Details

sample397.0ms

Algorithm

intervals

Results

124.0ms	45×	body	2560	valid
106.0ms	86×	body	1280	valid
88.0ms	56×	body	640	valid
14.0ms	34×	body	320	valid
5.0ms	20×	body	160	valid
3.0ms	15×	body	80	valid

simplify24.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.1b	(- x (tan x))
2.1b	(- x (sin x))

rewrite110.0ms

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:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (tan x))
12.0ms	(- x (sin x))

series225.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ (- x (sin x)) (- x (tan x)))
77.0ms	(- x (tan x))
48.0ms	(- x (sin x))

simplify1.8s

Counts: 89 → 89

prune357.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
2.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.1b	(- x (tan x))
2.1b	(- x (tan x))

rewrite180.0ms

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:

17.0ms	(/ (sin x) (- x (tan x)))
142.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
9.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series565.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (sin x) (- x (tan x)))
297.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
110.0ms	(- x (tan x))
78.0ms	(- x (tan x))

simplify577.0ms

Counts: 106 → 106

prune380.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
13.0b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
13.0b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 136

Calls

4 calls:

4.0ms	(pow (sin x) 2)
8.0ms	(pow (sin x) 2)
24.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
33.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)
103.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
93.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify665.0ms

Counts: 148 → 148

prune597.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 27 2800) (pow x 4))
0.1b	(* (/ 9 40) (pow x 2))
13.8b	(- (* (/ 9 40) (pow x 2)) (+ (* (/ 27 2800) (pow x 4)) (/ 1 2)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
29×	`add-exp-log`
26×	`associate-l`
25×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r`
14×	`unswap-sqr`
13×	`add-cbrt-cube`
12×	`prod-exp`
10×	`unpow-prod-down`
8×	`add-log-exp`
6×	`div-exp` `associate-*l/` `sqr-pow`
4×	`pow-to-exp` `pow-exp` `cbrt-unprod`
3×	`pow1` `frac-sub` `unpow2`
2×	`cbrt-undiv` `diff-log` `*-commutative` `div-inv`
1×	`sub-neg` `flip3--` `flip3-+` `frac-add` `sum-log` `flip--` `flip-+` `associate--r+`

Counts

3 → 106

Calls

3 calls:

29.0ms	(* (/ 27 2800) (pow x 4))
24.0ms	(* (/ 9 40) (pow x 2))
92.0ms	(- (* (/ 9 40) (pow x 2)) (+ (* (/ 27 2800) (pow x 4)) (/ 1 2)))

series161.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (/ 27 2800) (pow x 4))
33.0ms	(* (/ 9 40) (pow x 2))
78.0ms	(- (* (/ 9 40) (pow x 2)) (+ (* (/ 27 2800) (pow x 4)) (/ 1 2)))

simplify1.3s

Counts: 115 → 115

prune489.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes77.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch205.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.03007487465186483
9	-1501.2167507114543	-0.006495210018506858	-0.027057923325783554

simplify1.5s

end0.0ms

sample14.1s

Algorithm

intervals

Results

6.0s	2810×	body	1280	valid
5.6s	1545×	body	2560	valid
1.4s	1867×	body	640	valid
534.0ms	952×	body	320	valid
138.0ms	463×	body	160	valid
63.0ms	363×	body	80	valid