Details

sample505.0ms

Algorithm

intervals

Results

88.0ms	45×	body	1280	valid
48.0ms	26×	body	320	valid
30.0ms	42×	body	640	valid
27.0ms	133×	body	80	valid
4.0ms	10×	body	160	valid

simplify56.0ms

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: 0.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 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))

rewrite63.0ms

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:

18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
13.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))

series495.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
157.0ms	(- 1.0 (* (tan x) (tan x)))
84.0ms	(* (tan x) (tan x))
50.0ms	(* (tan x) (tan x))

simplify2.8s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
3	4089
2	1071
1	374
0	151

prune626.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (exp (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(exp (- 1.0 (* (tan x) (tan x))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`pow1`
17×	`*-un-lft-identity` `add-cube-cbrt`
10×	`exp-sum`
8×	`log-prod` `exp-prod` `add-cbrt-cube` `tan-quot` `add-exp-log`
7×	`add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l` `prod-diff`
5×	`log-pow`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow2` `frac-times` `sub-neg` `pow-plus` `exp-diff` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `difference-of-squares` `unswap-sqr` `rem-exp-log`
1×	`log-div` `diff-log` `rem-log-exp`

Counts

4 → 105

Calls

4 calls:

10.0ms	(log (exp (- 1.0 (* (tan x) (tan x)))))
24.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))
19.0ms	(exp (- 1.0 (* (tan x) (tan x))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(log (exp (- 1.0 (* (tan x) (tan x)))))
41.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))
104.0ms	(exp (- 1.0 (* (tan x) (tan x))))

simplify2.8s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
4	4504
3	1261
2	545
1	245
0	120

prune741.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(+ (sqrt 1.0) (tan x))
0.3b	(* (tan x) (tan x))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

10.0ms	(- (sqrt 1.0) (tan x))
88.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
20.0ms	(+ (sqrt 1.0) (tan x))
17.0ms	(* (tan x) (tan x))

series274.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (sqrt 1.0) (tan x))
132.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
59.0ms	(+ (sqrt 1.0) (tan x))
35.0ms	(* (tan x) (tan x))

simplify1.8s

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
2	1754
1	625
0	208

prune770.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`pow1`
16×	`add-cube-cbrt`
12×	`fma-def`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
4×	`expm1-log1p-u` `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 → 100

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
14.0ms	(+ (sqrt 1.0) (tan x))
13.0ms	(* (tan x) (tan x))
22.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (sqrt 1.0) (tan x))
61.0ms	(+ (sqrt 1.0) (tan x))
49.0ms	(* (tan x) (tan x))
38.0ms	(* (tan x) (tan x))

simplify3.4s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
4	4934
3	1486
2	577
1	211
0	83

prune618.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes486.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.2s	1467×	body	1280	valid
849.0ms	1249×	body	640	valid
678.0ms	4349×	body	80	valid
342.0ms	626×	body	320	valid
83.0ms	309×	body	160	valid