Details

sample140.0ms

Algorithm

intervals

Results

26.0ms	44×	body	1280	valid
13.0ms	148×	body	80	valid
12.0ms	29×	body	640	valid
7.0ms	24×	body	320	valid
2.0ms	11×	body	160	valid

simplify64.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	39
3	31
2	24
1	15
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite64.0ms

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:

26.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(- 1 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))

series224.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
36.0ms	(- 1 (* (tan x) (tan x)))
42.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify3.0s

Counts

140 → 140

Iterations

Iter	Nodes
done	5126
3	3513
2	1102
1	401
0	157

prune619.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ 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))

rewrite107.0ms

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:

42.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(+ 1 (tan x))
27.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
30.0ms	(* (tan x) (tan x))

series292.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
25.0ms	(+ 1 (tan x))
66.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
57.0ms	(* (tan x) (tan x))

simplify2.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2348
1	716
0	233

prune662.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite414.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `pow1` `*-un-lft-identity`
14×	`add-cube-cbrt`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log` `add-log-exp`
6×	`fma-def` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`pow2` `frac-times` `+-commutative` `sum-log` `flip3-+` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

5.0ms	(+ 1 (tan x))
9.0ms	(+ 1 (tan x))
371.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))

series129.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ 1 (tan x))
18.0ms	(+ 1 (tan x))
49.0ms	(* (tan x) (tan x))
39.0ms	(* (tan x) (tan x))

simplify3.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
4	4789
3	1775
2	683
1	213
0	82

prune491.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- 1 (tan x)) (* (- 1 (tan x)) (tan x))) (+ 1 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (- 1 (tan x)) (tan x))
0.3b	(+ (- 1 (tan x)) (* (- 1 (tan x)) (tan x)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

109.0ms	(/ (+ (- 1 (tan x)) (* (- 1 (tan x)) (tan x))) (+ 1 (* (tan x) (tan x))))
14.0ms	(* (tan x) (tan x))
35.0ms	(* (- 1 (tan x)) (tan x))
57.0ms	(+ (- 1 (tan x)) (* (- 1 (tan x)) (tan x)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (+ (- 1 (tan x)) (* (- 1 (tan x)) (tan x))) (+ 1 (* (tan x) (tan x))))
67.0ms	(* (tan x) (tan x))
74.0ms	(* (- 1 (tan x)) (tan x))
44.0ms	(+ (- 1 (tan x)) (* (- 1 (tan x)) (tan x)))

simplify3.0s

Counts

160 → 160

Iterations

Iter	Nodes
done	5004
2	2841
1	681
0	252

prune793.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes264.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	11

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	1494×	body	1280	valid
792.0ms	1210×	body	640	valid
688.0ms	4324×	body	80	valid
322.0ms	626×	body	320	valid
96.0ms	346×	body	160	valid