Details

sample56.0ms

Algorithm

intervals

Results

25.0ms	271×	body	80	valid
7.0ms	79×	body	80	nan

simplify203.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (30.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize119.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
0.6b	(- (* b b) (* (* 4.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

15.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* 4.0 a) c))
66.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
143.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts

78 → 78

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	71	1146
1	168	1050
2	574	952
3	2407	952
done	5000	936

prune497.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize117.0ms

Local error

Found 4 expressions with local error:

21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `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:

16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
145.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
138.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts

74 → 74

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	94	1258
1	216	1182
2	617	1076
3	2159	1058
done	5001	1028

prune641.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

localize124.0ms

Local error

Found 4 expressions with local error:

8.8b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

36.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
146.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
171.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

84 → 84

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	152	1636
1	389	1532
2	1307	1322
done	5000	1289

prune779.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

localize139.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 63

Calls

4 calls:

18.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series923.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* b b) (* (* 4.0 a) c))
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
523.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
194.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts

75 → 75

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	111	1207
1	245	1133
2	747	1040
3	2814	1014
done	5001	984

prune661.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.8b

regimes331.0ms

Accuracy

91.8% (1.0b remaining)

Error of 8.7b against oracle of 7.7b and baseline of 20.3b

bsearch182.0ms

Steps

Iters	Range		Point
0	2.0836136179885362e+135	2.1675125417143413e+135	2.1255630798514387e+135
10	-7.092886765712621e+82	-3.4482088762076956e+69	-3.2734862173190983e+79

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	143
1	53	143
done	53	143

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	8745×	body	80	valid
319.0ms	2922×	body	80	nan