Details

sample112.0ms

Algorithm

intervals

Results

25.0ms	43×	body	1280	valid
14.0ms	38×	body	640	valid
11.0ms	140×	body	80	valid
7.0ms	26×	body	320	valid
3.0ms	9×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (59.0ms)

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

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:

13.0ms	(- 1.0 (* (tan x) (tan x)))
0.0ms	(fma (tan x) (tan x) 1.0)
57.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
78.0ms	(* (tan x) (tan x))

series486.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- 1.0 (* (tan x) (tan x)))
142.0ms	(fma (tan x) (tan x) 1.0)
142.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
94.0ms	(* (tan x) (tan x))

simplify2.1s

Counts

109 → 109

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	155	1557
1	371	1472
2	1609	1347
done	5001	1335

prune425.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
194×	`*-un-lft-identity`
184×	`add-sqr-sqrt`
104×	`add-cube-cbrt`
40×	`difference-of-squares`
32×	`sqrt-prod`
30×	`associate-/r*`
25×	`distribute-lft-out`
20×	`distribute-lft-out--`
18×	`prod-diff`
13×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
7×	`flip3--` `flip--` `div-inv` `associate-/l*`
6×	`fma-neg` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`sub-neg` `flip3-+` `diff-log` `flip-+` `fma-udef`

Counts

4 → 237

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
14.0ms	(- (sqrt 1.0) (tan x))
23.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))
99.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma (tan x) (tan x) 1.0)
51.0ms	(- (sqrt 1.0) (tan x))
201.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))
303.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))

simplify2.5s

Counts

249 → 249

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	321	6853
1	813	6377
2	4460	5990
done	5000	5988

prune880.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
15.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
33.0ms	(* (tan x) (tan x))
32.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma (tan x) (tan x) 1.0)
184.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
55.0ms	(* (tan x) (tan x))
140.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))

simplify1.6s

Counts

119 → 119

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	188	1945
1	388	1807
2	1581	1668
done	5000	1656

prune569.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))
0.2b	(/ (+ (sqrt 1.0) (tan x)) (cbrt (pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3)))
0.3b	(cbrt (pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3))
0.3b	(pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3)

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

498×	`times-frac`
433×	`*-un-lft-identity`
409×	`add-sqr-sqrt`
324×	`cbrt-prod`
225×	`add-cube-cbrt`
168×	`unpow-prod-down` `cube-prod`
92×	`difference-of-squares`
63×	`associate-/r*`
58×	`distribute-lft-out`
46×	`sqrt-prod` `distribute-lft-out--`
31×	`associate-/r/`
16×	`div-inv`
15×	`flip3--` `flip--`
11×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`cube-mult` `unpow3` `associate-/l*` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `cube-div` `pow-unpow` `div-exp`
2×	`cbrt-div` `frac-2neg` `pow-exp` `clear-num` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `rem-cbrt-cube` `flip-+`

Counts

4 → 485

Calls

4 calls:

30.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))
111.0ms	(/ (+ (sqrt 1.0) (tan x)) (cbrt (pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3)))
41.0ms	(cbrt (pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3))
32.0ms	(pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3)

series1.1s

Counts

4 → 12

Calls

4 calls:

230.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))
326.0ms	(/ (+ (sqrt 1.0) (tan x)) (cbrt (pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3)))
196.0ms	(cbrt (pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3))
358.0ms	(pow (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))) 3)

simplify789.0ms

Counts

497 → 497

Iterations

Useful iterations: done (746.0ms)

Iter	Nodes	Cost
0	427	17501
1	1079	15049
done	5000	14284

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes144.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	10	18
done	10	18

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	1243×	body	640	valid
1.5s	1481×	body	1280	valid
659.0ms	4361×	body	80	valid
331.0ms	602×	body	320	valid
80.0ms	313×	body	160	valid