Details

sample165.0ms

Algorithm

intervals

Results

31.0ms	46×	body	1280	valid
21.0ms	49×	body	640	valid
10.0ms	125×	body	80	valid
6.0ms	21×	body	320	valid
3.0ms	15×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

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:

7.0ms	(- 1.0 (* (tan x) (tan x)))
24.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
20.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (* (tan x) (tan x)))
139.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(* (tan x) (tan x))
71.0ms	(* (tan x) (tan x))

simplify2.6s

Counts

117 → 117

Iterations

Iter	Nodes
done	5033
3	3680
2	996
1	349
0	138

prune676.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-/r*` `flip3-+` `div-sub` `flip-+`
2×	`pow2` `neg-sub0` `frac-times` `associate-+r-` `sum-log` `pow-plus` `unsub-neg` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `div-exp` `neg-log` `div-inv`

Counts

4 → 110

Calls

4 calls:

10.0ms	(+ 1.0 (- (* (tan x) (tan x))))
44.0ms	(/ (+ 1.0 (- (* (tan x) (tan x)))) (+ 1.0 (* (tan x) (tan x))))
24.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))

series308.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ 1.0 (- (* (tan x) (tan x))))
129.0ms	(/ (+ 1.0 (- (* (tan x) (tan x)))) (+ 1.0 (* (tan x) (tan x))))
67.0ms	(* (tan x) (tan x))
64.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1107
1	356
0	139

prune642.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

11.0ms	(/ (* (tan x) (sin x)) (cos x))
25.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
12.0ms	(* (tan x) (sin x))
30.0ms	(* (tan x) (tan x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (* (tan x) (sin x)) (cos x))
162.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
60.0ms	(* (tan x) (sin x))
40.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	1573
1	479
0	190

prune804.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
58×	`times-frac`
54×	`*-un-lft-identity`
46×	`add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
16×	`associate-r` `associate-l`
13×	`pow1` `swap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l`
5×	`unswap-sqr`
4×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-*l/` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `tan-quot` `associate-/r/` `*-commutative`
1×	`pow2` `frac-times` `flip3-+` `pow-plus` `flip3--` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip-+` `flip--`

Counts

4 → 148

Calls

4 calls:

12.0ms	(/ (* (tan x) (sin x)) (cos x))
45.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
10.0ms	(* (tan x) (sin x))
22.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (* (tan x) (sin x)) (cos x))
171.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
70.0ms	(* (tan x) (sin x))
65.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify2.6s

Counts

160 → 160

Iterations

Iter	Nodes
done	5002
2	2523
1	755
0	255

prune915.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes290.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	8

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	1532×	body	1280	valid
896.0ms	1251×	body	640	valid
647.0ms	4281×	body	80	valid
417.0ms	603×	body	320	valid
86.0ms	333×	body	160	valid