Details

sample589.0ms

Algorithm

intervals

Results

215.0ms	63×	body	2560	valid
150.0ms	75×	body	1280	valid
60.0ms	69×	body	640	valid
17.0ms	26×	body	320	valid
6.0ms	14×	body	160	valid
2.0ms	9×	body	80	valid

simplify53.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.8b	(- x (sin x))
0.8b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite39.0ms

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:

Slowest

23.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series307.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

128.0ms	(/ (- x (sin x)) (- x (tan x)))
110.0ms	(- x (tan x))
64.0ms	(- x (sin x))

simplify1.1s

Counts: 92 → 92

prune928.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

15.3b	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
0.3b	(* (* (* x x) (* x x)) 27/2800)
0.1b	(* (* x x) 9/40)
0.1b	(* (* x x) (* x x))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

138×	`pow1`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
36×	`pow-prod-up`
24×	`prod-exp` `cbrt-unprod`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`insert-posit16`
3×	`associate-l` `*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 126

Calls

4 calls:

Slowest

90.0ms	(* (* (* x x) (* x x)) 27/2800)
41.0ms	(* (* x x) (* x x))
22.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
17.0ms	(* (* x x) 9/40)

series344.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

182.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
65.0ms	(* (* x x) (* x x))
52.0ms	(* (* (* x x) (* x x)) 27/2800)
46.0ms	(* (* x x) 9/40)

simplify1.6s

Counts: 138 → 138

prune948.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b	(- x (sin x))
0.8b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))

rewrite83.0ms

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:

Slowest

45.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
21.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (sin x))
4.0ms	(- x (tan x))

series412.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
130.0ms	(/ (- x (sin x)) (- x (tan x)))
75.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify1.0s

Counts: 140 → 140

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

37.6b	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))
0.8b	(- x (sin x))
0.8b	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))

rewrite152.0ms

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:

Slowest

101.0ms	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))
30.0ms	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
14.0ms	(* (tan x) (tan x))
5.0ms	(- x (sin x))

series622.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

323.0ms	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))
198.0ms	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
63.0ms	(- x (sin x))
38.0ms	(* (tan x) (tan x))

simplify658.0ms

Counts: 107 → 107

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes115.0ms

Accuracy

100% (0.0b remaining)

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

bsearch135.0ms

end0.0ms

sample15.7s

Algorithm

intervals

Results

7.0s	1665×	body	2560	valid
4.5s	2706×	body	1280	valid
3.1s	1831×	body	640	valid
633.0ms	943×	body	320	valid
215.0ms	502×	body	160	valid
106.0ms	353×	body	80	valid