Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	195×	body	80	valid
8.0ms	26×	body	2560	valid
5.0ms	256×	pre	80	true
4.0ms	16×	body	1280	valid
2.0ms	10×	body	320	valid
1.0ms	5×	body	640	valid
0.0ms	4×	body	160	valid

simplify72.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	27	17
2	34	17
3	38	17
4	40	17
5	41	17
done	41	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.9b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite174.0ms

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:

18.0ms	(+ (* (* 4.0 p) p) (* x x))
40.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
37.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* (* 4.0 p) p) (* x x))
79.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
112.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts

91 → 91

Iterations

Useful iterations: 3 (563.0ms)

Iter	Nodes	Cost
0	128	1657
1	277	1506
2	773	1400
3	2062	1385
done	5000	1385

prune502.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.9b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.4b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite240.0ms

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:

75.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
64.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
42.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
122.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
329.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
88.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts

72 → 72

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	110	1434
1	231	1313
2	551	1163
3	1288	1114
4	3086	1106
done	5001	1105

prune282.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize29.0ms

Local error

Found 4 expressions with local error:

3.4b	(log (- (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0))))
4.0b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`pow1`
6×	`sqrt-prod`
4×	`log-div` `sqrt-div` `add-log-exp`
3×	`log-prod` `flip3-+` `times-frac` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-*r/` `div-exp` `associate-/r/` `frac-sub` `flip--`
1×	`frac-2neg` `rem-log-exp` `prod-exp` `clear-num` `log-pow` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

77.0ms	(log (- (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0))))
35.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
33.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(log (- (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0))))
56.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
65.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify764.0ms

Counts

81 → 81

Iterations

Useful iterations: done (761.0ms)

Iter	Nodes	Cost
0	138	1984
1	366	1853
2	1317	1653
done	5000	1627

prune497.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.9b	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.5b	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt`
26×	`log-pow`
24×	`exp-prod` `sqrt-prod`
7×	`pow1`
6×	`add-exp-log` `log-prod` `sqrt-div` `associate-/r*` `add-cbrt-cube`
5×	`add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-+r+` `associate-/l*`
2×	`div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

4 → 108

Calls

4 calls:

31.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
176.0ms	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
72.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
85.0ms	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
64.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts

120 → 120

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	176	2216
1	309	1886
2	676	1786
3	1459	1767
4	3345	1761
done	5001	1761

prune358.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

regimes292.0ms

Accuracy

0% (0.6b remaining)

Error of 13.7b against oracle of 13.1b and baseline of 13.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	54
1	25	54
done	25	54

end0.0ms

sample1.8s

Algorithm

intervals

Results

662.0ms	5977×	body	80	valid
345.0ms	850×	body	2560	valid
218.0ms	638×	body	1280	valid
155.0ms	8000×	pre	80	true
83.0ms	284×	body	640	valid
53.0ms	165×	body	320	valid
8.0ms	86×	body	160	valid