Details

sample810.0ms

Algorithm

intervals

Results

245.0ms	52×	body	1280	valid
158.0ms	141×	body	80	valid
125.0ms	24×	body	320	valid
74.0ms	53×	body	640	valid
52.0ms	67×	body	80	nan
6.0ms	9×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1755
4	384
3	169
2	91
1	43
0	20

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
7.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`*-un-lft-identity` `add-cube-cbrt`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube` `associate-l`
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×	`neg-sub0` `pow-to-exp` `cbrt-undiv` `associate-/r` `pow-exp` `associate-r/` `associate-/l*` `pow-sub`
2×	`frac-times` `tan-quot` `associate-/r/` `*-commutative`
1×	`clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `un-div-inv`

Counts

4 → 163

Calls

4 calls:

5.0ms	(/ 1.0 (tan B))
14.0ms	(* x (/ 1.0 (tan B)))
205.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
96.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series892.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1.0 (tan B))
155.0ms	(* x (/ 1.0 (tan B)))
434.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
247.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	3970
1	883
0	314

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
7.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

16.0ms	(/ (* x 1.0) (tan B))
5.0ms	(/ F (sin B))
192.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
64.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series867.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (* x 1.0) (tan B))
82.0ms	(/ F (sin B))
410.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
229.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.4s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	3860
1	822
0	296

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
6.9b	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
14.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 214

Calls

4 calls:

16.0ms	(/ (* x 1.0) (tan B))
7.0ms	(/ F (sin B))
85.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
46.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series794.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (* x 1.0) (tan B))
56.0ms	(/ F (sin B))
369.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
207.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.1s

Counts

226 → 226

Iterations

Iter	Nodes
done	5000
2	4907
1	1032
0	416

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize132.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin B))
14.9b	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))
14.9b	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))
14.9b	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
29×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
9×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-pow` `pow-exp` `div-inv` `sqr-pow`
1×	`pow1/3`

Counts

4 → 100

Calls

4 calls:

1.0ms	(cbrt (sin B))
3.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))
3.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))
3.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

series717.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (sin B))
219.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))
195.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))
167.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

simplify2.5s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4563
2	964
1	306
0	123

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes426.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.7b

bsearch352.0ms

Steps

Iters	Range		Point
10	3.036164441574392e-08	17065.88877981157	10637.379562884495
2	-246150028812460.4	-222229246420781.72	-225219344219741.56

simplify18.0ms

Iterations

Iter	Nodes
done	66
2	66
1	59
0	42

end0.0ms

sample10.4s

Algorithm

intervals

Results

5.0s	1707×	body	1280	valid
1.8s	1351×	body	640	valid
1.7s	4755×	body	80	valid
765.0ms	691×	body	320	valid
418.0ms	1653×	body	80	nan
192.0ms	353×	body	160	valid