Details

sample194.0ms

Algorithm

intervals

Results

71.0ms	40×	body	640	valid
26.0ms	41×	body	1280	valid
16.0ms	145×	body	80	valid
6.0ms	22×	body	320	valid
2.0ms	8×	body	160	valid

simplify79.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

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))

rewrite141.0ms

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)))
40.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
51.0ms	(* (tan x) (tan x))

series328.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- 1.0 (* (tan x) (tan x)))
147.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
63.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

131 → 131

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	151	1789
1	377	1658
2	1702	1455
done	5001	1439

prune365.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

6.0ms	(pow (sin x) 2)
8.0ms	(pow (sin x) 2)
7.0ms	(pow (cos x) 2)
7.0ms	(pow (cos x) 2)

series124.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (sin x) 2)
43.0ms	(pow (sin x) 2)
27.0ms	(pow (cos x) 2)
18.0ms	(pow (cos x) 2)

simplify1.5s

Counts

92 → 92

Iterations

Useful iterations: 2 (176.0ms)

Iter	Nodes	Cost
0	68	616
1	194	530
2	664	466
3	2409	466
done	5001	466

prune326.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

14.0ms	(pow (sin x) 2)
7.0ms	(pow (sin x) 2)
7.0ms	(pow (cos x) 2)
7.0ms	(pow (cos x) 2)

series83.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin x) 2)
22.0ms	(pow (sin x) 2)
22.0ms	(pow (cos x) 2)
19.0ms	(pow (cos x) 2)

simplify1.3s

Counts

92 → 92

Iterations

Useful iterations: 2 (150.0ms)

Iter	Nodes	Cost
0	68	616
1	194	530
2	664	466
3	2409	466
done	5001	466

prune502.0ms

Pruning

10 alts after pruning (9 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)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.3b	(* (tan x) (tan x))
0.3b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
17×	`log-pow`
16×	`exp-prod`
12×	`pow1`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`log-prod` `fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `associate-/r*`
2×	`flip3--` `div-sub` `flip--` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sub-neg` `log-div` `frac-2neg` `pow-plus` `exp-diff` `diff-log` `associate-r/` `div-exp` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

6.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
23.0ms	(* (tan x) (tan x))
23.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- 1.0 (* (tan x) (tan x)))
201.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
51.0ms	(* (tan x) (tan x))
175.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))

simplify1.9s

Counts

130 → 130

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	202	2124
1	426	1966
2	1792	1811
done	5000	1799

prune527.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes244.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	15	25
done	15	25

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.8s	1540×	body	1280	valid
902.0ms	1265×	body	640	valid
722.0ms	610×	body	320	valid
709.0ms	4278×	body	80	valid
77.0ms	307×	body	160	valid