Details

sample520.0ms

Algorithm

intervals

Results

300.0ms	98×	body	2560	valid
138.0ms	79×	body	1280	valid
33.0ms	41×	body	640	valid
15.0ms	23×	body	320	valid
12.0ms	256×	pre	80	true
5.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	14
2	14
1	10
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.6b

localize53.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
3.6b	(- (/ 1 x) (/ 1 (tan x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
12×	`add-cube-cbrt`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
5×	`div-inv`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
2×	`div-exp` `insert-posit16`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

2 → 63

Calls

2 calls:

6.0ms	(/ 1 (tan x))
25.0ms	(- (/ 1 x) (/ 1 (tan x)))

series465.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ 1 (tan x))
423.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify1.0s

Counts

69 → 69

Iterations

Iter	Nodes
4	2080
3	1198
2	566
1	236
0	120

prune524.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/3 (* (* x x) 1/45))
0.1b	(* 2/945 (pow x 5))
0.2b	(* (* x x) 1/45)
0.4b	(* (+ 1/3 (* (* x x) 1/45)) x)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l` `prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `associate-*l/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-exp`

Counts

4 → 79

Calls

4 calls:

5.0ms	(+ 1/3 (* (* x x) 1/45))
9.0ms	(* 2/945 (pow x 5))
28.0ms	(* (* x x) 1/45)
23.0ms	(* (+ 1/3 (* (* x x) 1/45)) x)

series322.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ 1/3 (* (* x x) 1/45))
89.0ms	(* 2/945 (pow x 5))
31.0ms	(* (* x x) 1/45)
129.0ms	(* (+ 1/3 (* (* x x) 1/45)) x)

simplify1.5s

Counts

91 → 91

Iterations

Iter	Nodes
3	3131
2	963
1	322
0	131

prune923.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) 1/45)
0.2b	(* 1/3 (* (* x x) 1/45))
0.3b	(* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27))
0.3b	(/ (* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27)) (+ (* 1/3 1/3) (- (* (* (* x x) 1/45) (* (* x x) 1/45)) (* 1/3 (* (* x x) 1/45)))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

25×	`add-cbrt-cube` `add-exp-log`
20×	`pow1`
13×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
10×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`associate-/r` `flip3-+` `times-frac` `-commutative` `flip-+`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `unswap-sqr` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

29.0ms	(* (* x x) 1/45)
70.0ms	(* 1/3 (* (* x x) 1/45))
1.1s	(* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27))
800.0ms	(/ (* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27)) (+ (* 1/3 1/3) (- (* (* (* x x) 1/45) (* (* x x) 1/45)) (* 1/3 (* (* x x) 1/45)))))

series758.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* x x) 1/45)
33.0ms	(* 1/3 (* (* x x) 1/45))
281.0ms	(* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27))
411.0ms	(/ (* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27)) (+ (* 1/3 1/3) (- (* (* (* x x) 1/45) (* (* x x) 1/45)) (* 1/3 (* (* x x) 1/45)))))

simplify7.2s

Counts

103 → 103

Iterations

Iter	Nodes
3	10880
2	1815
1	465
0	163

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.2b	(* 1/45 (* x x))
0.2b	(* 1/45 (* x x))
0.2b	(* (+ -1/3 (* 1/45 (* x x))) (* 1/45 (* x x)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

134×	`pow1`
36×	`pow-prod-up`
35×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
22×	`pow-sqr`
20×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
10×	`associate-l`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `*-commutative` `insert-posit16` `add-log-exp`
3×	`unswap-sqr`
2×	`associate-*l/`
1×	`flip3-+` `swap-sqr` `flip-+`

Counts

4 → 128

Calls

4 calls:

43.0ms	(* (* x x) (* x x))
23.0ms	(* 1/45 (* x x))
22.0ms	(* 1/45 (* x x))
57.0ms	(* (+ -1/3 (* 1/45 (* x x))) (* 1/45 (* x x)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* x x) (* x x))
47.0ms	(* 1/45 (* x x))
45.0ms	(* 1/45 (* x x))
150.0ms	(* (+ -1/3 (* 1/45 (* x x))) (* 1/45 (* x x)))

simplify3.1s

Counts

140 → 140

Iterations

Iter	Nodes
3	6687
2	1086
1	285
0	107

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	31
1	31
0	22

end0.0ms

sample15.8s

Algorithm

intervals

Results

9.7s	3293×	body	2560	valid
3.9s	2450×	body	1280	valid
1.1s	1255×	body	640	valid
371.0ms	8000×	pre	80	true
340.0ms	632×	body	320	valid
177.0ms	329×	body	160	valid
8.0ms	41×	body	80	valid