Details

sample1.1s

Algorithm

intervals

Results

439.0ms	49×	body	1280	valid
151.0ms	57×	body	640	valid
80.0ms	162×	body	80	valid
40.0ms	17×	body	320	valid
20.0ms	59×	body	80	nan
15.0ms	10×	body	160	valid

simplify10.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2696
5	850
4	325
3	161
2	90
1	43
0	20

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
8.1b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite530.0ms

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:

14.0ms	(/ 1.0 (tan B))
68.0ms	(* x (/ 1.0 (tan B)))
319.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
114.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ 1.0 (tan B))
222.0ms	(* x (/ 1.0 (tan B)))
543.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
306.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify3.6s

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
2	2527
1	865
0	314

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
8.1b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
42×	`times-frac`
39×	`add-cube-cbrt` `*-un-lft-identity`
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×	`div-exp` `associate-/r*` `unswap-sqr`
5×	`pow1` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `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` `frac-2neg` `associate-*r/` `clear-num`
1×	`tan-quot` `neg-mul-1` `pow-pow` `associate-l/` `associate-/r/` `un-div-inv` `-commutative`

Counts

4 → 151

Calls

4 calls:

18.0ms	(/ (* x 1.0) (tan B))
13.0ms	(/ F (sin B))
341.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
99.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (* x 1.0) (tan B))
102.0ms	(/ F (sin B))
603.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
280.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify3.6s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	2444
1	807
0	296

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
0.2b	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
19.4b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite105.0ms

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:

36.0ms	(/ (* x 1.0) (tan B))
23.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
32.0ms	(* (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))

series3.4s

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ (* x 1.0) (tan B))
725.0ms	(/ 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))
614.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify3.7s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	2181
1	682
0	268

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
0.2b	(* F (/ 1 (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))))
0.2b	(/ 1 (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
19.4b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
34×	`prod-exp`
27×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
16×	`div-exp`
15×	`times-frac`
13×	`pow-unpow`
10×	`associate-r` `associate-l`
8×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp`
7×	`unpow-prod-down`
6×	`cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`pow-flip` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `inv-pow`

Counts

4 → 131

Calls

4 calls:

35.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
87.0ms	(* F (/ 1 (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))))
49.0ms	(/ 1 (* (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))

series5.6s

Counts

4 → 12

Calls

4 calls:

1.9s	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
762.0ms	(* F (/ 1 (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))))
2.4s	(/ 1 (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
612.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify4.0s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2420
1	797
0	296

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes639.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch1.1s

Steps

Iters	Range		Point
10	6.402043939282351e-10	87.84726908649233	86.69108830173802
6	-2.1978428081120028e+18	-4.916262034846559e+17	-5.06492498426377e+17

simplify64.0ms

Iterations

Iter	Nodes
done	56
2	56
1	50
0	37

end0.0ms

sample13.2s

Algorithm

intervals

Results

5.0s	1667×	body	1280	valid
2.6s	1408×	body	640	valid
2.6s	4750×	body	80	valid
1.4s	1640×	body	80	nan
843.0ms	666×	body	320	valid
232.0ms	341×	body	160	valid