Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
5.0ms	24×	body	2560	valid
4.0ms	24×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	11×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	9
done	53	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize15.0ms

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	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

55.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
28.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
55.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify80.0ms

Counts

104 → 104

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	297	948
1	884	898
2	2732	885
3	5001	883
done	5001	883

prune333.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.2b	(log (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
15.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

216.0ms	(exp (log (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
53.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(log (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series813.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(exp (log (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
83.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
379.0ms	(log (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify64.0ms

Counts

89 → 89

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	293	923
1	743	848
2	2030	831
3	5002	826
done	5002	826

prune349.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize27.0ms

Local error

Found 4 expressions with local error:

15.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify87.0ms

Counts

80 → 80

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	106	544
1	323	524
2	963	524
3	2523	524
4	5002	524
done	5002	524

prune550.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
6.8b	(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
16.7b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.7b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
53×	`times-frac`
37×	`*-un-lft-identity`
33×	`add-cube-cbrt` `associate-r`
26×	`add-exp-log`
24×	`sqrt-prod`
18×	`cbrt-prod`
16×	`add-cbrt-cube`
13×	`associate-l`
12×	`unswap-sqr`
8×	`div-exp` `prod-exp`
6×	`pow1` `cbrt-div` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u`
3×	`fma-def`
2×	`rec-exp` `pow1/3` `sqrt-div` `1-exp` `associate-/r/` `div-inv`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 130

Calls

4 calls:

88.0ms	(* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms	(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
13.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series776.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
269.0ms	(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
142.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
136.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify85.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	759	2409
1	3416	2165
2	5002	2114
done	5002	2114

prune606.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.3b

regimes291.0ms

Accuracy

77% (1.4b remaining)

Error of 8.6b against oracle of 7.3b and baseline of 13.1b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	56
1	52	56
done	52	56

end0.0ms

sample846.0ms

Algorithm

intervals

Results

203.0ms	6053×	body	80	valid
160.0ms	772×	body	2560	valid
113.0ms	662×	body	1280	valid
105.0ms	8000×	pre	80	true
37.0ms	281×	body	640	valid
17.0ms	154×	body	320	valid
5.0ms	78×	body	160	valid