Details

sample440.0ms

Algorithm

intervals

Results

117.0ms	50×	body	1280	valid
89.0ms	40×	body	640	valid
55.0ms	135×	body	80	valid
11.0ms	21×	body	320	valid
3.0ms	10×	body	160	valid

simplify165.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	43	14
6	45	14
done	45	14

prune58.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite112.0ms

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:

28.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
10.0ms	(- 1.0 (* (tan x) (tan x)))
27.0ms	(* (tan x) (tan x))
41.0ms	(* (tan x) (tan x))

series353.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
38.0ms	(- 1.0 (* (tan x) (tan x)))
44.0ms	(* (tan x) (tan x))
57.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

131 → 131

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	151	1789
1	376	1658
2	1700	1455
done	5001	1439

prune565.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* (tan x) (tan x)))
0.2b	(/ (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x)))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))
0.3b	(* (tan x) (tan x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `tan-quot` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

6.0ms	(+ 1.0 (* (tan x) (tan x)))
53.0ms	(/ (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x)))) (+ 1.0 (* (tan x) (tan x))))
0.0ms	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))
13.0ms	(* (tan x) (tan x))

series356.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ 1.0 (* (tan x) (tan x)))
164.0ms	(/ (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x)))) (+ 1.0 (* (tan x) (tan x))))
106.0ms	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))
41.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

101 → 101

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	155	2099
1	398	1837
2	1854	1532
done	5001	1349

prune670.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (- (tan x)) (tan x) 1.0)
0.3b	(fma (- (tan x)) (tan x) 1.0)
0.3b	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))
0.3b	(pow (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) 3)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow-prod-down` `cube-prod` `fma-udef`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

1.0ms	(fma (- (tan x)) (tan x) 1.0)
0.0ms	(fma (- (tan x)) (tan x) 1.0)
0.0ms	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))
4.0ms	(pow (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) 3)

series392.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(fma (- (tan x)) (tan x) 1.0)
92.0ms	(fma (- (tan x)) (tan x) 1.0)
60.0ms	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))
140.0ms	(pow (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) 3)

simplify737.0ms

Counts

67 → 67

Iterations

Useful iterations: 2 (146.0ms)

Iter	Nodes	Cost
0	74	934
1	194	705
2	742	664
done	5000	664

prune645.0ms

Pruning

11 alts after pruning (10 fresh and 1 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)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `pow-unpow` `unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `add-cbrt-cube` `pow-exp` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series119.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (cos x) 2)
36.0ms	(pow (cos x) 2)
33.0ms	(pow (sin x) 2)
27.0ms	(pow (sin x) 2)

simplify1.0s

Counts

92 → 92

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	68	616
1	194	530
2	673	466
3	2387	466
done	5002	466

prune324.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes227.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	60
1	28	60
done	28	60

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.7s	1466×	body	1280	valid
1.6s	4372×	body	80	valid
822.0ms	1241×	body	640	valid
243.0ms	592×	body	320	valid
90.0ms	329×	body	160	valid