Details

sample433.0ms

Algorithm

intervals

Results

94.0ms	52×	body	640	valid
62.0ms	38×	body	1280	valid
40.0ms	138×	body	80	valid
18.0ms	20×	body	320	valid
5.0ms	8×	body	160	valid

simplify154.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

153.0ms

(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize128.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b	(- 1 (* (tan x) (tan x)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-neg` `prod-diff`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 128

Calls

4 calls:

Slowest

73.0ms	(* (tan x) (tan x))
32.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
10.0ms	(- 1 (* (tan x) (tan x)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
89.0ms	(* (tan x) (tan x))
61.0ms	(- 1 (* (tan x) (tan x)))
36.0ms	(* (tan x) (tan x))

simplify7.0s

Counts

119 → 140

Calls

119 calls:

Slowest

661.0ms	(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
657.0ms	(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
575.0ms	(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
396.0ms	(- 1 (+ (pow x 2) (* 2/3 (pow x 4))))
379.0ms	(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.1b	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow1`
8×	`difference-of-squares`
7×	`associate-/l*`
6×	`associate-/r` `associate-r` `associate-l*` `tan-quot`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3-+` `pow-plus` `flip3--` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip-+` `flip--`

Counts

4 → 125

Calls

4 calls:

Slowest

30.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
29.0ms	(/ (* (tan x) (sin x)) (cos x))
25.0ms	(* (tan x) (sin x))
18.0ms	(* (tan x) (tan x))

series383.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
96.0ms	(/ (* (tan x) (sin x)) (cos x))
84.0ms	(* (tan x) (sin x))
59.0ms	(* (tan x) (tan x))

simplify9.3s

Counts

113 → 137

Calls

113 calls:

Slowest

602.0ms	(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
555.0ms	(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
519.0ms	(- (pow 1 3) (pow (/ (* (tan x) (sin x)) (cos x)) 3))
364.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))
308.0ms	(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(/ (* (tan x) (sin x)) (cos x))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-/r` `times-frac` `associate-r` `associate-l*`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `tan-quot` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr` `associate-/l/`

Counts

4 → 94

Calls

4 calls:

Slowest

30.0ms	(/ (* (tan x) (sin x)) (cos x))
25.0ms	(/ (* (tan x) (sin x)) (cos x))
18.0ms	(* (tan x) (sin x))
12.0ms	(* (tan x) (sin x))

series332.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(/ (* (tan x) (sin x)) (cos x))
99.0ms	(/ (* (tan x) (sin x)) (cos x))
85.0ms	(* (tan x) (sin x))
48.0ms	(* (tan x) (sin x))

simplify3.3s

Counts

64 → 106

Calls

64 calls:

Slowest

341.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))
306.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))
283.0ms	(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
282.0ms	(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
273.0ms	(+ (pow x 2) (+ (* 1/6 (pow x 4)) (* 31/360 (pow x 6))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (/ (cos x) (* (tan x) (sin x))))
0.3b	(/ (cos x) (* (tan x) (sin x)))
0.2b	(* (tan x) (sin x))
0.2b	(* (tan x) (sin x))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
34×	`add-exp-log`
31×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1` `associate-/r*`
7×	`cbrt-undiv` `associate-*l/` `tan-quot`
6×	`associate-r` `associate-l` `prod-exp` `associate-/r/` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow-flip` `inv-pow`

Counts

4 → 132

Calls

4 calls:

Slowest

37.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))
29.0ms	(/ (cos x) (* (tan x) (sin x)))
18.0ms	(* (tan x) (sin x))
14.0ms	(* (tan x) (sin x))

series289.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

84.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))
82.0ms	(/ (cos x) (* (tan x) (sin x)))
64.0ms	(* (tan x) (sin x))
60.0ms	(* (tan x) (sin x))

simplify7.1s

Counts

117 → 144

Calls

117 calls:

Slowest

347.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))
316.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))
309.0ms	(+ (pow x 2) (+ (* 1/6 (pow x 4)) (* 31/360 (pow x 6))))
309.0ms	(+ (pow x 2) (+ (* 1/6 (pow x 4)) (* 31/360 (pow x 6))))
293.0ms	(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	1477×	body	1280	valid
1.3s	1263×	body	640	valid
873.0ms	4308×	body	80	valid
388.0ms	634×	body	320	valid
127.0ms	318×	body	160	valid