Details

sample412.0ms

Algorithm

intervals

Results

161.0ms	55×	body	1280	valid
65.0ms	50×	body	640	valid
44.0ms	144×	body	80	valid
25.0ms	24×	body	320	valid
15.0ms	59×	body	80	nan
7.0ms	11×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	91	24
3	169	24
4	366	24
5	915	24
6	3219	24
done	5001	24

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.4b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite406.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`expm1-log1p-u` `pow-neg` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 163

Calls

4 calls:

6.0ms	(/ 1.0 (tan B))
37.0ms	(* x (/ 1.0 (tan B)))
288.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
67.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series968.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1.0 (tan B))
192.0ms	(* x (/ 1.0 (tan B)))
499.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
209.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.6s

Counts

175 → 175

Iterations

Useful iterations: 2 (583.0ms)

Iter	Nodes	Cost
0	314	2836
1	764	2557
2	2104	2297
done	5000	2297

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
16.6b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
17×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
10×	`associate-l`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
5×	`div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 116

Calls

4 calls:

11.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
20.0ms	(* x (/ 1.0 (tan B)))
18.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
21.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

540.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
179.0ms	(* x (/ 1.0 (tan B)))
1.4s	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
509.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.8s

Counts

128 → 128

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	283	2182
1	692	2070
2	2048	1897
done	5000	1843

prune794.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
0.3b	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
16.6b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`pow-unpow`
7×	`unpow-prod-down` `associate-l` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 105

Calls

4 calls:

19.0ms	(/ (* x 1.0) (tan B))
19.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
26.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
7.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series3.0s

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (* x 1.0) (tan B))
544.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
1.8s	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
501.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.6s

Counts

117 → 117

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	268	2084
1	649	1982
2	2018	1809
done	5001	1755

prune748.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
16.6b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
112×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
29×	`associate-/l*`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp`
8×	`div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 222

Calls

4 calls:

15.0ms	(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
22.0ms	(/ (* x 1.0) (tan B))
50.0ms	(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
9.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

373.0ms	(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
149.0ms	(/ (* x 1.0) (tan B))
586.0ms	(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
473.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify2.0s

Counts

234 → 234

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	437	5816
1	1001	5583
2	2684	5386
done	5001	5363

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

Details

sample412.0ms

simplify3.5s

prune13.0ms

localize53.0ms

rewrite406.0ms

series968.0ms

simplify1.6s

prune1.2s

localize51.0ms

rewrite73.0ms

series2.6s

simplify1.8s

prune794.0ms

localize49.0ms

rewrite76.0ms

series3.0s

simplify1.6s

prune748.0ms

localize48.0ms

rewrite119.0ms

series1.6s

simplify2.0s

prune1.4s

regimes226.0ms

bsearch2.0ms