Details

sample150.0ms

Algorithm

intervals

Results

43.0ms	54×	body	1280	valid
19.0ms	39×	body	640	valid
15.0ms	135×	body	80	valid
7.0ms	20×	body	320	valid
2.0ms	8×	body	160	valid

simplify310.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

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))

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`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×	`associate-/l*`
3×	`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 → 105

Calls

4 calls:

18.0ms	(- 1.0 (* (tan x) (tan x)))
191.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
81.0ms	(* (tan x) (tan x))
86.0ms	(* (tan x) (tan x))

series486.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- 1.0 (* (tan x) (tan x)))
211.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
97.0ms	(* (tan x) (tan x))
129.0ms	(* (tan x) (tan x))

simplify634.0ms

Counts: 117 → 117

prune343.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
0.3b	(* (tan x) (tan x))
0.6b	(pow (tan x) 6)
12.2b	(cbrt (pow (tan x) 6))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
16×	`times-frac`
12×	`pow1`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`cbrt-prod`
6×	`unpow-prod-down`
5×	`distribute-lft-out` `difference-of-squares`
4×	`tan-quot` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `pow-plus` `pow1/3` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

65.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
31.0ms	(* (tan x) (tan x))
7.0ms	(pow (tan x) 6)
3.0ms	(cbrt (pow (tan x) 6))

series316.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
54.0ms	(* (tan x) (tan x))
92.0ms	(pow (tan x) 6)
39.0ms	(cbrt (pow (tan x) 6))

simplify798.0ms

Counts: 113 → 113

prune467.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

7.0ms	(pow (cos x) 2)
7.0ms	(pow (cos x) 2)
8.0ms	(pow (sin x) 2)
8.0ms	(pow (sin x) 2)

series117.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
35.0ms	(pow (sin x) 2)
35.0ms	(pow (sin x) 2)

simplify927.0ms

Counts: 84 → 84

prune400.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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))
0.3b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
19×	`pow1` `log-pow`
18×	`exp-prod`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
7×	`difference-of-squares`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`associate-/r/` `associate-/l*` `add-log-exp`
3×	`log-prod` `associate-/r*`
2×	`pow2` `frac-times` `flip3-+` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 123

Calls

4 calls:

39.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
53.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
66.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))
130.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify3.0s

Counts: 135 → 135

prune415.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes388.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify480.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.4s	1567×	body	1280	valid
802.0ms	1238×	body	640	valid
630.0ms	4303×	body	80	valid
211.0ms	589×	body	320	valid
86.0ms	303×	body	160	valid