Details

sample44.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
13	4505
12	1018
11	659
10	458
9	359
8	296
7	201
6	156
5	140
4	126
3	94
2	60
1	31
0	16

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 2.30753 (* x 0.27061))
0.0b	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
13.9b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
90×	`prod-diff`
89×	`add-cube-cbrt`
64×	`times-frac`
48×	`distribute-rgt-in` `distribute-lft-in`
14×	`associate-/r/`
10×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
9×	`associate-r`
8×	`pow1`
7×	`div-inv`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `associate-/l`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `flip--` `distribute-lft-out--`

Counts

4 → 192

Calls

4 calls:

5.0ms	(+ 2.30753 (* x 0.27061))
188.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
30.0ms	(* x (+ 0.99229 (* x 0.04481)))
37.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ 2.30753 (* x 0.27061))
130.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
97.0ms	(* x (+ 0.99229 (* x 0.04481)))
108.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify2.0s

Counts

204 → 204

Iterations

Iter	Nodes
done	5000
2	3724
1	919
0	366

prune713.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (* (fma x 0.27061 2.30753) 0.70711) (fma (fma x 0.04481 0.99229) x 1.0)) (* 0.70711 (- x)))
0.1b	(fma (fma x 0.04481 0.99229) x 1.0)
0.1b	(* (fma x 0.27061 2.30753) 0.70711)
13.9b	(/ (* (fma x 0.27061 2.30753) 0.70711) (fma (fma x 0.04481 0.99229) x 1.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`fma-def`
6×	`pow1` `times-frac` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `associate-r` `associate-l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `distribute-rgt-neg-out` `cbrt-unprod` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `unsub-neg` `pow-prod-down` `-commutative` `flip-+` `fma-udef` `associate-/l` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

13.0ms	(+ (/ (* (fma x 0.27061 2.30753) 0.70711) (fma (fma x 0.04481 0.99229) x 1.0)) (* 0.70711 (- x)))
0.0ms	(fma (fma x 0.04481 0.99229) x 1.0)
5.0ms	(* (fma x 0.27061 2.30753) 0.70711)
8.0ms	(/ (* (fma x 0.27061 2.30753) 0.70711) (fma (fma x 0.04481 0.99229) x 1.0))

series331.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (/ (* (fma x 0.27061 2.30753) 0.70711) (fma (fma x 0.04481 0.99229) x 1.0)) (* 0.70711 (- x)))
31.0ms	(fma (fma x 0.04481 0.99229) x 1.0)
89.0ms	(* (fma x 0.27061 2.30753) 0.70711)
127.0ms	(/ (* (fma x 0.27061 2.30753) 0.70711) (fma (fma x 0.04481 0.99229) x 1.0))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
2	1413
1	332
0	136

prune512.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0))) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
0.3b	(/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
13.8b	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))
13.8b	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
66×	`sqrt-prod`
55×	`add-sqr-sqrt`
53×	`*-un-lft-identity` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 154

Calls

4 calls:

15.0ms	(/ (/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0))) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
8.0ms	(/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
1.0ms	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))
1.0ms	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))

series626.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0))) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
293.0ms	(/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
118.0ms	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))
114.0ms	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))

simplify1.8s

Counts

166 → 166

Iterations

Iter	Nodes
done	5001
2	2838
1	672
0	261

prune922.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
0.5b	(expm1 (log1p (/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))))
13.8b	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))
13.8b	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r*` `times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`
1×	`expm1-log1p` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*` `expm1-udef`

Counts

4 → 70

Calls

4 calls:

8.0ms	(/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
0.0ms	(expm1 (log1p (/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))))
1.0ms	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))
1.0ms	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))
1.6s	(expm1 (log1p (/ (* (fma x 0.27061 2.30753) 0.70711) (sqrt (fma (fma x 0.04481 0.99229) x 1.0)))))
135.0ms	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))
104.0ms	(sqrt (fma (fma x 0.04481 0.99229) x 1.0))

simplify2.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	3226
1	712
0	260

prune718.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	29
3	29
2	28
1	24
0	19

end0.0ms

sample913.0ms

Algorithm

intervals

Results

704.0ms

8000×

body

valid