Details

sample458.0ms

Algorithm

intervals

Results

279.0ms	114×	body	2560	valid
107.0ms	69×	body	1280	valid
36.0ms	47×	body	640	valid
11.0ms	256×	pre	80	true
11.0ms	19×	body	320	valid
2.0ms	5×	body	160	valid
0.0ms	2×	body	80	valid

simplify46.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize11.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (/ 1 x) (/ 1 (tan x)))
0.0b	(/ 1 (tan x))

rewrite29.0ms

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:

Slowest

15.0ms	(- (/ 1 x) (/ 1 (tan x)))
13.0ms	(/ 1 (tan x))

series120.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

89.0ms	(- (/ 1 x) (/ 1 (tan x)))
31.0ms	(/ 1 (tan x))

simplify1.1s

Counts: 69 → 69

prune532.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* x (* 1/45 x)) 1/3) x)
0.3b	(* 1/45 x)
0.1b	(* x (* 1/45 x))
0.1b	(* 2/945 (pow x 5))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`associate-r`
13×	`pow1`
12×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
8×	`prod-exp`
6×	`cbrt-unprod`
5×	`pow-prod-down` `unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `insert-posit16` `add-log-exp`
2×	`associate-*l/` `sqr-pow`
1×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 85

Calls

4 calls:

Slowest

58.0ms	(* (+ (* x (* 1/45 x)) 1/3) x)
28.0ms	(* x (* 1/45 x))
10.0ms	(* 1/45 x)
10.0ms	(* 2/945 (pow x 5))

series231.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

102.0ms	(* (+ (* x (* 1/45 x)) 1/3) x)
78.0ms	(* 2/945 (pow x 5))
34.0ms	(* x (* 1/45 x))
16.0ms	(* 1/45 x)

simplify1.2s

Counts: 97 → 97

prune846.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`associate-*l/` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r` `flip3-+` `times-frac` `pow-prod-down` `-commutative` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 85

Calls

4 calls:

Slowest

141.0ms	(/ (* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x) (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))
13.0ms	(* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x)
6.0ms	(* 1/45 x)
5.0ms	(* 1/45 x)

series694.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

370.0ms	(/ (* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x) (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))
291.0ms	(* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x)
17.0ms	(* 1/45 x)
16.0ms	(* 1/45 x)

simplify4.6s

Counts: 97 → 97

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize99.0ms

Local error

Found 4 expressions with local error:

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

rewrite879.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
66×	`times-frac`
49×	`*-un-lft-identity` `add-cube-cbrt`
36×	`sqrt-prod`
30×	`associate-r` `associate-l`
22×	`add-cbrt-cube` `add-exp-log`
11×	`unswap-sqr`
10×	`pow1`
6×	`associate-/r*` `sqrt-div` `prod-exp` `associate-/r/` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp`
4×	`insert-posit16` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 158

Calls

4 calls:

Slowest

716.0ms	(* (/ (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))) (/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))))
150.0ms	(/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3)))))
5.0ms	(* 1/45 x)
5.0ms	(* 1/45 x)

series554.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

373.0ms	(* (/ (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))) (/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))))
128.0ms	(/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3)))))
27.0ms	(* 1/45 x)
26.0ms	(* 1/45 x)

simplify1.6s

Counts: 170 → 170

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.2b remaining)

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

bsearch11.0ms

end0.0ms

sample16.4s

Algorithm

intervals

Results

10.0s	3303×	body	2560	valid
4.2s	2452×	body	1280	valid
1.1s	1218×	body	640	valid
406.0ms	617×	body	320	valid
313.0ms	8000×	pre	80	true
171.0ms	369×	body	160	valid
8.0ms	41×	body	80	valid