Details

sample295.0ms

Algorithm

intervals

Results

67.0ms	45×	body	1280	valid
56.0ms	42×	body	640	valid
20.0ms	133×	body	80	valid
13.0ms	26×	body	320	valid
3.0ms	10×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
5	37
4	34
3	26
2	21
1	13
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize95.0ms

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))

rewrite105.0ms

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))))
8.0ms	(- 1.0 (* (tan x) (tan x)))
23.0ms	(* (tan x) (tan x))
26.0ms	(* (tan x) (tan x))

series671.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
79.0ms	(- 1.0 (* (tan x) (tan x)))
354.0ms	(* (tan x) (tan x))
87.0ms	(* (tan x) (tan x))

simplify1.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	1540
1	350
0	138

prune544.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))))

rewrite43.0ms

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)))))
11.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))
9.0ms	(exp (- 1.0 (* (tan x) (tan x))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(log (exp (- 1.0 (* (tan x) (tan x)))))
39.0ms	(* (tan x) (tan x))
65.0ms	(* (tan x) (tan x))
98.0ms	(exp (- 1.0 (* (tan x) (tan x))))

simplify795.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	903
1	216
0	99

prune610.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

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))

rewrite77.0ms

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:

16.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
19.0ms	(/ (* (sin x) (tan x)) (cos x))
17.0ms	(* (sin x) (tan x))
20.0ms	(* (tan x) (tan x))

series294.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
102.0ms	(/ (* (sin x) (tan x)) (cos x))
76.0ms	(* (sin x) (tan x))
48.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	2006
1	333
0	134

prune614.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(* (sin x) (tan x))
0.2b	(* (sin x) (tan x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-/r` `times-frac` `associate-r` `associate-l*`
4×	`cbrt-undiv` `div-exp` `prod-exp` `tan-quot` `associate-*r/` `cbrt-unprod` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr` `associate-/l/`

Counts

4 → 82

Calls

4 calls:

11.0ms	(/ (* (sin x) (tan x)) (cos x))
11.0ms	(/ (* (sin x) (tan x)) (cos x))
10.0ms	(* (sin x) (tan x))
17.0ms	(* (sin x) (tan x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (* (sin x) (tan x)) (cos x))
81.0ms	(/ (* (sin x) (tan x)) (cos x))
52.0ms	(* (sin x) (tan x))
69.0ms	(* (sin x) (tan x))

simplify990.0ms

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1138
1	195
0	86

prune545.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes687.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	1467×	body	1280	valid
1.4s	1249×	body	640	valid
482.0ms	4349×	body	80	valid
265.0ms	626×	body	320	valid
143.0ms	309×	body	160	valid