Details

sample74.0ms

Algorithm

intervals

Results

25.0ms	188×	body	80	valid
12.0ms	27×	body	2560	valid
7.0ms	21×	body	1280	valid
6.0ms	256×	pre	80	true
3.0ms	13×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	41
5	41
4	40
3	38
2	34
1	27
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

36.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
31.0ms	(+ (* (* 4.0 p) p) (* x x))
87.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
45.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
51.0ms	(+ (* (* 4.0 p) p) (* x x))
116.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1423
1	305
0	127

prune662.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* p (* p 4.0)))
0.4b	(+ (/ x (sqrt (+ (* x x) (* p (* p 4.0))))) 1.0)
0.4b	(log (exp (+ (/ x (sqrt (+ (* x x) (* p (* p 4.0))))) 1.0)))
14.0b	(sqrt (+ (* x x) (* p (* p 4.0))))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

8.0ms	(+ (* x x) (* p (* p 4.0)))
45.0ms	(+ (/ x (sqrt (+ (* x x) (* p (* p 4.0))))) 1.0)
149.0ms	(log (exp (+ (/ x (sqrt (+ (* x x) (* p (* p 4.0))))) 1.0)))
11.0ms	(sqrt (+ (* x x) (* p (* p 4.0))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* x x) (* p (* p 4.0)))
117.0ms	(+ (/ x (sqrt (+ (* x x) (* p (* p 4.0))))) 1.0)
100.0ms	(log (exp (+ (/ x (sqrt (+ (* x x) (* p (* p 4.0))))) 1.0)))
65.0ms	(sqrt (+ (* x x) (* p (* p 4.0))))

simplify1.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	1218
1	254
0	101

prune554.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.6b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite132.0ms

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`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`flip3-+` `sqrt-div` `prod-exp` `flip-+`
3×	`associate-l`
2×	`+-commutative` `sum-log` `div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

15.0ms	(+ (* (* 4.0 p) p) (* x x))
79.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
30.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* (* 4.0 p) p) (* x x))
75.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
90.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
65.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1909
1	429
0	151

prune520.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.6b	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

39×	`sqrt-prod`
27×	`associate-r`
22×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
11×	`pow1`
10×	`sqrt-div`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
4×	`flip3-+` `flip-+`
3×	`pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`frac-times` `+-commutative` `sum-log` `associate-l` `associate-l/` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

159.0ms	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
20.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
110.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
73.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
81.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1922
1	396
0	157

prune565.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.9b

regimes545.0ms

Accuracy

0% (0.3b remaining)

Error of 13.9b against oracle of 13.6b and baseline of 13.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	16

end0.0ms

sample1.7s

Algorithm

intervals

Results

581.0ms	756×	body	2560	valid
348.0ms	5946×	body	80	valid
250.0ms	651×	body	1280	valid
226.0ms	8000×	pre	80	true
63.0ms	322×	body	640	valid
30.0ms	182×	body	320	valid
24.0ms	61×	body	5120	valid
8.0ms	82×	body	160	valid