Details

sample1.3s

Algorithm

intervals

Results

854.0ms	59×	body	2560	valid
183.0ms	74×	body	1280	valid
65.0ms	60×	body	640	valid
55.0ms	14×	body	80	valid
33.0ms	36×	body	320	valid
7.0ms	13×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize21.0ms

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))

rewrite57.0ms

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:

17.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
31.0ms	(- x (sin x))

series254.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(/ (- x (sin x)) (- x (tan x)))
61.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify1.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1396
1	375
0	160

prune317.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (* x x) (- 9/40 (* (* x x) 27/2800))) 1/2)
0.0b	(- 9/40 (* (* x x) 27/2800))
0.1b	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
0.6b	(* (* x x) 27/2800)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`sub-neg` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `insert-posit16`
3×	`flip3--` `flip--`
2×	`diff-log` `associate-l` `associate-r/` `-commutative` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

20.0ms	(- (* (* x x) (- 9/40 (* (* x x) 27/2800))) 1/2)
4.0ms	(- 9/40 (* (* x x) 27/2800))
32.0ms	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
33.0ms	(* (* x x) 27/2800)

series330.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* (* x x) (- 9/40 (* (* x x) 27/2800))) 1/2)
77.0ms	(- 9/40 (* (* x x) 27/2800))
158.0ms	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
34.0ms	(* (* x x) 27/2800)

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1901
1	320
0	116

prune267.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* x (cos x)))
0.2b	(/ (sin x) (* x (cos x)))
0.2b	(/ (sin x) (* x (cos x)))
0.6b	(- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`times-frac` `associate-/l*` `add-log-exp`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `insert-posit16`
3×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `frac-sub` `cbrt-unprod` `div-inv`
2×	`diff-log` `distribute-lft-out--`
1×	`sum-log` `sub-neg` `flip3-+` `flip3--` `frac-add` `flip-+` `flip--` `distribute-lft-out` `associate--r+` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

12.0ms	(/ (sin x) (* x (cos x)))
13.0ms	(/ (sin x) (* x (cos x)))
21.0ms	(/ (sin x) (* x (cos x)))
114.0ms	(- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (sin x) (* x (cos x)))
73.0ms	(/ (sin x) (* x (cos x)))
55.0ms	(/ (sin x) (* x (cos x)))
229.0ms	(- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))

simplify1.5s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	1796
1	365
0	126

prune579.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* x (cos x)))
0.2b	(/ (sin x) (* x (cos x)))
0.6b	(- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))
3.5b	(log (exp (- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))))

rewrite487.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
10×	`add-cube-cbrt`
9×	`add-log-exp`
7×	`log-pow`
6×	`exp-prod` `times-frac` `associate-/l*`
5×	`pow1` `log-prod`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `distribute-lft-out--`
3×	`frac-sub`
2×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `exp-sum` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`log-div` `sum-log` `flip3-+` `flip3--` `exp-diff` `rem-log-exp` `frac-add` `flip-+` `flip--` `associate--r+`

Counts

4 → 87

Calls

4 calls:

23.0ms	(/ (sin x) (* x (cos x)))
26.0ms	(/ (sin x) (* x (cos x)))
119.0ms	(- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))
317.0ms	(log (exp (- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (sin x) (* x (cos x)))
70.0ms	(/ (sin x) (* x (cos x)))
199.0ms	(- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))
184.0ms	(log (exp (- (/ (sin x) (* x (cos x))) (+ (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) (/ (sin x) x)))))

simplify1.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	2278
1	421
0	154

prune553.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.4b

bsearch159.0ms

Steps

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

simplify14.0ms

Iterations

Iter	Nodes
done	41
1	41
0	30

end0.0ms

sample16.2s

Algorithm

intervals

Results

6.8s	1543×	body	2560	valid
5.2s	2735×	body	1280	valid
2.6s	1953×	body	640	valid
1.1s	908×	body	320	valid
228.0ms	499×	body	160	valid
112.0ms	362×	body	80	valid