Details

sample84.0ms

Algorithm

intervals

Results

22.0ms	39×	body	2560	valid
17.0ms	180×	body	80	valid
13.0ms	29×	body	1280	valid
11.0ms	21×	body	640	valid
6.0ms	70×	body	80	nan
2.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	95
7	95
6	94
5	92
4	84
3	67
2	43
1	24
0	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b	(- (* b b) (* 4 (* a c)))
19.1b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 74

Calls

4 calls:

58.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
14.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
92.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
49.0ms	(- (* b b) (* 4 (* a c)))
76.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1315
1	405
0	151

prune571.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4 (* a c)))
19.1b	(sqrt (- (* b b) (* 4 (* a c))))
19.1b	(sqrt (- (* b b) (* 4 (* a c))))
19.1b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

22.0ms	(- (* b b) (* 4 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* b b) (* 4 (* a c)))
84.0ms	(sqrt (- (* b b) (* 4 (* a c))))
84.0ms	(sqrt (- (* b b) (* 4 (* a c))))
119.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	1783
2	454
1	156
0	61

prune651.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

localize103.0ms

Local error

Found 4 expressions with local error:

19.1b	(sqrt (- (* b b) (* 4 (* a c))))
19.9b	(cbrt (- (* b b) (* 4 (* a c))))
19.9b	(cbrt (- (* b b) (* 4 (* a c))))
19.9b	(cbrt (- (* b b) (* 4 (* a c))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

12.0ms	(sqrt (- (* b b) (* 4 (* a c))))
10.0ms	(cbrt (- (* b b) (* 4 (* a c))))
9.0ms	(cbrt (- (* b b) (* 4 (* a c))))
9.0ms	(cbrt (- (* b b) (* 4 (* a c))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt (- (* b b) (* 4 (* a c))))
115.0ms	(cbrt (- (* b b) (* 4 (* a c))))
104.0ms	(cbrt (- (* b b) (* 4 (* a c))))
97.0ms	(cbrt (- (* b b) (* 4 (* a c))))

simplify1.7s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	1889
2	564
1	203
0	88

prune905.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 4.2b

localize39.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4 (* a c)))
1.0b	(- (* b b) (* 4 (* a c)))
19.1b	(sqrt (- (* b b) (* 4 (* a c))))
19.1b	(sqrt (- (* b b) (* 4 (* 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×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

13.0ms	(- (* b b) (* 4 (* a c)))
9.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))
13.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* 4 (* a c)))
66.0ms	(- (* b b) (* 4 (* a c)))
98.0ms	(sqrt (- (* b b) (* 4 (* a c))))
95.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.7s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	1783
2	454
1	156
0	61

prune467.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.2b

regimes579.0ms

Accuracy

84.9% (4.1b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 33.2b

bsearch283.0ms

Steps

Iters	Range		Point
9	1.542649851819534e-86	4.188981380654902e-77	5.930445637544082e-86
10	-9.235597319251238e+162	-1.2115114540629089e+151	-4.600306435637794e+151

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.6s	1057×	body	2560	valid
1.1s	895×	body	1280	valid
891.0ms	5900×	body	80	valid
473.0ms	2938×	body	80	nan
318.0ms	455×	body	640	valid
148.0ms	211×	body	320	valid
103.0ms	106×	body	5120	valid
52.0ms	97×	body	160	valid