Details

sample119.0ms

Algorithm

intervals

Results

60.0ms	69×	body	1280	valid
21.0ms	52×	body	640	valid
15.0ms	26×	body	2560	valid
8.0ms	29×	body	320	valid
5.0ms	69×	body	80	valid
2.0ms	11×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
1.0b	(+ x (hypot 1 x))
2.8b	(log (+ x (hypot 1 x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
4×	`pow1` `log-prod` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `sum-log` `rem-log-exp` `log-pow`

Counts

3 → 47

Calls

3 calls:

0.0ms	(hypot 1 x)
4.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))

series299.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(hypot 1 x)
69.0ms	(+ x (hypot 1 x))
160.0ms	(log (+ x (hypot 1 x)))

simplify519.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
2	666
1	244
0	108

prune226.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.1b	(* (* x x) x)
17.6b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma 3/40 (pow x 5) x)
23.0ms	(* (* x x) x)
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

series298.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(fma 3/40 (pow x 5) x)
51.0ms	(* (* x x) x)
72.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

simplify723.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	2000
3	1455
2	362
1	133
0	69

prune203.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (fma 3/40 (pow x 5) x)) (sqrt (fma 3/40 (pow x 5) x)))
3.5b	(sqrt (fma 3/40 (pow x 5) x))
3.5b	(sqrt (fma 3/40 (pow x 5) x))
8.6b	(fma -1/6 (* (* x x) x) (* (sqrt (fma 3/40 (pow x 5) x)) (sqrt (fma 3/40 (pow x 5) x))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 95

Calls

4 calls:

14.0ms	(* (sqrt (fma 3/40 (pow x 5) x)) (sqrt (fma 3/40 (pow x 5) x)))
2.0ms	(sqrt (fma 3/40 (pow x 5) x))
2.0ms	(sqrt (fma 3/40 (pow x 5) x))
0.0ms	(fma -1/6 (* (* x x) x) (* (sqrt (fma 3/40 (pow x 5) x)) (sqrt (fma 3/40 (pow x 5) x))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (sqrt (fma 3/40 (pow x 5) x)) (sqrt (fma 3/40 (pow x 5) x)))
57.0ms	(sqrt (fma 3/40 (pow x 5) x))
61.0ms	(sqrt (fma 3/40 (pow x 5) x))
66.0ms	(fma -1/6 (* (* x x) x) (* (sqrt (fma 3/40 (pow x 5) x)) (sqrt (fma 3/40 (pow x 5) x))))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	2000
3	1628
2	470
1	204
0	97

prune415.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2 x (/ 1/2 x))
0.1b	(* (* x x) x)
0.1b	(/ -1/8 (* (* x x) x))
10.9b	(log (+ (/ -1/8 (* (* x x) x)) (fma 2 x (/ 1/2 x))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
19×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`expm1-log1p-u` `log-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `pow-sqr`
1×	`clear-num` `associate-/r` `frac-2neg` `flip3-+` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma 2 x (/ 1/2 x))
23.0ms	(* (* x x) x)
26.0ms	(/ -1/8 (* (* x x) x))
36.0ms	(log (+ (/ -1/8 (* (* x x) x)) (fma 2 x (/ 1/2 x))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 2 x (/ 1/2 x))
44.0ms	(* (* x x) x)
51.0ms	(/ -1/8 (* (* x x) x))
103.0ms	(log (+ (/ -1/8 (* (* x x) x)) (fma 2 x (/ 1/2 x))))

simplify685.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	2113
2	1162
1	337
0	151

prune329.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.3b

bsearch144.0ms

Steps

Iters	Range		Point
11	0.0038666078177206752	9.350013159855062e+31	0.9619268999163055
10	-121993772661.31783	-0.0015977726548224043	-1.0757153356474918

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	31

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.8s	2390×	body	1280	valid
739.0ms	1524×	body	640	valid
544.0ms	736×	body	320	valid
514.0ms	801×	body	2560	valid
186.0ms	2141×	body	80	valid
95.0ms	408×	body	160	valid