Details

sample72.0ms

Algorithm

intervals

Results

16.0ms	189×	body	80	valid
14.0ms	27×	body	2560	valid
9.0ms	24×	body	1280	valid
6.0ms	256×	pre	80	true
4.0ms	10×	body	640	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize44.0ms

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))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

52.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
29.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
62.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
30.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series693.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
101.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
140.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
84.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	2553
2	838
1	295
0	137

prune593.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.6b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-/r*` `sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+`
3×	`associate-l` `pow-flip` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 122

Calls

4 calls:

37.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
112.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
19.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
87.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
146.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
74.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.8s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
3	3291
2	1247
1	391
0	158

prune721.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))))
0.2b	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
3.6b	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
16.7b	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
7×	`unpow-prod-down` `associate-r`
6×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `sqrt-pow1` `flip3-+` `sqrt-div` `pow-exp` `associate-*r/` `flip-+`
1×	`+-commutative` `sum-log` `pow-pow` `pow1/2` `pow-prod-down` `*-commutative` `sqrt-prod` `cbrt-unprod`

Counts

4 → 66

Calls

4 calls:

5.0ms	(sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))))
96.0ms	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
6.0ms	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
28.0ms	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

series842.0ms

Counts

4 → 12

Calls

4 calls:

455.0ms	(sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))))
90.0ms	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
116.0ms	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
181.0ms	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

simplify2.3s

Counts

78 → 78

Iterations

Iter	Nodes
done	5007
3	2678
2	808
1	289
0	123

prune562.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
3.5b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))))))
3.6b	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
16.7b	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-exp-log`
7×	`unpow-prod-down` `associate-r`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`log-pow`
4×	`exp-prod`
3×	`pow-unpow` `log-prod` `associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `pow-exp`
1×	`+-commutative` `sum-log` `pow-pow` `flip3-+` `rem-log-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `flip-+`

Counts

4 → 69

Calls

4 calls:

120.0ms	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
4.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))))))
12.0ms	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
20.0ms	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

series789.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
416.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))))))
114.0ms	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
190.0ms	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

simplify2.1s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
3	2174
2	754
1	299
0	136

prune531.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.1b

regimes430.0ms

Accuracy

0% (0.4b remaining)

Error of 13.3b against oracle of 12.9b and baseline of 13.3b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample2.1s

Algorithm

intervals

Results

903.0ms	6045×	body	80	valid
392.0ms	755×	body	2560	valid
249.0ms	652×	body	1280	valid
186.0ms	8000×	pre	80	true
120.0ms	297×	body	640	valid
27.0ms	46×	body	5120	valid
25.0ms	134×	body	320	valid
9.0ms	71×	body	160	valid