Details

sample254.0ms

Algorithm

intervals

Results

40.0ms	44×	body	1280	valid
25.0ms	47×	body	640	valid
18.0ms	137×	body	80	valid
6.0ms	19×	body	320	valid
2.0ms	9×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

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

rewrite69.0ms

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)
16.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
30.0ms	(* (tan x) (tan x))

series360.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma (tan x) (tan x) 1.0)
60.0ms	(- 1.0 (* (tan x) (tan x)))
164.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
57.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

109 → 109

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	155	1557
1	371	1472
2	1610	1347
done	5001	1335

prune424.0ms

Pruning

13 alts after pruning (13 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)))
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 159

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
6.0ms	(- 1.0 (* (tan x) (tan x)))
38.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
26.0ms	(* (tan x) (tan x))

series347.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(fma (tan x) (tan x) 1.0)
60.0ms	(- 1.0 (* (tan x) (tan x)))
187.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
51.0ms	(* (tan x) (tan x))

simplify2.5s

Counts

171 → 171

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	270	3573
1	664	3221
2	3589	3024
done	5000	3008

prune487.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.2b	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))
0.2b	(* (tan x) (tan x))
0.3b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

24.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.0ms	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))
16.0ms	(* (tan x) (tan x))
1.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
451.0ms	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))
37.0ms	(* (tan x) (tan x))
381.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

simplify1.4s

Counts

100 → 100

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	174	1763
1	411	1670
2	1659	1471
done	5000	1459

prune479.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
16×	`associate-l`
14×	`pow1`
13×	`add-cbrt-cube`
9×	`prod-diff`
7×	`associate-r`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
4×	`tan-quot` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `unswap-sqr`
3×	`frac-times` `sub-neg` `flip3--` `fma-neg` `associate-r/` `swap-sqr` `associate-/r` `flip--` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `difference-of-squares`
1×	`pow2` `pow-flip` `frac-2neg` `pow-plus` `diff-log` `clear-num` `pow-sqr` `pow-prod-up` `inv-pow`

Counts

4 → 136

Calls

4 calls:

5.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
7.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (/ 1 (fma (tan x) (tan x) 1.0)) (- 1.0 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))

series357.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
62.0ms	(- 1.0 (* (tan x) (tan x)))
158.0ms	(* (/ 1 (fma (tan x) (tan x) 1.0)) (- 1.0 (* (tan x) (tan x))))
47.0ms	(* (tan x) (tan x))

simplify3.3s

Counts

148 → 148

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	201	2346
1	523	2195
2	3016	1875
done	5000	1839

prune460.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes127.0ms

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: 0 (1.0ms)

Iter	Nodes	Cost
0	9	16
done	9	16

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	1528×	body	1280	valid
1.3s	1234×	body	640	valid
569.0ms	4305×	body	80	valid
279.0ms	616×	body	320	valid
121.0ms	317×	body	160	valid