Details

sample355.0ms

Algorithm

intervals

Results

43.0ms	55×	body	640	valid
40.0ms	42×	body	1280	valid
16.0ms	121×	body	80	valid
14.0ms	27×	body	320	valid
4.0ms	11×	body	160	valid

simplify185.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 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))

rewrite137.0ms

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:

12.0ms	(- 1.0 (* (tan x) (tan x)))
51.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))

series422.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- 1.0 (* (tan x) (tan x)))
191.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
74.0ms	(* (tan x) (tan x))
91.0ms	(* (tan x) (tan x))

simplify6.0s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
3	4550
2	1078
1	375
0	151

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 155

Calls

4 calls:

20.0ms	(+ (sqrt 1.0) (tan x))
100.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
125.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
33.0ms	(* (tan x) (tan x))

series739.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (sqrt 1.0) (tan x))
407.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
212.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
69.0ms	(* (tan x) (tan x))

simplify4.6s

Counts

167 → 167

Iterations

Iter	Nodes
done	5001
2	2752
1	833
0	268

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
0.2b	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
42×	`add-cube-cbrt`
37×	`times-frac`
23×	`sqrt-prod`
22×	`associate-r`
18×	`prod-diff`
16×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `add-log-exp`
6×	`pow1` `fma-def` `fma-neg` `associate-/l*`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 153

Calls

4 calls:

25.0ms	(- (sqrt 1.0) (tan x))
23.0ms	(+ (sqrt 1.0) (tan x))
124.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
57.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

series819.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt 1.0) (tan x))
70.0ms	(+ (sqrt 1.0) (tan x))
403.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
273.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

simplify3.2s

Counts

165 → 165

Iterations

Iter	Nodes
done	5000
2	1795
1	570
0	220

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

240×	`pow1`
74×	`pow-prod-up`
72×	`tan-quot`
48×	`pow-prod-down`
46×	`pow-sqr`
38×	`pow-plus`
36×	`frac-times`
32×	`add-exp-log` `add-cbrt-cube`
28×	`pow2`
24×	`associate-r/` `associate-l/`
18×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 220

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
136.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
148.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (tan x) (tan x))
69.0ms	(* (tan x) (tan x))
92.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
101.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify3.8s

Counts

232 → 232

Iterations

Iter	Nodes
done	5002
3	2318
2	921
1	323
0	110

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes514.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	18
1	18
0	14

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.8s	1508×	body	1280	valid
1.7s	1255×	body	640	valid
916.0ms	4280×	body	80	valid
465.0ms	643×	body	320	valid
188.0ms	314×	body	160	valid