Details

sample351.0ms

Algorithm

intervals

Results

21.0ms	45×	body	1280	valid
11.0ms	40×	body	640	valid
10.0ms	140×	body	80	valid
5.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9
done	45	9

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

10.0ms	(- 1.0 (* (tan x) (tan x)))
19.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
14.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1.0 (* (tan x) (tan x)))
99.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))

simplify45.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882
done	5001	882

prune290.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (tan x) (sin x))
0.2b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.3b	(* (tan x) (tan x))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
6×	`tan-quot` `associate-r` `associate-l` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip--` `flip-+`

Counts

4 → 117

Calls

4 calls:

15.0ms	(* (tan x) (sin x))
34.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
17.0ms	(/ (* (tan x) (sin x)) (cos x))
15.0ms	(* (tan x) (tan x))

series254.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (tan x) (sin x))
113.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
63.0ms	(/ (* (tan x) (sin x)) (cos x))
33.0ms	(* (tan x) (tan x))

simplify60.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	455	1207
1	1904	1097
2	5001	1088
done	5001	1088

prune358.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (/ (tan x) (/ (cos x) (sin x)))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(/ (cos x) (sin x))
0.3b	(* (tan x) (tan x))
0.3b	(/ (tan x) (/ (cos x) (sin x)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
108×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
70×	`add-cube-cbrt`
19×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`difference-of-squares`
11×	`pow1`
7×	`div-inv`
5×	`tan-quot` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

90.0ms	(/ (- 1.0 (/ (tan x) (/ (cos x) (sin x)))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(/ (cos x) (sin x))
15.0ms	(* (tan x) (tan x))
12.0ms	(/ (tan x) (/ (cos x) (sin x)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- 1.0 (/ (tan x) (/ (cos x) (sin x)))) (+ 1.0 (* (tan x) (tan x))))
20.0ms	(/ (cos x) (sin x))
33.0ms	(* (tan x) (tan x))
66.0ms	(/ (tan x) (/ (cos x) (sin x)))

simplify82.0ms

Counts

194 → 194

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	699	2125
1	2915	2007
2	5001	2003
done	5001	2003

prune590.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (tan x) (tan x) 1.0) (tan x))
0.2b	(/ 1.0 (fma (tan x) (tan x) 1.0))
0.2b	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
0.3b	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

1436×	`times-frac`
888×	`add-sqr-sqrt`
873×	`*-un-lft-identity`
867×	`add-cube-cbrt`
611×	`prod-diff`
107×	`div-inv`
58×	`associate-/r/`
45×	`tan-quot`
20×	`associate-/r*`
13×	`add-exp-log` `fma-neg` `add-cbrt-cube`
9×	`associate-/l*`
6×	`add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 783

Calls

4 calls:

6.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
4.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
12.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
70.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
72.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
108.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
190.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

simplify283.0ms

Counts

795 → 795

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2457	44315
1	5001	35123
done	5001	35123

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes155.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	8	12
done	8	12

end0.0ms

sample1.7s

Algorithm

intervals

Results

711.0ms	1522×	body	1280	valid
369.0ms	1260×	body	640	valid
252.0ms	4259×	body	80	valid
131.0ms	639×	body	320	valid
49.0ms	320×	body	160	valid