Details

sample347.0ms

Algorithm

intervals

Results

91.0ms	46×	body	1280	valid
72.0ms	49×	body	640	valid
22.0ms	125×	body	80	valid
11.0ms	21×	body	320	valid
6.0ms	15×	body	160	valid

simplify513.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	42
5	42
4	37
3	29
2	22
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

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))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-neg` `prod-diff`
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 → 119

Calls

4 calls:

6.0ms	(- 1.0 (* (tan x) (tan x)))
29.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
12.0ms	(* (tan x) (tan x))
25.0ms	(* (tan x) (tan x))

series317.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- 1.0 (* (tan x) (tan x)))
131.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
73.0ms	(* (tan x) (tan x))
48.0ms	(* (tan x) (tan x))

simplify3.3s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
3	4563
2	1073
1	374
0	151

prune740.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 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

29×	`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`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`associate-/r*`
2×	`pow2` `frac-times` `pow-plus` `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` `log1p-udef` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-sub` `div-exp` `log1p-expm1` `flip-+` `div-inv` `flip--`

Counts

4 → 109

Calls

4 calls:

34.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
1.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
18.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))

series564.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
337.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
42.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify3.0s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
3	4333
2	1133
1	409
0	162

prune663.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (sin x))
0.2b	(log1p (/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

55.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
22.0ms	(* (tan x) (sin x))
1.0ms	(log1p (/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x)))))
23.0ms	(* (tan x) (tan x))

series622.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
52.0ms	(* (tan x) (sin x))
339.0ms	(log1p (/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x)))))
47.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	1416
1	488
0	195

prune740.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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))
0.2b	(log1p (/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))))
0.3b	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
55×	`times-frac`
52×	`*-un-lft-identity`
44×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-r` `associate-l`
13×	`pow1` `swap-sqr`
5×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*` `unswap-sqr`
4×	`log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r*`
2×	`pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/`
1×	`pow2` `frac-times` `log1p-udef` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `flip3--` `div-sub` `tan-quot` `log1p-expm1` `associate-*r/` `pow-sqr` `pow-prod-up` `flip-+` `flip--`

Counts

4 → 143

Calls

4 calls:

34.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
15.0ms	(* (tan x) (sin x))
0.0ms	(log1p (/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))))
37.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series766.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
86.0ms	(* (tan x) (sin x))
378.0ms	(log1p (/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))))
87.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify2.6s

Counts

155 → 155

Iterations

Iter	Nodes
done	5001
2	2562
1	781
0	269

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes289.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	1532×	body	1280	valid
1.4s	4281×	body	80	valid
765.0ms	1251×	body	640	valid
262.0ms	603×	body	320	valid
76.0ms	333×	body	160	valid