Details

sample50.0ms

Algorithm

intervals

Results

34.0ms

452×

body

valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (686.0ms)

Iter	Nodes	Cost
0	28	67
1	70	66
2	242	47
3	941	35
4	3244	34
done	5001	34

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
0.1b	(* (/ 1.0 (sqrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
0.2b	(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0b	(sqrt PI)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`associate-l`
33×	`times-frac`
29×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
16×	`associate-r`
14×	`add-cbrt-cube`
13×	`sqrt-prod`
11×	`unswap-sqr`
8×	`prod-exp`
7×	`pow1`
5×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `sqr-pow`
2×	`cbrt-undiv` `pow-to-exp` `pow-exp` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `cube-mult` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 123

Calls

4 calls:

0.0ms	(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
11.0ms	(* (/ 1.0 (sqrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
12.0ms	(* (pow (fabs x) 3) (/ 2.0 3.0))
4.0ms	(sqrt PI)

series518.0ms

Counts

4 → 10

Calls

4 calls:

182.0ms	(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
292.0ms	(* (/ 1.0 (sqrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
44.0ms	(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms	(sqrt PI)

simplify784.0ms

Counts

133 → 133

Iterations

Useful iterations: 2 (273.0ms)

Iter	Nodes	Cost
0	213	3168
1	505	3074
2	1986	2788
done	5000	2788

prune609.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
0.2b	(* (pow (fabs x) 3) (/ 2.0 3.0))
0.4b	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt PI))
1.0b	(sqrt PI)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
31×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log`
15×	`sqrt-prod`
13×	`associate-r`
12×	`associate-l`
11×	`add-cbrt-cube`
8×	`unswap-sqr`
6×	`prod-exp` `associate-/r*`
5×	`pow1` `unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `sqr-pow`
2×	`cbrt-undiv` `pow-to-exp` `pow-exp` `cbrt-unprod` `div-inv`
1×	`cube-mult` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `unpow3` `associate-r/` `clear-num` `-commutative` `fma-udef`

Counts

4 → 118

Calls

4 calls:

0.0ms	(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
11.0ms	(* (pow (fabs x) 3) (/ 2.0 3.0))
3.0ms	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt PI))
1.0ms	(sqrt PI)

series488.0ms

Counts

4 → 10

Calls

4 calls:

185.0ms	(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
48.0ms	(* (pow (fabs x) 3) (/ 2.0 3.0))
254.0ms	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt PI))
0.0ms	(sqrt PI)

simplify740.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (206.0ms)

Iter	Nodes	Cost
0	196	3342
1	420	3220
2	1515	3010
done	5000	3010

prune741.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (fabs x) 3) (/ 2.0 3.0))
0.4b	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
22×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`times-frac`
14×	`add-cbrt-cube`
13×	`associate-r`
12×	`associate-l`
8×	`unswap-sqr`
7×	`prod-exp`
6×	`pow1` `sqrt-prod`
5×	`unpow-prod-down` `cube-prod` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `cbrt-unprod` `associate-/l*` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `div-inv`
1×	`cube-mult` `frac-2neg` `unpow3` `associate-r/` `clear-num` `associate-/r` `*-commutative`

Counts

4 → 105

Calls

4 calls:

11.0ms	(* (pow (fabs x) 3) (/ 2.0 3.0))
8.0ms	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series295.0ms

Counts

4 → 8

Calls

4 calls:

43.0ms	(* (pow (fabs x) 3) (/ 2.0 3.0))
252.0ms	(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify744.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (193.0ms)

Iter	Nodes	Cost
0	177	2041
1	411	1814
2	1523	1602
done	5000	1602

prune536.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (expm1 (log1p (sqrt PI)))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
0.2b	(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0b	(expm1 (log1p (sqrt PI)))
1.0b	(sqrt PI)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
25×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
22×	`add-exp-log`
16×	`associate-r`
14×	`add-cbrt-cube`
10×	`unswap-sqr`
8×	`prod-exp`
7×	`pow1`
5×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`cbrt-undiv` `pow-to-exp` `pow-exp` `*-commutative` `fma-udef` `div-inv`
1×	`distribute-rgt-in` `cube-mult` `rem-sqrt-square` `expm1-log1p` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `expm1-udef`

Counts

4 → 114

Calls

4 calls:

7.0ms	(* (/ 1.0 (expm1 (log1p (sqrt PI)))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
11.0ms	(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms	(expm1 (log1p (sqrt PI)))
1.0ms	(sqrt PI)

series540.0ms

Counts

4 → 8

Calls

4 calls:

496.0ms	(* (/ 1.0 (expm1 (log1p (sqrt PI)))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
44.0ms	(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms	(expm1 (log1p (sqrt PI)))
0.0ms	(sqrt PI)

simplify786.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (265.0ms)

Iter	Nodes	Cost
0	214	2482
1	501	2279
2	1953	2049
done	5000	2049

prune581.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes66.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	34
1	27	34
done	27	34

end0.0ms

sample1.1s

Algorithm

intervals

Results

942.0ms

13952×

body

valid