Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

327×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	6	7
1	14	7
2	23	6
3	28	6
done	28	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize4.0ms

Local error

Found 1 expressions with local error:

7.1b	(* (fma y y 1.0) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
1×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

1 → 20

Calls

1 calls:

3.0ms

(* (fma y y 1.0) x)

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(* (fma y y 1.0) x)

simplify821.0ms

Counts

23 → 23

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	39	204
1	79	198
2	276	168
3	1323	168
done	5000	168

prune42.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.5b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (fma y y 1.0)) x)
0.1b	(* (sqrt (fma y y 1.0)) (* (sqrt (fma y y 1.0)) x))
7.1b	(sqrt (fma y y 1.0))
7.1b	(sqrt (fma y y 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`pow1` `sqrt-prod`
12×	`associate-l`
11×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

4.0ms	(* (sqrt (fma y y 1.0)) x)
10.0ms	(* (sqrt (fma y y 1.0)) (* (sqrt (fma y y 1.0)) x))
1.0ms	(sqrt (fma y y 1.0))
1.0ms	(sqrt (fma y y 1.0))

series230.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sqrt (fma y y 1.0)) x)
42.0ms	(* (sqrt (fma y y 1.0)) (* (sqrt (fma y y 1.0)) x))
48.0ms	(sqrt (fma y y 1.0))
52.0ms	(sqrt (fma y y 1.0))

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: 3 (351.0ms)

Iter	Nodes	Cost
0	103	1047
1	246	828
2	818	734
3	3532	671
done	5001	671

prune243.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (hypot y (sqrt 1.0)) x)
0.1b	(* (sqrt (sqrt (fma y y 1.0))) (* (sqrt (hypot y (sqrt 1.0))) (* (hypot y (sqrt 1.0)) x)))
0.1b	(* (sqrt (hypot y (sqrt 1.0))) (* (hypot y (sqrt 1.0)) x))
7.1b	(sqrt (fma y y 1.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-l`
15×	`add-sqr-sqrt` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

3.0ms	(* (hypot y (sqrt 1.0)) x)
25.0ms	(* (sqrt (sqrt (fma y y 1.0))) (* (sqrt (hypot y (sqrt 1.0))) (* (hypot y (sqrt 1.0)) x)))
8.0ms	(* (sqrt (hypot y (sqrt 1.0))) (* (hypot y (sqrt 1.0)) x))
1.0ms	(sqrt (fma y y 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (hypot y (sqrt 1.0)) x)
560.0ms	(* (sqrt (sqrt (fma y y 1.0))) (* (sqrt (hypot y (sqrt 1.0))) (* (hypot y (sqrt 1.0)) x)))
299.0ms	(* (sqrt (hypot y (sqrt 1.0))) (* (hypot y (sqrt 1.0)) x))
51.0ms	(sqrt (fma y y 1.0))

simplify644.0ms

Counts

99 → 99

Iterations

Useful iterations: done (641.0ms)

Iter	Nodes	Cost
0	215	1730
1	557	1599
2	2055	1235
done	5000	1231

prune340.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (fma y y 1.0))) (sqrt (cbrt (fma y y 1.0))))
7.1b	(sqrt (fma y y 1.0))
7.3b	(cbrt (fma y y 1.0))
7.3b	(cbrt (fma y y 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
10×	`cbrt-prod`
9×	`associate-r`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

6.0ms	(* (fabs (cbrt (fma y y 1.0))) (sqrt (cbrt (fma y y 1.0))))
1.0ms	(sqrt (fma y y 1.0))
0.0ms	(cbrt (fma y y 1.0))
1.0ms	(cbrt (fma y y 1.0))

series606.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (fabs (cbrt (fma y y 1.0))) (sqrt (cbrt (fma y y 1.0))))
49.0ms	(sqrt (fma y y 1.0))
182.0ms	(cbrt (fma y y 1.0))
176.0ms	(cbrt (fma y y 1.0))

simplify588.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	180	1221
1	420	1136
2	1568	1032
done	5001	1032

prune290.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes73.0ms

Accuracy

98.7% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 5.8b

bsearch90.0ms

Steps

Iters	Range		Point
10	5.867806433176675e+143	6.696365043910614e+157	4.450802574869413e+153
9	-4.9681890457189857e+33	-1.2562549030609593e+26	-6.685152828313653e+28

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	64
1	36	64
done	36	64

end0.0ms

sample354.0ms

Algorithm

intervals

Results

191.0ms

10636×

body

valid