Details

sample241.0ms

Algorithm

intervals

Results

42.0ms	40×	body	1280	valid
33.0ms	46×	body	640	valid
18.0ms	138×	body	80	valid
11.0ms	22×	body	320	valid
3.0ms	10×	body	160	valid

simplify151.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	43	14
6	45	14
done	45	14

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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)))
0.3b	(* (tan x) (tan x))

rewrite103.0ms

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:

1.0ms	(fma (tan x) (tan x) 1.0)
45.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
13.0ms	(- 1.0 (* (tan x) (tan x)))
37.0ms	(* (tan x) (tan x))

series445.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma (tan x) (tan x) 1.0)
210.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
73.0ms	(- 1.0 (* (tan x) (tan x)))
78.0ms	(* (tan x) (tan x))

simplify2.0s

Counts

109 → 109

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	155	1557
1	371	1472
2	1607	1347
done	5000	1335

prune753.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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))) (pow (fma (tan x) (tan x) 1.0) 1))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
39.0ms	(/ (- 1.0 (* (tan x) (tan x))) (pow (fma (tan x) (tan x) 1.0) 1))
21.0ms	(- 1.0 (* (tan x) (tan x)))
35.0ms	(* (tan x) (tan x))

series458.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (tan x) (tan x) 1.0)
225.0ms	(/ (- 1.0 (* (tan x) (tan x))) (pow (fma (tan x) (tan x) 1.0) 1))
80.0ms	(- 1.0 (* (tan x) (tan x)))
67.0ms	(* (tan x) (tan x))

simplify2.9s

Counts

131 → 131

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	198	2340
1	481	2044
2	2801	1854
done	5002	1842

prune803.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
182×	`*-un-lft-identity`
168×	`add-sqr-sqrt`
92×	`add-cube-cbrt`
38×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
22×	`sqrt-prod`
19×	`distribute-lft-out--`
13×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `fma-def` `flip--` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

4 → 216

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
23.0ms	(+ (sqrt 1.0) (tan x))
108.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))
37.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))

series842.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(fma (tan x) (tan x) 1.0)
65.0ms	(+ (sqrt 1.0) (tan x))
430.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))
249.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))

simplify3.0s

Counts

228 → 228

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	286	6237
1	740	5983
2	4081	5641
done	5000	5635

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

32.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
26.0ms	(- 1.0 (* (tan x) (tan x)))
38.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))
34.0ms	(* (tan x) (tan x))

series598.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
79.0ms	(- 1.0 (* (tan x) (tan x)))
227.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))
67.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

130 → 130

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	202	2124
1	427	1966
2	1787	1811
done	5000	1799

prune835.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes352.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	23
1	12	23
done	12	23

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.9s	4254×	body	80	valid
1.9s	1544×	body	1280	valid
1.2s	1260×	body	640	valid
297.0ms	624×	body	320	valid
173.0ms	318×	body	160	valid