Details

sample432.0ms

Algorithm

intervals

Results

117.0ms	143×	body	80	valid
102.0ms	39×	body	1280	valid
52.0ms	41×	body	640	valid
15.0ms	17×	body	320	valid
9.0ms	16×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	42
5	42
4	37
3	29
2	22
1	13
0	7

prune12.0ms

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 (* (tan x) (tan x)))
0.2b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 128

Calls

4 calls:

11.0ms	(- 1 (* (tan x) (tan x)))
71.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
78.0ms	(* (tan x) (tan x))
106.0ms	(* (tan x) (tan x))

series291.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- 1 (* (tan x) (tan x)))
101.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
36.0ms	(* (tan x) (tan x))
94.0ms	(* (tan x) (tan x))

simplify4.9s

Counts

140 → 140

Iterations

Iter	Nodes
3	2926
2	985
1	383
0	157

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
0.2b	(+ 1 (tan x))
0.2b	(* (+ 1 (tan x)) (- 1 (tan x)))
0.3b	(* (tan x) (tan x))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`add-cube-cbrt`
18×	`prod-diff`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`frac-times` `associate-r`
8×	`flip3-+` `flip-+` `associate-/l/`
7×	`associate-l`
6×	`flip3--` `flip--` `add-log-exp`
5×	`associate-l/` `associate-r/`
4×	`expm1-log1p-u` `tan-quot` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `times-frac` `swap-sqr` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `sub-neg` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 138

Calls

4 calls:

45.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
10.0ms	(+ 1 (tan x))
51.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
30.0ms	(* (tan x) (tan x))

series306.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
25.0ms	(+ 1 (tan x))
101.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
58.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

150 → 150

Iterations

Iter	Nodes
2	2342
1	690
0	233

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* 1 1) (* (tan x) (tan x)))
0.2b	(/ (* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x))) (* (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`frac-times` `flip3--` `flip--`
8×	`tan-quot` `associate-/r/` `associate-/l/`
6×	`swap-sqr` `associate-r` `associate-l` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

19.0ms	(- (* 1 1) (* (tan x) (tan x)))
32.0ms	(/ (* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x))) (* (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series273.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* 1 1) (* (tan x) (tan x)))
118.0ms	(/ (* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x))) (* (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
59.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))

simplify3.3s

Counts

132 → 132

Iterations

Iter	Nodes
2	3082
1	554
0	171

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (* (+ 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))) (* (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
0.2b	(+ 1 (tan x))
0.2b	(* (+ 1 (tan x)) (- 1 (tan x)))
0.3b	(* (tan x) (tan x))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

37×	`frac-times`
30×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cbrt-cube` `add-exp-log`
26×	`associate-/l/`
24×	`flip3--` `flip--`
23×	`add-cube-cbrt`
19×	`associate-*l/`
18×	`prod-diff`
16×	`flip3-+` `flip-+`
13×	`pow1` `associate-*r/`
11×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
9×	`associate-r`
8×	`associate-/r/`
7×	`associate-l`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `tan-quot` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `swap-sqr`
2×	`sub-neg` `pow-prod-down` `*-commutative` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`pow2` `+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `times-frac` `pow-plus` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

4 → 166

Calls

4 calls:

104.0ms	(/ (* (* (+ 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))) (* (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
9.0ms	(+ 1 (tan x))
29.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
27.0ms	(* (tan x) (tan x))

series337.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (* (* (+ 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))) (* (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
24.0ms	(+ 1 (tan x))
103.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
60.0ms	(* (tan x) (tan x))

simplify2.0s

Counts

178 → 178

Iterations

Iter	Nodes
2	5047
1	998
0	283

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes291.0ms

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
2	16
1	16
0	11

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.7s	1502×	body	1280	valid
2.0s	1267×	body	640	valid
954.0ms	4312×	body	80	valid
393.0ms	624×	body	320	valid
119.0ms	295×	body	160	valid