Details

sample58.0ms

Algorithm

intervals

Results

20.0ms	274×	body	80	valid
17.0ms	92×	body	80	nan

simplify174.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	20	38
1	36	38
2	66	37
3	122	37
4	154	37
5	166	37
6	168	37
done	168	37

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

localize138.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
2.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

17.0ms	(- (* b b) (* (* 4.0 a) c))
53.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* (* 4.0 a) c))
123.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts

89 → 89

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	104	1247
1	261	1114
2	909	1017
3	3514	1006
done	5000	1005

prune568.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.1b

localize127.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.9b	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
5.4b	(/ (* a c) b)
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt`
10×	`fma-def`
9×	`times-frac` `associate-/r*`
8×	`add-log-exp`
6×	`distribute-rgt-neg-in`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `distribute-lft-out--`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `associate-/r/` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out` `associate-/l*` `difference-of-squares`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 98

Calls

4 calls:

51.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
20.0ms	(/ (* a c) b)
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
240.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
37.0ms	(/ (* a c) b)
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

110 → 110

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	187	1564
1	472	1463
2	1735	1281
done	5000	1212

prune737.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.6b

localize136.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.9b	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`times-frac`
30×	`add-exp-log`
25×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-r`
11×	`cbrt-prod`
10×	`fma-def`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`pow1` `associate-l`
6×	`distribute-rgt-neg-in` `associate-/r*` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`distribute-lft-neg-in` `sqrt-prod` `div-inv`
2×	`flip3--` `sqrt-div` `sum-log` `associate-/r/` `flip--` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `-commutative` `flip-+` `associate-/l`

Counts

4 → 136

Calls

4 calls:

31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
61.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series617.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
317.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

148 → 148

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	271	2697
1	749	2559
2	2920	2021
done	5001	1786

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize164.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b	(* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
3.9b	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite875.0ms

Algorithm

rewrite-expression-head

Rules

501×	`times-frac`
286×	`add-sqr-sqrt`
191×	`cbrt-prod`
165×	`*-un-lft-identity`
153×	`add-cube-cbrt`
140×	`associate-l`
74×	`add-exp-log`
43×	`add-cbrt-cube`
33×	`cbrt-undiv` `div-exp`
32×	`unswap-sqr`
31×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
10×	`fma-def` `div-inv`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-rgt-neg-in` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `associate-/r/` `flip--` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `-commutative` `flip-+` `associate-/l`

Counts

4 → 320

Calls

4 calls:

26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
286.0ms	(* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
505.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
303.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
136.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

332 → 332

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	557	8139
1	1688	7947
done	5000	7255

prune3.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

regimes449.0ms

Accuracy

91.3% (1.3b remaining)

Error of 7.9b against oracle of 6.7b and baseline of 21.4b

bsearch288.0ms

Steps

Iters	Range		Point
5	1.2073698495971617e+61	2.9312978430050554e+61	2.269665110513951e+61
10	-1.437929939467773e+163	-1.7004475472942417e+152	-1.3404533579516929e+154

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	54	139
1	66	139
done	66	139

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s	8718×	body	80	valid
303.0ms	2845×	body	80	nan