Details

sample68.0ms

Algorithm

intervals

Results

36.0ms	274×	body	80	valid
7.0ms	84×	body	80	nan

simplify123.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	176
6	176
5	174
4	161
3	122
2	66
1	36
0	20

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize149.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

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:

7.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	858
1	185
0	71

prune762.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

localize213.0ms

Local error

Found 4 expressions with local error:

12.9b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

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:

10.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1106
1	260
0	90

prune803.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

localize194.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

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)))
7.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
149.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
155.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

74 → 74

Iterations

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

prune988.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.9b

localize161.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
3.1b	(/ (fma -2 b (/ 2.0 (/ b (* a c)))) (* 2.0 a))
6.1b	(/ b (* a c))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`clear-num` `associate-/r*` `frac-2neg` `flip3--` `sqrt-div` `prod-exp` `cbrt-unprod` `div-inv` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 79

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(/ (fma -2 b (/ 2.0 (/ b (* a c)))) (* 2.0 a))
12.0ms	(/ b (* a c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* (* 4.0 a) c))
115.0ms	(/ (fma -2 b (/ 2.0 (/ b (* a c)))) (* 2.0 a))
37.0ms	(/ b (* a c))
107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1675
1	392
0	163

prune754.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

regimes547.0ms

Accuracy

93% (1.0b remaining)

Error of 8.1b against oracle of 7.0b and baseline of 21.5b

bsearch357.0ms

Steps

Iters	Range		Point
8	1.850288133117565e+153	8.492547483917043e+155	1.8793407135037563e+153
10	-2.0003538938970096e+122	-1.6569790030408257e+112	-5.6179139475653e+116

simplify27.0ms

Iterations

Iter	Nodes
done	69
1	69
0	55

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	8687×	body	80	valid
311.0ms	2881×	body	80	nan