Details

sample555.0ms

Algorithm

intervals

Results

197.0ms	54×	body	2560	valid
113.0ms	67×	body	640	valid
111.0ms	82×	body	1280	valid
18.0ms	29×	body	320	valid
6.0ms	13×	body	160	valid
2.0ms	11×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite45.0ms

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` `insert-posit16` `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 → 113

Calls

3 calls:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series202.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (- x (sin x)) (- x (tan x)))
67.0ms	(- x (tan x))
52.0ms	(- x (sin x))

simplify1.8s

Counts

122 → 122

Iterations

Iter	Nodes
3	4455
2	1297
1	502
0	212

prune456.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (tan x))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

14.0ms	(/ (sin x) (- x (tan x)))
85.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
8.0ms	(- x (tan x))

series419.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sin x) (- x (tan x)))
205.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
58.0ms	(- x (tan x))
67.0ms	(- x (tan x))

simplify2.0s

Counts

604 → 604

Iterations

Iter	Nodes
2	3382
1	1401
0	620

prune2.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (* x x) (- 9/40 (* 27/2800 (* x x)))) 1/2)
0.0b	(- 9/40 (* 27/2800 (* x x)))
0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.4b	(* 27/2800 (* x x))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
15×	`add-sqr-sqrt`
14×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
8×	`add-log-exp`
6×	`sub-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`diff-log` `associate-r/` `-commutative` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

28.0ms	(- (* (* x x) (- 9/40 (* 27/2800 (* x x)))) 1/2)
5.0ms	(- 9/40 (* 27/2800 (* x x)))
33.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
19.0ms	(* 27/2800 (* x x))

series336.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* (* x x) (- 9/40 (* 27/2800 (* x x)))) 1/2)
76.0ms	(- 9/40 (* 27/2800 (* x x)))
151.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
49.0ms	(* 27/2800 (* x x))

simplify2.7s

Counts

118 → 118

Iterations

Iter	Nodes
3	3837
2	1292
1	453
0	160

prune411.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 (* x (* x x)))
1.9b	(- x (tan x))
19.1b	(/ (fma (pow x 5) -1/120 (fma (pow x 7) 1/5040 (* 1/6 (* x (* x x))))) (- x (tan x)))
24.7b	(fma (pow x 5) -1/120 (fma (pow x 7) 1/5040 (* 1/6 (* x (* x x)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac` `add-cbrt-cube` `add-exp-log`
13×	`pow1`
9×	`prod-diff`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `associate-r` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 104

Calls

4 calls:

60.0ms	(* 1/6 (* x (* x x)))
9.0ms	(- x (tan x))
14.0ms	(/ (fma (pow x 5) -1/120 (fma (pow x 7) 1/5040 (* 1/6 (* x (* x x))))) (- x (tan x)))
0.0ms	(fma (pow x 5) -1/120 (fma (pow x 7) 1/5040 (* 1/6 (* x (* x x)))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 1/6 (* x (* x x)))
103.0ms	(- x (tan x))
141.0ms	(/ (fma (pow x 5) -1/120 (fma (pow x 7) 1/5040 (* 1/6 (* x (* x x))))) (- x (tan x)))
114.0ms	(fma (pow x 5) -1/120 (fma (pow x 7) 1/5040 (* 1/6 (* x (* x x)))))

simplify2.7s

Counts

116 → 116

Iterations

Iter	Nodes
3	5125
2	1274
1	452
0	208

prune618.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.8b

bsearch198.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	0.03210649578243009
9	-0.030639508246526274	-1.9696345359431407e-07	-0.025621427997812182

simplify8.0ms

Iterations

Iter	Nodes
2	26
1	26
0	21

end0.0ms

sample15.1s

Algorithm

intervals

Results

6.6s	1537×	body	2560	valid
5.0s	2771×	body	1280	valid
2.3s	1907×	body	640	valid
722.0ms	955×	body	320	valid
253.0ms	447×	body	160	valid
119.0ms	383×	body	80	valid