Details

sample348.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
11.0ms	40×	body	640	valid
8.0ms	133×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	13×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9
done	45	9

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

23.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify45.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	918
2	5001	882
done	5001	882

prune294.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`prod-diff`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`times-frac`
6×	`tan-quot` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 115

Calls

4 calls:

15.0ms	(/ (* (tan x) (sin x)) (cos x))
14.0ms	(* (tan x) (sin x))
11.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
17.0ms	(* (tan x) (tan x))

series194.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* (tan x) (sin x)) (cos x))
46.0ms	(* (tan x) (sin x))
52.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
36.0ms	(* (tan x) (tan x))

simplify67.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	432	1314
1	1873	967
2	5001	929
done	5001	929

prune314.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`tan-quot` `fma-neg` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `flip--` `associate-/l/` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

15.0ms	(/ (* (tan x) (sin x)) (cos x))
15.0ms	(* (tan x) (sin x))
13.0ms	(* (tan x) (sin x))
12.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (* (tan x) (sin x)) (cos x))
44.0ms	(* (tan x) (sin x))
47.0ms	(* (tan x) (sin x))
52.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))

simplify57.0ms

Counts

118 → 118

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	391	1295
1	1689	957
2	5001	923
done	5001	923

prune313.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
0.3b	(* (tan x) (tan x))
12.7b	(sqrt (/ (* (tan x) (sin x)) (cos x)))
12.7b	(sqrt (/ (* (tan x) (sin x)) (cos x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-prod`
40×	`add-sqr-sqrt`
28×	`pow1`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`swap-sqr`
13×	`associate-r` `associate-l`
10×	`sqrt-pow1` `pow1/2`
8×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-div` `pow-prod-up` `div-inv`
5×	`unswap-sqr`
4×	`tan-quot` `expm1-log1p-u` `pow-prod-down` `pow-sqr` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sqrt-unprod` `rem-square-sqrt`

Counts

4 → 136

Calls

4 calls:

40.0ms	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
15.0ms	(* (tan x) (tan x))
5.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))
6.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
34.0ms	(* (tan x) (tan x))
78.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))
80.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))

simplify51.0ms

Counts

148 → 148

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	252	1113
1	1134	996
2	5002	950
done	5002	950

prune373.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes240.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	14
1	17	14
done	17	14

end0.0ms

sample1.7s

Algorithm

intervals

Results

707.0ms	1533×	body	1280	valid
367.0ms	1249×	body	640	valid
255.0ms	4322×	body	80	valid
118.0ms	599×	body	320	valid
46.0ms	297×	body	160	valid