Details

sample332.0ms

Algorithm

intervals

Results

103.0ms	46×	body	1280	valid
29.0ms	44×	body	640	valid
18.0ms	132×	body	80	valid
9.0ms	20×	body	320	valid
5.0ms	14×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	14

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite273.0ms

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:

70.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
13.0ms	(- 1.0 (* (tan x) (tan x)))
51.0ms	(* (tan x) (tan x))
124.0ms	(* (tan x) (tan x))

series499.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
105.0ms	(- 1.0 (* (tan x) (tan x)))
49.0ms	(* (tan x) (tan x))
84.0ms	(* (tan x) (tan x))

simplify2.8s

Counts

131 → 131

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	151	1789
1	338	1638
2	938	1453
3	2987	1419
done	5000	1411

prune508.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
54×	`prod-diff`
50×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow1`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`fma-def` `fma-neg`
5×	`frac-times`
4×	`tan-quot` `expm1-log1p-u` `flip3--` `flip3-+` `flip--` `flip-+` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 163

Calls

4 calls:

17.0ms	(- (sqrt 1.0) (tan x))
10.0ms	(+ (sqrt 1.0) (tan x))
89.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
22.0ms	(* (tan x) (tan x))

series347.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (sqrt 1.0) (tan x))
37.0ms	(+ (sqrt 1.0) (tan x))
188.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
63.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

175 → 175

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	210	3440
1	509	2534
2	1589	1952
done	5000	1658

prune621.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

7.0ms	(pow (cos x) 2)
7.0ms	(pow (cos x) 2)
8.0ms	(pow (sin x) 2)
8.0ms	(pow (sin x) 2)

series114.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (cos x) 2)
23.0ms	(pow (cos x) 2)
39.0ms	(pow (sin x) 2)
32.0ms	(pow (sin x) 2)

simplify3.3s

Counts

92 → 92

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	68	616
1	138	530
2	293	466
3	807	466
4	3813	458
done	5000	458

prune411.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

17.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
27.0ms	(/ (* (sin x) (tan x)) (cos x))
14.0ms	(* (sin x) (tan x))
30.0ms	(* (tan x) (tan x))

series332.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
110.0ms	(/ (* (sin x) (tan x)) (cos x))
81.0ms	(* (sin x) (tan x))
49.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

127 → 127

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	192	2214
1	428	1825
2	1390	1486
done	5000	1235

prune384.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	21
1	12	21
done	12	21

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	1496×	body	1280	valid
1.2s	1269×	body	640	valid
580.0ms	4282×	body	80	valid
276.0ms	622×	body	320	valid
87.0ms	331×	body	160	valid