Details

sample240.0ms

Algorithm

intervals

Results

54.0ms	53×	body	1280	valid
29.0ms	45×	body	640	valid
20.0ms	131×	body	80	valid
5.0ms	12×	body	320	valid
5.0ms	15×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
6	45
5	43
4	37
3	29
2	22
1	13
0	7

prune62.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
0.4b	(fma (- (tan x)) (tan x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
7.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
3.0ms	(fma (- (tan x)) (tan x) 1.0)

series411.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(fma (tan x) (tan x) 1.0)
216.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
118.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify1.3s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	1873
2	456
1	161
0	87

prune372.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `tan-quot` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r` `distribute-rgt-neg-in` `associate-r` `associate-/l`
2×	`flip3-+` `flip-+` `distribute-neg-frac` `associate-/l/`
1×	`distribute-lft-neg-out` `frac-times` `cbrt-undiv` `+-commutative` `clear-num` `neg-mul-1` `sum-log` `fma-def` `frac-2neg` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
15.0ms	(+ (* (- (tan x)) (tan x)) 1.0)
30.0ms	(/ (+ (* (- (tan x)) (tan x)) 1.0) (fma (tan x) (tan x) 1.0))
15.0ms	(* (- (tan x)) (tan x))

series350.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma (tan x) (tan x) 1.0)
50.0ms	(+ (* (- (tan x)) (tan x)) 1.0)
164.0ms	(/ (+ (* (- (tan x)) (tan x)) 1.0) (fma (tan x) (tan x) 1.0))
91.0ms	(* (- (tan x)) (tan x))

simplify909.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1434
1	345
0	148

prune586.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.3b	(* (tan x) (tan x))
0.3b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
14.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
20.0ms	(* (tan x) (tan x))
0.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- 1.0 (* (tan x) (tan x)))
179.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
43.0ms	(* (tan x) (tan x))
304.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

simplify1.2s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	1833
1	429
0	177

prune591.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
0.3b	(log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))
0.3b	(log (exp (log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))))
0.4b	(fma (- (tan x)) (tan x) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`expm1-log1p-u` `pow1`
4×	`log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `log1p-expm1` `fma-udef` `div-inv`

Counts

4 → 67

Calls

4 calls:

4.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
0.0ms	(log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))
2.0ms	(log (exp (log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))))
0.0ms	(fma (- (tan x)) (tan x) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
388.0ms	(log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))
431.0ms	(log (exp (log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))))
91.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify1.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	3907
2	745
1	249
0	131

prune556.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes208.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.0s	1457×	body	1280	valid
858.0ms	1278×	body	640	valid
693.0ms	633×	body	320	valid
632.0ms	4297×	body	80	valid
146.0ms	335×	body	160	valid