Details

sample471.0ms

Algorithm

intervals

Results

303.0ms	109×	body	2560	valid
103.0ms	77×	body	1280	valid
20.0ms	31×	body	640	valid
12.0ms	256×	pre	80	true
12.0ms	22×	body	320	valid
5.0ms	15×	body	160	valid
1.0ms	2×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize59.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
3.8b	(- (/ 1 x) (/ 1 (tan x)))

rewrite43.0ms

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:

12.0ms	(/ 1 (tan x))
30.0ms	(- (/ 1 x) (/ 1 (tan x)))

series125.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ 1 (tan x))
97.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify1.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	2001
4	2001
3	1116
2	586
1	239
0	120

prune474.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* x x) 1/45) 1/3)
0.1b	(* 2/945 (pow x 5))
0.1b	(* (* x x) 1/45)
0.3b	(* x (+ (* (* x x) 1/45) 1/3))

rewrite115.0ms

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:

27.0ms	(+ (* (* x x) 1/45) 1/3)
16.0ms	(* 2/945 (pow x 5))
15.0ms	(* (* x x) 1/45)
55.0ms	(* x (+ (* (* x x) 1/45) 1/3))

series313.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (* (* x x) 1/45) 1/3)
92.0ms	(* 2/945 (pow x 5))
32.0ms	(* (* x x) 1/45)
106.0ms	(* x (+ (* (* x x) 1/45) 1/3))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	2028
3	2028
2	1205
1	383
0	134

prune720.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 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))))

rewrite330.0ms

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:

24.0ms	(* (* x x) 1/45)
74.0ms	(* (* (* x x) 1/45) 1/3)
21.0ms	(* (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) x)
208.0ms	(/ (* (+ 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))))

series770.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* x x) 1/45)
39.0ms	(* (* (* x x) 1/45) 1/3)
317.0ms	(* (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) x)
364.0ms	(/ (* (+ 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))))

simplify1.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	2001
2	2001
1	485
0	162

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize90.0ms

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))))))

rewrite1.0s

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:

67.0ms	(* (* (* x x) 1/45) 1/3)
57.0ms	(* (* (* x x) 1/45) 1/3)
141.0ms	(/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3)))))
740.0ms	(* (/ (+ 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))))))

series867.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* (* x x) 1/45) 1/3)
353.0ms	(* (* (* x x) 1/45) 1/3)
131.0ms	(/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3)))))
341.0ms	(* (/ (+ 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))))))

simplify1.3s

Counts

176 → 176

Iterations

Iter	Nodes
done	2002
2	2002
1	734
0	244

prune2.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample14.6s

Algorithm

intervals

Results

8.7s	3250×	body	2560	valid
3.6s	2533×	body	1280	valid
1.4s	1249×	body	640	valid
326.0ms	8000×	pre	80	true
322.0ms	631×	body	320	valid
97.0ms	292×	body	160	valid
8.0ms	45×	body	80	valid