Details

sample631.0ms

Algorithm

intervals

Results

169.0ms	47×	body	1280	valid
162.0ms	155×	body	80	valid
149.0ms	45×	body	640	valid
23.0ms	20×	body	320	valid
23.0ms	57×	body	80	nan
9.0ms	11×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	2153
5	683
4	275
3	137
2	81
1	45
0	20

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.1b	(/ x (tan B))
9.4b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
18.7b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

203×	`times-frac`
143×	`*-un-lft-identity`
113×	`add-sqr-sqrt` `add-cube-cbrt`
60×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`distribute-lft-out` `sqr-pow`
14×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`div-inv`
11×	`div-exp`
5×	`pow1` `cbrt-undiv`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-unpow` `clear-num` `frac-2neg` `pow-exp`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot`

Counts

4 → 217

Calls

4 calls:

13.0ms	(/ (sin B) F)
9.0ms	(/ x (tan B))
134.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
43.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series727.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (sin B) F)
179.0ms	(/ x (tan B))
196.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
318.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify1.7s

Counts

229 → 229

Iterations

Iter	Nodes
2	2599
1	916
0	392

prune3.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* F (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))
0.7b	(* (/ 1 (sin B)) (* F (pow (+ (+ (* 2 x) (* F F)) 2) -1/2)))
18.7b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`times-frac`
16×	`associate-l`
9×	`unpow-prod-down` `div-exp` `associate-r`
7×	`pow1` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv` `distribute-lft-out`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/r/`

Counts

4 → 116

Calls

4 calls:

9.0ms	(/ x (tan B))
144.0ms	(* F (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))
188.0ms	(* (/ 1 (sin B)) (* F (pow (+ (+ (* 2 x) (* F F)) 2) -1/2)))
34.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series777.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ x (tan B))
105.0ms	(* F (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))
213.0ms	(* (/ 1 (sin B)) (* F (pow (+ (+ (* 2 x) (* F F)) 2) -1/2)))
308.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify3.3s

Counts

128 → 128

Iterations

Iter	Nodes
3	4667
2	1520
1	586
0	254

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2))
0.7b	(/ (* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2)) (sin B))
18.7b	(pow (+ (* F F) (+ 2 (* 2 x))) -1/2)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

4.0ms	(/ x (tan B))
66.0ms	(* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2))
25.0ms	(/ (* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2)) (sin B))
29.0ms	(pow (+ (* F F) (+ 2 (* 2 x))) -1/2)

series571.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ x (tan B))
130.0ms	(* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2))
209.0ms	(/ (* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2)) (sin B))
89.0ms	(pow (+ (* F F) (+ 2 (* 2 x))) -1/2)

simplify1.7s

Counts

105 → 105

Iterations

Iter	Nodes
3	4140
2	1131
1	425
0	195

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.3b	(* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2))
0.7b	(/ (* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2)) (sin B))
18.7b	(pow (+ (* F F) (+ 2 (* 2 x))) -1/2)

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

24.0ms	(* (/ x (sin B)) (cos B))
112.0ms	(* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2))
48.0ms	(/ (* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2)) (sin B))
28.0ms	(pow (+ (* F F) (+ 2 (* 2 x))) -1/2)

series579.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (/ x (sin B)) (cos B))
119.0ms	(* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2))
204.0ms	(/ (* F (pow (+ (* F F) (+ 2 (* 2 x))) -1/2)) (sin B))
124.0ms	(pow (+ (* F F) (+ 2 (* 2 x))) -1/2)

simplify2.8s

Counts

109 → 109

Iterations

Iter	Nodes
3	5558
2	1473
1	483
0	202

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes429.0ms

Accuracy

98% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.4b

bsearch574.0ms

Steps

Iters	Range		Point
10	1.101565841888519e-09	50016.8179159125	33330.37501774117
5	-6.823279860778228e+28	-3.031846415249857e+28	-3.0687291899060427e+28

simplify13.0ms

Iterations

Iter	Nodes
2	36
1	36
0	32

end0.0ms

sample14.4s

Algorithm

intervals

Results

6.6s	1695×	body	1280	valid
3.0s	1357×	body	640	valid
2.2s	4754×	body	80	valid
1.1s	707×	body	320	valid
765.0ms	1757×	body	80	nan
358.0ms	365×	body	160	valid