Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
9.0ms	40×	body	2560	valid
5.0ms	28×	body	1280	valid
3.0ms	76×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	106	16
5	114	16
done	114	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(* (* 4.0 a) c)
46.0ms	(- (* b b) (* (* 4.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify491.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	135	1109
1	347	1006
2	1320	900
done	5000	900

prune272.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
3.6b	(exp (log (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1`
10×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
6×	`log-prod` `exp-sum` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `sqrt-prod` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`log-div` `exp-diff` `sqrt-div` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `log-pow` `*-commutative` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 75

Calls

4 calls:

6.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(exp (log (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* 4.0 a) c)
43.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(exp (log (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify499.0ms

Counts

87 → 87

Iterations

Useful iterations: done (497.0ms)

Iter	Nodes	Cost
0	161	1274
1	357	1114
2	1259	1009
done	5000	1006

prune253.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

22.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(* (* 4.0 a) c)
45.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify590.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	161	1863
1	383	1562
2	1514	1315
done	5000	1315

prune249.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

localize18.0ms

Local error

Found 4 expressions with local error:

24.7b	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (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)))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

34.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
93.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

109 → 109

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	193	3874
1	355	3361
2	913	2692
3	3423	2632
done	5000	2631

prune327.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.8b

regimes175.0ms

Accuracy

86.1% (3.1b remaining)

Error of 15.1b against oracle of 12.1b and baseline of 34.2b

bsearch145.0ms

Steps

Iters	Range		Point
8	1.9230140876291547e+24	5.884487837986356e+26	1.9426371746037666e+24
11	-1.829086240692416e+154	-2.187052964502477e+134	-1.3358786167585806e+154

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	51
1	39	49
2	41	49
done	41	49

end0.0ms

sample1.2s

Algorithm

intervals

Results

262.0ms	1104×	body	2560	valid
246.0ms	5868×	body	80	valid
173.0ms	910×	body	1280	valid
113.0ms	2861×	body	80	nan
66.0ms	422×	body	640	valid
28.0ms	96×	body	5120	valid
26.0ms	212×	body	320	valid
9.0ms	120×	body	160	valid