Details

sample61.0ms

Algorithm

intervals

Results

14.0ms	35×	body	2560	valid
12.0ms	188×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	14×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	40	16
3	47	16
4	49	16
5	51	16
6	52	16
done	52	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 63

Calls

4 calls:

64.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
21.0ms	(+ (* (* 4.0 p) p) (* x x))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series632.0ms

Counts

4 → 12

Calls

4 calls:

434.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
44.0ms	(+ (* (* 4.0 p) p) (* x x))
89.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
65.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.1s

Counts

75 → 75

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	108	1196
1	274	1037
2	1146	960
done	5001	946

prune312.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))
8.3b	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))))
14.5b	(sqrt (fma (* 4.0 p) p (pow x 2)))
14.5b	(sqrt (fma (* 4.0 p) p (pow x 2)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 124

Calls

4 calls:

40.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))
25.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))))
1.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
2.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))
138.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))))
90.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
85.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

simplify977.0ms

Counts

136 → 136

Iterations

Useful iterations: done (973.0ms)

Iter	Nodes	Cost
0	116	3008
1	256	1708
2	1242	1566
done	5001	1534

prune410.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.6b

localize34.0ms

Local error

Found 4 expressions with local error:

6.9b	(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))))))
14.5b	(sqrt (fma (* 4.0 p) p (pow x 2)))
14.5b	(sqrt (fma (* 4.0 p) p (pow x 2)))
14.5b	(sqrt (fma (* 4.0 p) p (pow x 2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-sqrt-square` `fma-def` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

23.0ms	(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))))))
1.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
1.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
2.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))))))
83.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
108.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
80.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

simplify2.2s

Counts

74 → 74

Iterations

Useful iterations: 3 (756.0ms)

Iter	Nodes	Cost
0	87	1497
1	203	1379
2	643	1280
3	4055	1275
done	5000	1275

prune553.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.6b

localize29.0ms

Local error

Found 4 expressions with local error:

6.9b	(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))))))
14.5b	(sqrt (fma (* 4.0 p) p (pow x 2)))
14.5b	(sqrt (fma (* 4.0 p) p (pow x 2)))
14.5b	(sqrt (fma (* 4.0 p) p (pow x 2)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-sqrt-square` `fma-def` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

44.0ms	(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))))))
2.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
2.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
2.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (pow x 2))))))))
85.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
87.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))
83.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

simplify2.0s

Counts

74 → 74

Iterations

Useful iterations: 3 (699.0ms)

Iter	Nodes	Cost
0	87	1497
1	203	1379
2	643	1280
3	4055	1275
done	5000	1275

prune507.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.6b

regimes235.0ms

Accuracy

84.6% (0.3b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 15.1b

bsearch70.0ms

Steps

Iters	Range		Point
4	-2.0633065558764823e-133	-1.0436236701804817e-133	-1.7221823146561012e-133

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	176
1	50	176
done	50	176

end0.0ms

sample2.3s

Algorithm

intervals

Results

617.0ms	631×	body	1280	valid
480.0ms	5977×	body	80	valid
355.0ms	793×	body	2560	valid
233.0ms	8000×	pre	80	true
147.0ms	318×	body	640	valid
68.0ms	58×	body	5120	valid
29.0ms	154×	body	320	valid
8.0ms	69×	body	160	valid