Details

sample197.0ms

Algorithm

intervals

Results

37.0ms	45×	body	1280	valid
21.0ms	42×	body	640	valid
17.0ms	133×	body	80	valid
9.0ms	26×	body	320	valid
2.0ms	10×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
5	36
4	34
3	26
2	21
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

30.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
7.0ms	(- 1.0 (* (tan x) (tan x)))
23.0ms	(* (tan x) (tan x))
26.0ms	(* (tan x) (tan x))

series309.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
60.0ms	(- 1.0 (* (tan x) (tan x)))
63.0ms	(* (tan x) (tan x))
63.0ms	(* (tan x) (tan x))

simplify2.7s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
3	3710
2	997
1	349
0	138

prune582.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (exp (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(exp (- 1.0 (* (tan x) (tan x))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`pow1`
15×	`*-un-lft-identity` `add-cube-cbrt`
8×	`exp-prod` `add-cbrt-cube` `tan-quot` `add-exp-log`
7×	`add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`log-prod` `log-pow`
4×	`exp-sum`
2×	`pow2` `frac-times` `sub-neg` `pow-plus` `exp-diff` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `difference-of-squares` `unswap-sqr` `rem-exp-log`
1×	`log-div` `diff-log` `rem-log-exp`

Counts

4 → 91

Calls

4 calls:

9.0ms	(log (exp (- 1.0 (* (tan x) (tan x)))))
16.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
9.0ms	(exp (- 1.0 (* (tan x) (tan x))))

series239.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(log (exp (- 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))
40.0ms	(* (tan x) (tan x))
118.0ms	(exp (- 1.0 (* (tan x) (tan x))))

simplify2.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5031
4	3137
3	1050
2	462
1	213
0	99

prune568.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.3b	(* (tan x) (tan x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
49×	`times-frac`
44×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
16×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`tan-quot`
3×	`associate-/r` `associate-/l`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/ (sin x) (cos x))
8.0ms	(- 1.0 (* (tan x) (tan x)))
39.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
15.0ms	(* (tan x) (tan x))

series204.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (sin x) (cos x))
49.0ms	(- 1.0 (* (tan x) (tan x)))
79.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
43.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	1806
1	579
0	191

prune865.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(* (sin x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

7.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
17.0ms	(/ (* (sin x) (tan x)) (cos x))
20.0ms	(* (sin x) (tan x))
25.0ms	(* (tan x) (tan x))

series309.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
103.0ms	(/ (* (sin x) (tan x)) (cos x))
65.0ms	(* (sin x) (tan x))
51.0ms	(* (tan x) (tan x))

simplify2.5s

Counts

95 → 95

Iterations

Iter	Nodes
done	5004
3	3503
2	1033
1	332
0	134

prune556.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes629.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.1s	1467×	body	1280	valid
860.0ms	1249×	body	640	valid
521.0ms	4349×	body	80	valid
241.0ms	626×	body	320	valid
83.0ms	309×	body	160	valid