Details

sample84.0ms

Algorithm

intervals

Results

17.0ms	27×	body	2560	valid
17.0ms	183×	body	80	valid
13.0ms	26×	body	1280	valid
8.0ms	256×	pre	80	true
4.0ms	11×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

103.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
28.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series257.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
111.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.7s

Counts

40 → 40

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	71	605
1	181	521
2	513	484
3	1328	464
4	3399	460
done	5000	460

prune246.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.4b	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
0.4b	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

106.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
15.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series379.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
141.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
97.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify3.9s

Counts

60 → 60

Iterations

Useful iterations: 4 (591.0ms)

Iter	Nodes	Cost
0	81	868
1	148	788
2	309	715
3	631	704
4	1602	703
5	4231	703
done	5000	703

prune407.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 15.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
8.6b	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite79.0ms

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:

36.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
32.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
127.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
90.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
104.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.6s

Counts

136 → 136

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	116	3008
1	217	1696
2	563	1566
3	1893	1513
done	5000	1470

prune605.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.1b

localize33.0ms

Local error

Found 4 expressions with local error:

8.6b	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
8.6b	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))))
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

26.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
87.0ms	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
120.0ms	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))))
92.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
128.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.6s

Counts

78 → 78

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	82	1591
1	151	958
2	368	878
3	952	867
4	2807	866
done	5001	866

prune502.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.1b

regimes199.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	18
1	18	18
done	18	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

785.0ms	8000×	pre	80	true
684.0ms	6044×	body	80	valid
443.0ms	740×	body	2560	valid
258.0ms	627×	body	1280	valid
99.0ms	286×	body	640	valid
37.0ms	59×	body	5120	valid
35.0ms	153×	body	320	valid
14.0ms	91×	body	160	valid