Details

sample88.0ms

Algorithm

intervals

Results

55.0ms	274×	body	80	valid
12.0ms	69×	body	80	nan

simplify191.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
7	168
6	166
5	160
4	151
3	125
2	75
1	38
0	20

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize167.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4 a) c))
1.0b	(- (* b b) (* (* 4 a) c))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite49.0ms

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:

8.0ms	(- (* b b) (* (* 4 a) c))
11.0ms	(- (* b b) (* (* 4 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* b b) (* (* 4 a) c))
71.0ms	(- (* b b) (* (* 4 a) c))
105.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
82.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	2009
2	517
1	158
0	63

prune662.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize198.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4 a) c))
1.0b	(- (* b b) (* (* a c) 4))
19.8b	(sqrt (- (* b b) (* (* a c) 4)))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite51.0ms

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:

8.0ms	(- (* b b) (* (* 4 a) c))
15.0ms	(- (* b b) (* (* a c) 4))
16.0ms	(sqrt (- (* b b) (* (* a c) 4)))
11.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* (* 4 a) c))
83.0ms	(- (* b b) (* (* a c) 4))
112.0ms	(sqrt (- (* b b) (* (* a c) 4)))
100.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5004
3	2629
2	686
1	242
0	98

prune650.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize213.0ms

Local error

Found 4 expressions with local error:

8.8b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* a c) 4)))) (sqrt (sqrt (- (* b b) (* (* a c) 4))))))
19.8b	(sqrt (- (* b b) (* (* a c) 4)))
19.8b	(sqrt (- (* b b) (* (* a c) 4)))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 62

Calls

4 calls:

15.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* a c) 4)))) (sqrt (sqrt (- (* b b) (* (* a c) 4))))))
8.0ms	(sqrt (- (* b b) (* (* a c) 4)))
8.0ms	(sqrt (- (* b b) (* (* a c) 4)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* a c) 4)))) (sqrt (sqrt (- (* b b) (* (* a c) 4))))))
103.0ms	(sqrt (- (* b b) (* (* a c) 4)))
90.0ms	(sqrt (- (* b b) (* (* a c) 4)))
102.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.6s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
3	3325
2	939
1	296
0	114

prune734.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize181.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4 a) c))
2.7b	(* (/ a b) c)
3.4b	(/ (* 2 c) (* 2 (- (* (/ a b) c) b)))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
11×	`times-frac`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`insert-posit16`
3×	`flip3--` `associate-r` `sqrt-prod` `flip--`
2×	`sqrt-div` `associate-*r/` `associate-/r/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `associate-/l`

Counts

4 → 86

Calls

4 calls:

19.0ms	(- (* b b) (* (* 4 a) c))
20.0ms	(* (/ a b) c)
24.0ms	(/ (* 2 c) (* 2 (- (* (/ a b) c) b)))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* b b) (* (* 4 a) c))
26.0ms	(* (/ a b) c)
98.0ms	(/ (* 2 c) (* 2 (- (* (/ a b) c) b)))
101.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts

98 → 98

Iterations

Iter	Nodes
done	5016
2	2089
1	468
0	177

prune713.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

regimes390.0ms

Accuracy

89% (1.7b remaining)

Error of 7.4b against oracle of 5.7b and baseline of 20.8b

bsearch227.0ms

Steps

Iters	Range		Point
6	4.8498614244770303e+48	2.0602804194761557e+49	2.0410715251838527e+49
9	-1.2107636771907174e+172	-9.235597319251238e+162	-9.448476596858411e+162

simplify12.0ms

Iterations

Iter	Nodes
done	59
1	59
0	48

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.6s	8711×	body	80	valid
434.0ms	2933×	body	80	nan