Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	196×	body	80	valid
6.0ms	20×	body	2560	valid
5.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify69.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	40	16
3	47	16
4	49	16
5	51	16
6	52	16
done	52	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize15.0ms

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))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`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×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
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 → 91

Calls

4 calls:

19.0ms	(+ (* (* 4.0 p) p) (* x x))
41.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
65.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
30.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* (* 4.0 p) p) (* x x))
64.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
92.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.7s

Counts

103 → 103

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	136	1755
1	294	1489
2	840	1391
3	2363	1379
done	5000	1375

prune403.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (pow p 2) (pow x 2))
0.2b	(* x (/ 1 (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
3.9b	(+ 1.0 (* x (/ 1 (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
14.0b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

0.0ms	(fma 4.0 (pow p 2) (pow x 2))
22.0ms	(* x (/ 1 (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma 4.0 (pow p 2) (pow x 2))
63.0ms	(* x (/ 1 (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
86.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
69.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify3.1s

Counts

102 → 102

Iterations

Useful iterations: 3 (439.0ms)

Iter	Nodes	Cost
0	137	1524
1	305	1244
2	674	1125
3	1720	1122
4	4773	1122
done	5000	1122

prune364.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))
0.7b	(log (exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
0.7b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
14.0b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

6.0ms	(/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))
56.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
14.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))
82.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
88.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
68.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify2.8s

Counts

104 → 104

Iterations

Useful iterations: 4 (562.0ms)

Iter	Nodes	Cost
0	131	1688
1	230	1514
2	462	1419
3	867	1419
4	2170	1418
done	5000	1418

prune443.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3) (pow 1.0 3))
2.1b	(/ x (fma 4.0 (pow p 2) (pow x 2)))
14.0b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
14.0b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
50×	`fma-def`
45×	`times-frac`
43×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
26×	`unpow-prod-down` `cube-prod`
24×	`sqrt-prod`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `frac-2neg` `flip3-+` `unpow3` `div-exp` `clear-num` `sum-log` `sum-cubes` `flip-+` `sqr-pow`

Counts

4 → 128

Calls

4 calls:

109.0ms	(+ (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3) (pow 1.0 3))
7.0ms	(/ x (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3) (pow 1.0 3))
62.0ms	(/ x (fma 4.0 (pow p 2) (pow x 2)))
65.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
62.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify1.5s

Counts

140 → 140

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	108	1392
1	229	1293
2	738	1191
3	3000	1191
done	5000	1191

prune622.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

regimes180.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	50
1	27	50
done	27	50

end0.0ms

sample1.7s

Algorithm

intervals

Results

639.0ms	723×	body	2560	valid
320.0ms	6047×	body	80	valid
205.0ms	8000×	pre	80	true
179.0ms	590×	body	1280	valid
65.0ms	333×	body	640	valid
58.0ms	77×	body	5120	valid
23.0ms	160×	body	320	valid
7.0ms	70×	body	160	valid