Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	191×	body	80	valid
8.0ms	30×	body	2560	valid
4.0ms	18×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	10×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (/ x (sqrt (+ (* x x) (* (* p p) 4.0))))) 0.5))
0.0b	(* (* p p) 4.0)
0.6b	(+ 1.0 (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))))
13.2b	(sqrt (+ (* x x) (* (* p p) 4.0)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
4×	`sqrt-div` `pow-prod-down` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `associate-r` `prod-exp` `cbrt-unprod` `flip-+`
2×	`pow1/2` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `associate-l` `*-commutative` `distribute-lft-out` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

31.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (+ (* x x) (* (* p p) 4.0))))) 0.5))
24.0ms	(* (* p p) 4.0)
29.0ms	(+ 1.0 (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))))
9.0ms	(sqrt (+ (* x x) (* (* p p) 4.0)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

353.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (+ (* x x) (* (* p p) 4.0))))) 0.5))
36.0ms	(* (* p p) 4.0)
105.0ms	(+ 1.0 (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))))
69.0ms	(sqrt (+ (* x x) (* (* p p) 4.0)))

simplify624.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1216
1	273
0	116

prune457.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (pow p 2))
0.5b	(log (exp (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)))))
0.6b	(+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
13.2b	(sqrt (+ (* x x) (* 4.0 (pow p 2))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`add-exp-log`
8×	`associate-r`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`log-pow`
4×	`exp-prod` `unpow-prod-down` `sqrt-prod` `unswap-sqr`
3×	`log-prod` `associate-l` `prod-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 70

Calls

4 calls:

13.0ms	(* 4.0 (pow p 2))
3.0ms	(log (exp (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)))))
51.0ms	(+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
8.0ms	(sqrt (+ (* x x) (* 4.0 (pow p 2))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 4.0 (pow p 2))
350.0ms	(log (exp (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)))))
95.0ms	(+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
66.0ms	(sqrt (+ (* x x) (* 4.0 (pow p 2))))

simplify2.6s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
3	4299
2	857
1	307
0	145

prune605.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (pow p 2))
0.3b	(* (sqrt (+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)) (sqrt 0.5))
0.6b	(+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
13.2b	(sqrt (+ (* x x) (* 4.0 (pow p 2))))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`associate-r` `sqrt-prod`
12×	`add-cube-cbrt`
11×	`add-exp-log`
10×	`associate-l`
9×	`pow1`
8×	`add-cbrt-cube` `unswap-sqr`
6×	`add-log-exp`
4×	`unpow-prod-down` `sqrt-div` `prod-exp`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`associate-l/` `-commutative` `cbrt-unprod` `distribute-lft-out` `unpow2` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `sum-log` `sqrt-unprod` `pow-exp`

Counts

4 → 87

Calls

4 calls:

9.0ms	(* 4.0 (pow p 2))
109.0ms	(* (sqrt (+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)) (sqrt 0.5))
48.0ms	(+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
9.0ms	(sqrt (+ (* x x) (* 4.0 (pow p 2))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 4.0 (pow p 2))
336.0ms	(* (sqrt (+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)) (sqrt 0.5))
89.0ms	(+ (/ x (sqrt (+ (* x x) (* 4.0 (pow p 2))))) 1.0)
63.0ms	(sqrt (+ (* x x) (* 4.0 (pow p 2))))

simplify674.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1284
1	345
0	155

prune505.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.8b

localize49.0ms

Local error

Found 4 expressions with local error:

5.8b	(log (exp (sqrt (* 0.5 (+ (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)))))
8.6b	(+ (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)
13.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

2.0ms	(log (exp (sqrt (* 0.5 (+ (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)))))
176.0ms	(+ (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)
30.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(log (exp (sqrt (* 0.5 (+ (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)))))
84.0ms	(+ (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
71.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	1940
2	620
1	225
0	103

prune474.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.8b

regimes411.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample1.9s

Algorithm

intervals

Results

664.0ms	774×	body	2560	valid
479.0ms	6025×	body	80	valid
220.0ms	620×	body	1280	valid
178.0ms	8000×	pre	80	true
89.0ms	268×	body	640	valid
32.0ms	70×	body	5120	valid
31.0ms	166×	body	320	valid
9.0ms	77×	body	160	valid