Details

sample55.0ms

Algorithm

intervals

Results

25.0ms	277×	body	80	valid
7.0ms	104×	body	80	nan

simplify181.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	193
6	193
5	189
4	179
3	143
2	79
1	39
0	20

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.8b

localize131.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (* b b) (* (* 4.0 a) c))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

13.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b b) (* (* 4.0 a) c))
58.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	858
1	185
0	71

prune612.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.6b

localize129.0ms

Local error

Found 4 expressions with local error:

7.6b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`fma-def` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `neg-mul-1` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 76

Calls

4 calls:

20.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
87.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
122.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1106
1	260
0	90

prune842.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.6b

localize174.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 62

Calls

4 calls:

10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series531.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
145.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
147.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
144.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	4267
2	767
1	224
0	94

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.6b

localize223.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 62

Calls

4 calls:

9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
175.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
156.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
146.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	4267
2	767
1	224
0	94

prune658.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.6b

regimes374.0ms

Accuracy

93.3% (0.8b remaining)

Error of 8.6b against oracle of 7.8b and baseline of 20.0b

bsearch233.0ms

Steps

Iters	Range		Point
8	1.0335802065380817e+152	4.346839969020365e+154	1.042426094136288e+152
9	-1.8060553248805222e+109	-1.4137780731624028e+101	-9.912992538019245e+108

simplify23.0ms

Iterations

Iter	Nodes
done	51
1	51
0	43

end0.0ms

sample2.0s

Algorithm

intervals

Results

983.0ms	8769×	body	80	valid
613.0ms	2889×	body	80	nan