b b))) (cbrt (fma -4 (* a c) (* b b)))) (cbrt (fma -4 (* a c) (* b b)))))
1.0ms	(cbrt (fma -4 (* a c) (* b b)))
1.0ms	(cbrt (fma -4 (* a c) (* b b)))
1.0ms	(cbrt (fma -4 (* a c) (* b b)))

series860.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt (* (* (cbrt (fma -4 (* a c) (* b b))) (cbrt (fma -4 (* a c) (* b b)))) (cbrt (fma -4 (* a c) (* b b)))))
224.0ms	(cbrt (fma -4 (* a c) (* b b)))
251.0ms	(cbrt (fma -4 (* a c) (* b b)))
247.0ms	(cbrt (fma -4 (* a c) (* b b)))

simplify794.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	1055
2	309
1	152
0	85

prune575.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 10.6b

regimes503.0ms

Accuracy

95% (0.4b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 20.6b

bsearch139.0ms

Steps

Iters	Range		Point
10	3.302865865338161e+140	2.8302951796802603e+150	5.270928603152398e+143

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	32

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.8s	8759×	body	80	valid
801.0ms	2919×	body	80	nan