Details

sample656.0ms

Algorithm

intervals

Results

262.0ms	51×	body	2560	valid
180.0ms	93×	body	1280	valid
69.0ms	55×	body	640	valid
15.0ms	33×	body	320	valid
4.0ms	12×	body	160	valid
2.0ms	12×	body	80	valid

simplify5.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite88.0ms

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:

51.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
18.0ms	(- x (sin x))

series460.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (- x (sin x)) (- x (tan x)))
165.0ms	(- x (tan x))
160.0ms	(- x (sin x))

simplify63.0ms

Counts: 89 → 89

prune214.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
17.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite46.0ms

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:

12.0ms	(* 27/2800 (pow x 4))
12.0ms	(* 9/40 (pow x 2))
19.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series134.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* 27/2800 (pow x 4))
35.0ms	(* 9/40 (pow x 2))
57.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify107.0ms

Counts: 75 → 75

prune212.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
17.1b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite59.0ms

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`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

24.0ms	(* 27/2800 (pow x 4))
15.0ms	(* 9/40 (pow x 2))
16.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series250.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* 27/2800 (pow x 4))
39.0ms	(* 9/40 (pow x 2))
162.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify108.0ms

Counts: 73 → 73

prune205.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.2b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

25.0ms	(/ (sin x) (- x (tan x)))
106.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series560.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (sin x) (- x (tan x)))
271.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
109.0ms	(- x (tan x))
86.0ms	(- x (tan x))

simplify99.0ms

Counts: 106 → 106

prune366.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes89.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch177.0ms

Steps

Iters	Range		Point
9	3.244205803610274e-06	1902.9075791774285	0.026773927356951697
8	-45.38980787391071	-0.005411406272604966	-0.02818082991146234

simplify232.0ms

end0.0ms

sample14.0s

Algorithm

intervals

Results

6.3s	1646×	body	2560	valid
4.2s	2707×	body	1280	valid
2.0s	1867×	body	640	valid
924.0ms	945×	body	320	valid
140.0ms	475×	body	160	valid
60.0ms	360×	body	80	valid