Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

327×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (3.0ms)

Iter	Nodes	Cost
0	6	7
1	14	7
2	22	6
3	26	6
done	26	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)

rewrite3.0ms

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:

45.0ms

(* (fma y y 1.0) x)

simplify1.5s

Counts

23 → 23

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	39	204
1	77	198
2	249	168
3	1110	168
done	5001	168

prune45.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.5b

localize7.0ms

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:

5.0ms	(* (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))

series246.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (sqrt (fma y y 1.0)) x)
47.0ms	(* (sqrt (fma y y 1.0)) (* (sqrt (fma y y 1.0)) x))
51.0ms	(sqrt (fma y y 1.0))
55.0ms	(sqrt (fma y y 1.0))

simplify1.5s

Counts

89 → 89

Iterations

Useful iterations: 3 (477.0ms)

Iter	Nodes	Cost
0	103	1047
1	242	828
2	734	734
3	3292	671
done	5001	671

prune250.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.5b

localize15.0ms

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))

rewrite36.0ms

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)
22.0ms	(* (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:

189.0ms	(* (hypot y (sqrt 1.0)) x)
573.0ms	(* (sqrt (sqrt (fma y y 1.0))) (* (sqrt (hypot y (sqrt 1.0))) (* (hypot y (sqrt 1.0)) x)))
307.0ms	(* (sqrt (hypot y (sqrt 1.0))) (* (hypot y (sqrt 1.0)) x))
58.0ms	(sqrt (fma y y 1.0))

simplify590.0ms

Counts

99 → 99

Iterations

Useful iterations: done (587.0ms)

Iter	Nodes	Cost
0	215	1730
1	555	1599
2	1917	1235
done	5001	1231

prune352.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

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))

rewrite10.0ms

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:

7.0ms	(* (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))

series647.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (fabs (cbrt (fma y y 1.0))) (sqrt (cbrt (fma y y 1.0))))
54.0ms	(sqrt (fma y y 1.0))
189.0ms	(cbrt (fma y y 1.0))
195.0ms	(cbrt (fma y y 1.0))

simplify480.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (133.0ms)

Iter	Nodes	Cost
0	180	1221
1	417	1131
2	1375	1032
done	5000	1032

prune315.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes74.0ms

Accuracy

98.7% (0.1b remaining)

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

bsearch92.0ms

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

sample374.0ms

Algorithm

intervals

Results

212.0ms

10636×

body

valid