Details

sample81.0ms

Algorithm

intervals

Results

15.0ms	181×	body	80	valid
14.0ms	23×	body	2560	valid
10.0ms	21×	body	1280	valid
7.0ms	256×	pre	80	true
6.0ms	18×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

19.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
32.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* (* 4.0 p) p) (* x x))
99.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
102.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
89.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts

103 → 103

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	136	1755
1	294	1489
2	840	1391
3	2363	1379
done	5000	1375

prune482.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
10.4b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
10.4b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
10.4b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite30.0ms

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:

22.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
67.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
67.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
77.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify3.8s

Counts

74 → 74

Iterations

Useful iterations: 4 (498.0ms)

Iter	Nodes	Cost
0	56	882
1	125	793
2	287	746
3	610	735
4	1565	734
5	4109	734
done	5000	734

prune547.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.1b

localize59.0ms

Local error

Found 4 expressions with local error:

10.4b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
10.4b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
10.4b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
12.9b	(+ 1.0 (/ x (* (* (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))

rewrite45.0ms

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:

3.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
3.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
3.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
34.0ms	(+ 1.0 (/ x (* (* (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))

series422.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
86.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
103.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
132.0ms	(+ 1.0 (/ x (* (* (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))

simplify2.4s

Counts

74 → 74

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	57	1365
1	129	1253
2	348	800
3	1122	735
4	4193	698
done	5000	698

prune460.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.1b

localize22.0ms

Local error

Found 4 expressions with local error:

10.4b	(sqrt (* (* (cbrt (fma 4.0 (pow p 2) (pow x 2))) (cbrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (fma 4.0 (pow p 2) (pow x 2)))))
11.2b	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
11.2b	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
11.2b	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
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 → 65

Calls

4 calls:

29.0ms	(sqrt (* (* (cbrt (fma 4.0 (pow p 2) (pow x 2))) (cbrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (fma 4.0 (pow p 2) (pow x 2)))))
1.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (* (* (cbrt (fma 4.0 (pow p 2) (pow x 2))) (cbrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (fma 4.0 (pow p 2) (pow x 2)))))
145.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
148.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
145.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

simplify2.6s

Counts

77 → 77

Iterations

Useful iterations: 5 (1.2s)

Iter	Nodes	Cost
0	79	1160
1	140	1042
2	254	777
3	499	723
4	1140	711
5	3114	705
done	5001	705

prune272.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.1b

regimes109.0ms

Accuracy

0% (0.5b remaining)

Error of 13.6b against oracle of 13.1b and baseline of 13.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	70
1	29	70
done	29	70

end0.0ms

sample1.8s

Algorithm

intervals

Results

743.0ms	6016×	body	80	valid
298.0ms	746×	body	2560	valid
205.0ms	601×	body	1280	valid
162.0ms	8000×	pre	80	true
100.0ms	341×	body	640	valid
22.0ms	155×	body	320	valid
21.0ms	56×	body	5120	valid
8.0ms	85×	body	160	valid