Details

sample369.0ms

Algorithm

intervals

Results

168.0ms	51×	body	2560	valid
79.0ms	88×	body	1280	valid
27.0ms	63×	body	640	valid
8.0ms	27×	body	320	valid
4.0ms	18×	body	160	valid
1.0ms	9×	body	80	valid

simplify5.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.0b	(- x (tan x))
1.0b	(- x (sin x))

rewrite64.0ms

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

Counts

3 → 80

Calls

3 calls:

44.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series195.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/ (- x (sin x)) (- x (tan x)))
65.0ms	(- x (tan x))
45.0ms	(- x (sin x))

simplify141.0ms

Counts: 89 → 89

prune217.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.0b	(- x (tan x))
1.0b	(- x (sin x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 188

Calls

4 calls:

28.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
24.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
6.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series287.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
87.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
61.0ms	(- x (tan x))
35.0ms	(- x (sin x))

simplify74.0ms

Counts: 200 → 200

prune329.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
14.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

17.0ms	(* 27/2800 (pow x 4))
13.0ms	(* 9/40 (pow x 2))
21.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series120.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* 27/2800 (pow x 4))
32.0ms	(* 9/40 (pow x 2))
48.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify36.0ms

Counts: 75 → 75

prune159.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin x) 3)
1.0b	(- (pow x 3) (pow (sin x) 3))
1.0b	(- x (tan x))
21.4b	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
49×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
16×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`frac-times`
3×	`difference-cubes` `pow-unpow` `flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 147

Calls

4 calls:

4.0ms	(pow (sin x) 3)
29.0ms	(- (pow x 3) (pow (sin x) 3))
6.0ms	(- x (tan x))
104.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sin x) 3)
113.0ms	(- (pow x 3) (pow (sin x) 3))
62.0ms	(- x (tan x))
284.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

simplify92.0ms

Counts: 159 → 159

prune450.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.1b

bsearch115.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.21963308938311268	0.031458382400945506
11	-2445851338.3862987	-4.2674702477225e-16	-0.03213985651385342

simplify1.0ms

end0.0ms

sample9.8s

Algorithm

intervals

Results

4.4s	1598×	body	2560	valid
3.1s	2730×	body	1280	valid
1.4s	1873×	body	640	valid
423.0ms	943×	body	320	valid
135.0ms	479×	body	160	valid
89.0ms	377×	body	80	valid