Details

sample528.0ms

Algorithm

intervals

Results

272.0ms	59×	body	2560	valid
99.0ms	74×	body	1280	valid
47.0ms	60×	body	640	valid
23.0ms	36×	body	320	valid
5.0ms	13×	body	160	valid
3.0ms	14×	body	80	valid

simplify93.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize103.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.4b	(- x (sin x))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
16.0ms	(- x (tan x))
29.0ms	(- x (sin x))

series347.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(/ (- x (sin x)) (- x (tan x)))
109.0ms	(- x (tan x))
106.0ms	(- x (sin x))

simplify6.0s

Counts

92 → 92

Iterations

Iter	Nodes
done	5022
3	3361
2	965
1	375
0	160

prune901.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize134.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* 9/40 x))
0.1b	(* 9/40 x)
0.6b	(* (* x x) 27/2800)
14.6b	(- (* x (* 9/40 x)) (+ (* (* x x) (* (* x x) 27/2800)) 1/2))

rewrite482.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16`
3×	`*-commutative`
2×	`diff-log` `unswap-sqr`
1×	`sum-log` `sub-neg` `flip3--` `flip--` `associate--r+`

Counts

4 → 73

Calls

4 calls:

66.0ms	(* x (* 9/40 x))
25.0ms	(* 9/40 x)
57.0ms	(* (* x x) 27/2800)
326.0ms	(- (* x (* 9/40 x)) (+ (* (* x x) (* (* x x) 27/2800)) 1/2))

series256.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* x (* 9/40 x))
33.0ms	(* 9/40 x)
62.0ms	(* (* x x) 27/2800)
102.0ms	(- (* x (* 9/40 x)) (+ (* (* x x) (* (* x x) 27/2800)) 1/2))

simplify9.6s

Counts

85 → 85

Iterations

Iter	Nodes
done	5006
3	4361
2	1003
1	309
0	116

prune643.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize233.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin x))
1.4b	(- (/ (/ (* (sin x) (sin x)) (cos x)) (* x x)) 1)
2.0b	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
15.7b	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
33×	`times-frac`
27×	`add-cbrt-cube` `add-exp-log`
23×	`*-un-lft-identity`
12×	`add-cube-cbrt` `difference-of-squares`
11×	`pow1`
10×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`prod-exp` `cbrt-unprod`
4×	`div-sub` `insert-posit16`
3×	`difference-of-sqr-1` `swap-sqr` `associate-r` `associate-l` `sqr-sin` `div-inv` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`associate--l-` `pow2` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `frac-sub` `sin-mult` `unswap-sqr` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

27.0ms	(* (sin x) (sin x))
141.0ms	(- (/ (/ (* (sin x) (sin x)) (cos x)) (* x x)) 1)
178.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
84.0ms	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))

series627.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin x) (sin x))
217.0ms	(- (/ (/ (* (sin x) (sin x)) (cos x)) (* x x)) 1)
208.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
160.0ms	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))

simplify5.0s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	2186
1	596
0	239

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize222.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
1.4b	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
1.4b	(- x (sin x))
32.6b	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
10×	`cube-unmult`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`difference-cubes`
4×	`tan-quot` `insert-posit16` `associate-/l*`
3×	`associate-/r` `flip3--` `swap-sqr` `associate-r` `associate-l*` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

49.0ms	(* (tan x) (tan x))
84.0ms	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
23.0ms	(- x (sin x))
281.0ms	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (tan x) (tan x))
286.0ms	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
53.0ms	(- x (sin x))
975.0ms	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))

simplify4.3s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1792
1	524
0	201

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes181.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.6b

bsearch236.0ms

Steps

Iters	Range		Point
8	1.874259372897972	986.1969312707462	2.4203399319729506
9	-209901990.47645873	-0.28008678268591264	-2.508948866519329

simplify34.0ms

Iterations

Iter	Nodes
done	41
1	41
0	30

end0.0ms

sample14.1s

Algorithm

intervals

Results

6.3s	1543×	body	2560	valid
4.8s	2735×	body	1280	valid
1.9s	1953×	body	640	valid
527.0ms	908×	body	320	valid
226.0ms	499×	body	160	valid
77.0ms	362×	body	80	valid