Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	34×	body	2560	valid
7.0ms	185×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	20×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	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: 15.0b

localize13.0ms

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))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite167.0ms

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:

56.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
28.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

Counts

104 → 104

Iterations

Useful iterations: 3 (67.0ms)

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

prune298.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.7b

localize24.0ms

Local error

Found 4 expressions with local error:

14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite95.0ms

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)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Counts

80 → 80

Iterations

Useful iterations: 1 (4.0ms)

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

prune418.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`sqrt-prod`
12×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp` `unswap-sqr`
4×	`sqrt-div` `prod-exp`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `associate-l` `flip-+` `log1p-expm1-u`
2×	`div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

3 → 84

Calls

3 calls:

73.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series185.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify42.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	366	763
1	1642	687
2	5001	651
done	5001	651

prune243.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.2b	(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt 1) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
31×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 105

Calls

4 calls:

29.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt 1) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt 1) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify143.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	360	1367
1	1267	1275
2	4989	1243
3	5001	1243
done	5001	1243

prune400.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.7b

regimes177.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	36
1	31	36
done	31	36

end0.0ms

sample856.0ms

Algorithm

intervals

Results

207.0ms	6050×	body	80	valid
190.0ms	835×	body	2560	valid
98.0ms	568×	body	1280	valid
91.0ms	8000×	pre	80	true
45.0ms	316×	body	640	valid
18.0ms	161×	body	320	valid
5.0ms	70×	body	160	valid