Details

sample40.0ms

Algorithm

intervals

Results

10.0ms	27×	body	2560	valid
7.0ms	190×	body	80	valid
4.0ms	22×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	11×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	9
done	53	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize12.0ms

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))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

55.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
30.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
57.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
60.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify82.0ms

Counts

104 → 104

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	297	948
1	884	898
2	2732	885
3	5001	883
done	5001	883

prune320.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.5b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
8×	`exp-prod`
6×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `distribute-lft-out`
2×	`flip3-+` `sqrt-div` `exp-sum` `sum-log` `flip-+` `rem-exp-log`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 69

Calls

4 calls:

206.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
210.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
83.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify122.0ms

Counts

81 → 81

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	219	628
1	680	566
2	1814	565
3	4609	564
4	5001	564
done	5001	564

prune303.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-r/` `associate-l*`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `1-exp` `sum-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 99

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
73.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
57.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
64.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify50.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	407	969
1	1772	880
2	5001	845
done	5001	845

prune325.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.2b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
24×	`-un-lft-identity` `associate-r*`
22×	`add-cube-cbrt` `times-frac`
15×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`log-pow` `unswap-sqr`
4×	`expm1-log1p-u` `exp-prod` `sqrt-div` `prod-exp` `log1p-expm1-u`
3×	`log-prod` `fma-def` `flip3-+` `associate-l` `flip-+`
2×	`div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 102

Calls

4 calls:

73.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
285.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
83.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	416	1033
1	1736	917
2	5001	881
done	5001	881

prune360.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.3b

regimes145.0ms

Accuracy

0% (0.4b remaining)

Error of 13.4b against oracle of 12.9b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	14
1	28	14
done	28	14

end0.0ms

sample908.0ms

Algorithm

intervals

Results

223.0ms	6055×	body	80	valid
185.0ms	809×	body	2560	valid
107.0ms	8000×	pre	80	true
107.0ms	589×	body	1280	valid
48.0ms	323×	body	640	valid
16.0ms	146×	body	320	valid
6.0ms	78×	body	160	valid