Details

sample455.0ms

Algorithm

intervals

Results

92.0ms	41×	body	2560	valid
68.0ms	98×	body	1280	valid
20.0ms	59×	body	640	valid
6.0ms	28×	body	320	valid
3.0ms	21×	body	160	valid
1.0ms	9×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
40.0ms	(- x (sin x))

simplify754.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (310.0ms)

Iter	Nodes	Cost
0	209	1823
1	476	1563
2	1413	1384
done	5001	1384

prune254.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
214×	`add-sqr-sqrt` `*-un-lft-identity`
106×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
18×	`prod-diff`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`fma-neg` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 260

Calls

4 calls:

12.0ms	(/ (- x (tan x)) (- x (sin x)))
14.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
3.0ms	(- x (tan x))
3.0ms	(- x (sin x))

series237.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- x (tan x)) (- x (sin x)))
76.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
53.0ms	(- x (tan x))
31.0ms	(- x (sin x))

simplify1.3s

Counts

272 → 272

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	374	5190
1	861	4532
2	2518	4000
done	5000	3992

prune390.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
0.1b	(* 9/40 (pow x 2))
16.3b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
5.0ms	(* 9/40 (pow x 2))
4.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series156.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
25.0ms	(* 9/40 (pow x 2))
49.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.6s

Counts

67 → 67

Iterations

Useful iterations: 3 (585.0ms)

Iter	Nodes	Cost
0	106	845
1	223	700
2	650	642
3	2833	594
done	5001	594

prune150.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.9b

bsearch89.0ms

Steps

Iters	Range		Point
9	0.00016167321766412214	1766.3470775505596	0.028078975194333212
10	-3752817.331716861	-5.670122129476186e-07	-0.02894118494710049

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	24	42
1	30	32
done	30	32

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.4s	1564×	body	2560	valid
1.8s	2744×	body	1280	valid
677.0ms	1876×	body	640	valid
244.0ms	925×	body	320	valid
86.0ms	494×	body	160	valid
37.0ms	397×	body	80	valid