Details

sample330.0ms

Algorithm

intervals

Results

178.0ms	93×	body	2560	valid
98.0ms	81×	body	1280	valid
21.0ms	44×	body	640	valid
9.0ms	25×	body	320	valid
8.0ms	256×	pre	80	true
3.0ms	13×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
4.1b	(- (/ 1 x) (/ 1 (tan x)))

rewrite62.0ms

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:

9.0ms	(/ 1 (tan x))
51.0ms	(- (/ 1 x) (/ 1 (tan x)))

series117.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ 1 (tan x))
83.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify2.4s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
4	2091
3	1116
2	586
1	239
0	120

prune233.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite194.0ms

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-*r/` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `+-commutative` `sum-log` `distribute-lft-in` `pow-exp`

Counts

4 → 81

Calls

4 calls:

20.0ms	(+ (* (* x x) 1/45) 1/3)
22.0ms	(* 2/945 (pow x 5))
39.0ms	(* (* x x) 1/45)
110.0ms	(* x (+ (* (* x x) 1/45) 1/3))

series311.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* (* x x) 1/45) 1/3)
86.0ms	(* 2/945 (pow x 5))
32.0ms	(* (* x x) 1/45)
129.0ms	(* x (+ (* (* x x) 1/45) 1/3))

simplify1.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1205
1	383
0	134

prune431.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) 1/45)
0.2b	(* (* (* x x) 1/45) 1/3)
0.4b	(* (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) x)
0.4b	(/ (* (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) x) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))

rewrite414.0ms

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`
9×	`associate-r`
5×	`associate-l`
4×	`associate-*l/` `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×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

18.0ms	(* (* x x) 1/45)
111.0ms	(* (* (* x x) 1/45) 1/3)
32.0ms	(* (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) x)
251.0ms	(/ (* (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) x) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))

series723.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* x x) 1/45)
34.0ms	(* (* (* x x) 1/45) 1/3)
255.0ms	(* (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) x)
405.0ms	(/ (* (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) x) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))

simplify2.5s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	2301
1	490
0	163

prune656.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* x x) 1/45) 1/3)
0.2b	(* (* (* x x) 1/45) 1/3)
0.3b	(/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3)))))
0.4b	(* (/ (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))) (/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
66×	`times-frac`
47×	`*-un-lft-identity` `add-cube-cbrt`
36×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
30×	`associate-r`
26×	`associate-l`
24×	`pow1`
16×	`prod-exp` `cbrt-unprod`
13×	`pow-prod-down`
9×	`unswap-sqr`
6×	`associate-/r*` `sqrt-div` `associate-/r/`
5×	`cbrt-undiv` `div-exp`
4×	`insert-posit16` `add-log-exp`
3×	`flip3-+` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 164

Calls

4 calls:

107.0ms	(* (* (* x x) 1/45) 1/3)
109.0ms	(* (* (* x x) 1/45) 1/3)
316.0ms	(/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3)))))
1.4s	(* (/ (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))) (/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))))

series654.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* (* x x) 1/45) 1/3)
40.0ms	(* (* (* x x) 1/45) 1/3)
139.0ms	(/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3)))))
431.0ms	(* (/ (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))) (/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))))

simplify2.6s

Counts

176 → 176

Iterations

Iter	Nodes
done	5004
2	2952
1	733
0	245

prune856.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	23

end0.0ms

sample11.2s

Algorithm

intervals

Results

7.6s	3245×	body	2560	valid
2.4s	2537×	body	1280	valid
588.0ms	1242×	body	640	valid
246.0ms	8000×	pre	80	true
178.0ms	612×	body	320	valid
62.0ms	313×	body	160	valid
5.0ms	51×	body	80	valid