Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	199×	body	80	valid
5.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	18×	body	1280	valid
2.0ms	11×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	27	17
2	33	17
3	37	17
4	39	17
5	40	17
done	40	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize11.0ms

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))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite55.0ms

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×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
24.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
34.0ms	(+ (* (* 4.0 p) p) (* x x))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.4s

Counts

91 → 91

Iterations

Useful iterations: 3 (469.0ms)

Iter	Nodes	Cost
0	128	1657
1	279	1506
2	786	1400
3	2661	1385
done	5000	1385

prune284.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

24.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
26.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
9.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
180.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts

72 → 72

Iterations

Useful iterations: 4 (679.0ms)

Iter	Nodes	Cost
0	110	1434
1	232	1313
2	525	1163
3	1245	1114
4	2819	1106
done	5001	1106

prune253.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-log-exp`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `log-prod` `cube-prod`
3×	`pow-unpow` `flip3-+` `sqrt-prod` `log-pow` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

2.0ms	(pow (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
26.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series688.0ms

Counts

4 → 12

Calls

4 calls:

380.0ms	(pow (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
181.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.5s

Counts

79 → 79

Iterations

Useful iterations: 3 (438.0ms)

Iter	Nodes	Cost
0	117	1630
1	284	1481
2	771	1337
3	3088	1301
done	5001	1301

prune289.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-log-exp`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `log-prod` `cube-prod`
3×	`pow-unpow` `flip3-+` `sqrt-prod` `log-pow` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

2.0ms	(pow (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
23.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series675.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(pow (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
174.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.6s

Counts

79 → 79

Iterations

Useful iterations: 3 (442.0ms)

Iter	Nodes	Cost
0	117	1630
1	284	1481
2	771	1337
3	3088	1301
done	5001	1301

prune295.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.0b

regimes297.0ms

Accuracy

65.6% (1.3b remaining)

Error of 10.9b against oracle of 9.6b and baseline of 13.3b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	61
1	48	61
done	48	61

end0.0ms

sample783.0ms

Algorithm

intervals

Results

199.0ms	6026×	body	80	valid
171.0ms	809×	body	2560	valid
109.0ms	597×	body	1280	valid
95.0ms	8000×	pre	80	true
41.0ms	317×	body	640	valid
16.0ms	166×	body	320	valid
6.0ms	85×	body	160	valid