Details

sample635.0ms

Algorithm

intervals

Results

279.0ms	55×	body	2560	valid
141.0ms	84×	body	1280	valid
61.0ms	60×	body	640	valid
17.0ms	22×	body	320	valid
12.0ms	20×	body	160	valid
4.0ms	15×	body	80	valid

simplify45.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize19.0ms

Local error

Found 3 expressions with local error:

1.6b	(- x (sin x))
1.6b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite32.0ms

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

18.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (sin x))
6.0ms	(- x (tan x))

series252.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

113.0ms	(/ (- x (sin x)) (- x (tan x)))
82.0ms	(- x (tan x))
57.0ms	(- x (sin x))

simplify1.1s

Counts: 92 → 92

prune827.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

1.6b	(- 1 (/ (sin x) x))
0.2b	(/ (sin x) (* (cos x) x))
0.2b	(/ (sin x) (* (cos x) x))
0.2b	(/ (sin x) (* (cos x) x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

Slowest

19.0ms	(/ (sin x) (* (cos x) x))
18.0ms	(/ (sin x) (* (cos x) x))
14.0ms	(/ (sin x) (* (cos x) x))
8.0ms	(- 1 (/ (sin x) x))

series255.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(- 1 (/ (sin x) x))
63.0ms	(/ (sin x) (* (cos x) x))
62.0ms	(/ (sin x) (* (cos x) x))
59.0ms	(/ (sin x) (* (cos x) x))

simplify796.0ms

Counts: 96 → 96

prune972.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

16.6b	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) (* x x)) 27/2800)
0.1b	(* (* x x) 9/40)

rewrite154.0ms

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

98.0ms	(* (* (* x x) (* x x)) 27/2800)
22.0ms	(* (* x x) (* x x))
16.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
16.0ms	(* (* x x) 9/40)

series334.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
61.0ms	(* (* x x) (* x x))
59.0ms	(* (* (* x x) (* x x)) 27/2800)
35.0ms	(* (* x x) 9/40)

simplify2.1s

Counts: 138 → 138

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

15.4b	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
1.6b	(- x (sin x))
1.6b	(- (* x x) (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`difference-of-squares`
5×	`distribute-lft-out`
4×	`associate-/r` `tan-quot` `insert-posit16` `associate-/l`
3×	`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--` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

Slowest

31.0ms	(* (tan x) (tan x))
21.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
14.0ms	(- (* x x) (* (tan x) (tan x)))
10.0ms	(- x (sin x))

series448.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

200.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
139.0ms	(- (* x x) (* (tan x) (tan x)))
60.0ms	(* (tan x) (tan x))
49.0ms	(- x (sin x))

simplify1.9s

Counts: 112 → 112

prune958.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes55.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.9b

bsearch149.0ms

end0.0ms

sample17.5s

Algorithm

intervals

Results

7.8s	1637×	body	2560	valid
6.0s	2744×	body	1280	valid
2.1s	1865×	body	640	valid
851.0ms	938×	body	320	valid
346.0ms	465×	body	160	valid
132.0ms	351×	body	80	valid