Details

sample482.0ms

Algorithm

intervals

Results

147.0ms	42×	body	2560	valid
102.0ms	86×	body	1280	valid
44.0ms	68×	body	640	valid
15.0ms	33×	body	320	valid
5.0ms	18×	body	160	valid
1.0ms	9×	body	80	valid

simplify36.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (tan x))
0.8b	(- x (sin x))

rewrite65.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 110

Calls

3 calls:

30.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series256.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(/ (- x (sin x)) (- x (tan x)))
79.0ms	(- x (tan x))
45.0ms	(- x (sin x))

simplify2.7s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	4708
2	1277
1	501
0	209

prune530.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.8b	(- x (tan x))
0.8b	(- x (sin x))
0.8b	(- x (sin x))
0.8b	(- x (sin x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

5.0ms	(- x (tan x))
9.0ms	(- x (sin x))
6.0ms	(- x (sin x))
8.0ms	(- x (sin x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- x (tan x))
39.0ms	(- x (sin x))
56.0ms	(- x (sin x))
51.0ms	(- x (sin x))

simplify3.1s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
4	4582
3	1650
2	622
1	277
0	127

prune470.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.8b	(- x (tan x))
0.8b	(- x (sin x))

rewrite37.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 110

Calls

3 calls:

19.0ms	(/ (- x (tan x)) (- x (sin x)))
5.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series209.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(/ (- x (tan x)) (- x (sin x)))
64.0ms	(- x (tan x))
36.0ms	(- x (sin x))

simplify2.5s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	4526
2	1255
1	495
0	207

prune447.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* x x) (* x x))
0.3b	(fma -27/2800 (* (* x x) (* x x)) -1/2)
16.3b	(fma 9/40 (* x x) (fma -27/2800 (* (* x x) (* x x)) -1/2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 85

Calls

3 calls:

44.0ms	(* (* x x) (* x x))
0.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
0.0ms	(fma 9/40 (* x x) (fma -27/2800 (* (* x x) (* x x)) -1/2))

series247.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (* x x) (* x x))
117.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
80.0ms	(fma 9/40 (* x x) (fma -27/2800 (* (* x x) (* x x)) -1/2))

simplify2.1s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	2180
2	489
1	182
0	78

prune241.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes97.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch163.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.02985439976441334
10	-17239113253358.373	-4.96108325192681e-05	-0.026748202540908116

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	25

end0.0ms

sample12.7s

Algorithm

intervals

Results

5.6s	1666×	body	2560	valid
4.3s	2699×	body	1280	valid
1.7s	1879×	body	640	valid
593.0ms	944×	body	320	valid
183.0ms	474×	body	160	valid
50.0ms	338×	body	80	valid