Details

sample478.0ms

Algorithm

intervals

Results

176.0ms	63×	body	2560	valid
103.0ms	91×	body	1280	valid
92.0ms	54×	body	640	valid
7.0ms	18×	body	320	valid
4.0ms	15×	body	160	valid
2.0ms	15×	body	80	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.4b	(- x (sin x))
0.4b	(- x (tan x))

rewrite67.0ms

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:

35.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
6.0ms	(- x (tan x))

series292.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(/ (- x (sin x)) (- x (tan x)))
49.0ms	(- x (sin x))
118.0ms	(- x (tan x))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5003
3	3300
2	963
1	375
0	160

prune391.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 27/2800 (* x x)) (* x x))
0.1b	(* 9/40 (* x x))
0.4b	(* 27/2800 (* x x))
15.3b	(- (* 9/40 (* x x)) (* (* 27/2800 (* x x)) (* x x)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

71.0ms	(* (* 27/2800 (* x x)) (* x x))
13.0ms	(* 9/40 (* x x))
18.0ms	(* 27/2800 (* x x))
39.0ms	(- (* 9/40 (* x x)) (* (* 27/2800 (* x x)) (* x x)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* 27/2800 (* x x)) (* x x))
37.0ms	(* 9/40 (* x x))
35.0ms	(* 27/2800 (* x x))
171.0ms	(- (* 9/40 (* x x)) (* (* 27/2800 (* x x)) (* x x)))

simplify1.6s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1173
1	302
0	106

prune261.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
0.4b	(- x (sin x))
0.4b	(- x (tan x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
32×	`log-pow`
31×	`exp-prod`
28×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`associate-/r/` `insert-posit16`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp`

Counts

4 → 128

Calls

4 calls:

23.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
31.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (sin x))
9.0ms	(- x (tan x))

series338.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
98.0ms	(/ (- x (sin x)) (- x (tan x)))
42.0ms	(- x (sin x))
67.0ms	(- x (tan x))

simplify1.9s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
3	3294
2	1056
1	445
0	223

prune636.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.4b	(- x (tan x))
0.4b	(- x (tan x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1` `insert-posit16`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 98

Calls

4 calls:

12.0ms	(/ (sin x) (- x (tan x)))
50.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
4.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series543.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (sin x) (- x (tan x)))
286.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
77.0ms	(- x (tan x))
96.0ms	(- x (tan x))

simplify2.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	5183
3	4000
2	1111
1	392
0	180

prune485.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes81.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch182.0ms

Steps

Iters	Range		Point
11	4.21785760657603e-35	57.56933376468871	0.02825639784178301
9	-34.11472770615283	-3.67231414207575e-08	-0.027836888459983777

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample13.3s

Algorithm

intervals

Results

5.9s	1588×	body	2560	valid
4.6s	2730×	body	1280	valid
2.0s	1915×	body	640	valid
455.0ms	911×	body	320	valid
140.0ms	477×	body	160	valid
64.0ms	379×	body	80	valid