Details

sample505.0ms

Algorithm

intervals

Results

214.0ms	50×	body	2560	valid
177.0ms	94×	body	1280	valid
43.0ms	56×	body	640	valid
17.0ms	28×	body	320	valid
9.0ms	21×	body	160	valid
1.0ms	7×	body	80	valid

simplify46.0ms

Calls

1 calls:

Slowest

45.0ms

(/ (- x (sin x)) (- x (tan x)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize32.0ms

Local error

Found 3 expressions with local error:

2.5b	(- x (sin x))
2.5b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite419.0ms

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`

Calls

3 calls:

Slowest

391.0ms	(- x (sin x))
21.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))

series329.0ms

Calls

3 calls:

Slowest

150.0ms	(/ (- x (sin x)) (- x (tan x)))
99.0ms	(- x (tan x))
80.0ms	(- x (sin x))

simplify3.3s

Calls

82 calls:

Slowest

422.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
405.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
335.0ms	(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
293.0ms	(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
187.0ms	(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune836.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

15.6b	(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
0.2b	(* (* x x) 9/40)
0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) (* x x)) 27/2800)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

319×	`add-sqr-sqrt`
190×	`associate-l`
171×	`unswap-sqr`
138×	`pow1`
118×	`swap-sqr`
102×	`*-un-lft-identity`
63×	`associate-r`
54×	`*-commutative`
52×	`add-cube-cbrt`
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`
15×	`distribute-lft-out--`
13×	`pow2`
12×	`distribute-lft-out`
9×	`add-log-exp`
6×	`difference-of-squares`
4×	`insert-posit16`
2×	`diff-log` `associate--r+`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `flip--`

Calls

4 calls:

Slowest

933.0ms	(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
166.0ms	(* (* (* x x) (* x x)) 27/2800)
37.0ms	(* (* x x) (* x x))
24.0ms	(* (* x x) 9/40)

series168.0ms

Calls

4 calls:

Slowest

64.0ms	(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
40.0ms	(* (* (* x x) (* x x)) 27/2800)
36.0ms	(* (* x x) (* x x))
27.0ms	(* (* x x) 9/40)

simplify20.7s

Calls

416 calls:

Slowest

487.0ms	(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
484.0ms	(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
483.0ms	(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
481.0ms	(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
475.0ms	(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))

prune2.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

15.6b	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
0.2b	(* (* x x) 9/40)
0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) (* x x)) 27/2800)

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

1392×	`add-sqr-sqrt`
858×	`unswap-sqr`
318×	`swap-sqr`
279×	`associate-l`
228×	`difference-of-squares`
194×	`*-commutative`
138×	`pow1`
110×	`*-un-lft-identity`
73×	`associate-r`
66×	`add-cube-cbrt`
48×	`distribute-lft-out--`
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`
6×	`add-log-exp`
4×	`insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

4 calls:

Slowest

245.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
177.0ms	(* (* (* x x) (* x x)) 27/2800)
42.0ms	(* (* x x) (* x x))
26.0ms	(* (* x x) 9/40)

series327.0ms

Calls

4 calls:

Slowest

179.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
57.0ms	(* (* (* x x) (* x x)) 27/2800)
47.0ms	(* (* x x) 9/40)
44.0ms	(* (* x x) (* x x))

simplify57.1s

Calls

923 calls:

Slowest

503.0ms	(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
490.0ms	(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
480.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
471.0ms	(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
463.0ms	(* (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))) (* (* 27/2800 27/2800) 27/2800))

prune5.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b	(- x (sin x))
2.5b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))

rewrite77.0ms

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`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`associate-/r/` `insert-posit16`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `rem-log-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `exp-diff` `div-exp`

Calls

4 calls:

Slowest

34.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
30.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
4.0ms	(- x (tan x))

series391.0ms

Calls

4 calls:

Slowest

143.0ms	(/ (- x (sin x)) (- x (tan x)))
109.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
80.0ms	(- x (tan x))
58.0ms	(- x (sin x))

simplify5.3s

Calls

122 calls:

Slowest

448.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
441.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
404.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
403.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
302.0ms	(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch153.0ms

end0.0ms

sample16.9s

Algorithm

intervals

Results

7.5s	1534×	body	2560	valid
5.6s	2789×	body	1280	valid
2.6s	1884×	body	640	valid
772.0ms	933×	body	320	valid
239.0ms	500×	body	160	valid
96.0ms	360×	body	80	valid