Details

sample365.0ms

Algorithm

intervals

Results

21.0ms	44×	body	1280	valid
12.0ms	44×	body	640	valid
10.0ms	141×	body	80	valid
3.0ms	15×	body	320	valid
2.0ms	12×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
6.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(* (tan x) (tan x))

series233.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma (tan x) (tan x) 1.0)
109.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
34.0ms	(- 1.0 (* (tan x) (tan x)))
45.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

109 → 109

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	155	1557
1	330	1462
2	891	1345
3	2810	1320
done	5000	1314

prune267.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (* 1 (fma (tan x) (tan x) 1.0)))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
17.0ms	(/ (- 1.0 (* (tan x) (tan x))) (* 1 (fma (tan x) (tan x) 1.0)))
5.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))

series222.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma (tan x) (tan x) 1.0)
110.0ms	(/ (- 1.0 (* (tan x) (tan x))) (* 1 (fma (tan x) (tan x) 1.0)))
33.0ms	(- 1.0 (* (tan x) (tan x)))
36.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	153	1382
1	333	1220
2	950	1075
3	3267	1050
done	5000	1047

prune228.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (* 1 (fma (tan x) (tan x) 1.0)))
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)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
54×	`*-un-lft-identity` `prod-diff`
46×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log`
20×	`distribute-rgt-in` `distribute-lft-in`
18×	`add-cbrt-cube`
8×	`frac-times` `prod-exp` `associate-/l/` `add-log-exp`
7×	`flip3--` `flip3-+` `flip--` `flip-+`
6×	`pow1` `fma-def` `fma-neg` `div-exp` `associate-r`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `associate-l` `associate-l/` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg`
2×	`1-exp` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `frac-2neg` `times-frac` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

40.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (* 1 (fma (tan x) (tan x) 1.0)))
9.0ms	(+ (sqrt 1.0) (tan x))
11.0ms	(- (sqrt 1.0) (tan x))
57.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (* 1 (fma (tan x) (tan x) 1.0)))
35.0ms	(+ (sqrt 1.0) (tan x))
36.0ms	(- (sqrt 1.0) (tan x))
102.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))

simplify1.2s

Counts

178 → 178

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	245	4222
1	653	3114
2	2527	2378
done	5000	2319

prune358.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
33×	`times-frac`
29×	`add-cube-cbrt`
25×	`associate-r`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`distribute-lft-out`
9×	`difference-of-squares`
7×	`associate-l`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`tan-quot` `expm1-log1p-u` `associate-/r` `associate-/r/` `log1p-expm1-u` `associate-/l`
3×	`frac-times` `fma-def` `swap-sqr` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `pow2` `flip3--` `frac-2neg` `pow-plus` `div-sub` `clear-num` `sum-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 138

Calls

4 calls:

8.0ms	(+ (tan x) (sqrt 1.0))
24.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (tan x) (sqrt 1.0)))
15.0ms	(* (tan x) (tan x))
68.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- 1.0 (* (tan x) (tan x))) (+ (tan x) (sqrt 1.0))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (tan x) (sqrt 1.0))
112.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (tan x) (sqrt 1.0)))
32.0ms	(* (tan x) (tan x))
35.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- 1.0 (* (tan x) (tan x))) (+ (tan x) (sqrt 1.0))))

simplify2.0s

Counts

150 → 150

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	213	2573
1	528	2412
2	2236	2205
done	5000	1784

prune382.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	16	30
1	20	28
done	20	28

end0.0ms

sample1.6s

Algorithm

intervals

Results

667.0ms	1486×	body	1280	valid
338.0ms	1208×	body	640	valid
267.0ms	4384×	body	80	valid
115.0ms	593×	body	320	valid
44.0ms	329×	body	160	valid