Details

sample344.0ms

Algorithm

intervals

Results

48.0ms	46×	body	1280	valid
24.0ms	141×	body	80	valid
20.0ms	28×	body	640	valid
13.0ms	26×	body	320	valid
5.0ms	15×	body	160	valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	14

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(* (tan x) (tan x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

16.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
10.0ms	(- 1.0 (* (tan x) (tan x)))
1.0ms	(fma (tan x) (tan x) 1.0)
42.0ms	(* (tan x) (tan x))

series404.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
64.0ms	(- 1.0 (* (tan x) (tan x)))
71.0ms	(fma (tan x) (tan x) 1.0)
60.0ms	(* (tan x) (tan x))

simplify2.6s

Counts

109 → 109

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	155	1557
1	330	1462
2	893	1345
3	2805	1320
done	5000	1314

prune458.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(* (tan x) (tan x))
0.3b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`tan-quot` `log1p-expm1-u`
3×	`fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff`
1×	`pow2` `frac-times` `sub-neg` `log1p-udef` `flip3--` `pow-plus` `diff-log` `log1p-expm1` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `fma-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

6.0ms	(- 1.0 (* (tan x) (tan x)))
0.0ms	(fma (tan x) (tan x) 1.0)
17.0ms	(* (tan x) (tan x))
1.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- 1.0 (* (tan x) (tan x)))
65.0ms	(fma (tan x) (tan x) 1.0)
44.0ms	(* (tan x) (tan x))
314.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

simplify2.0s

Counts

84 → 84

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	131	993
1	263	914
2	663	820
3	2019	793
done	5000	767

prune316.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
0.1b	(* (sin x) (tan x))
0.1b	(/ (* (sin x) (tan x)) (cos x))
0.1b	(fma (tan x) (tan x) 1.0)

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`prod-diff`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-r` `associate-l` `associate-/r*`
2×	`tan-quot` `cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip--` `fma-udef` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

25.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
38.0ms	(* (sin x) (tan x))
31.0ms	(/ (* (sin x) (tan x)) (cos x))
1.0ms	(fma (tan x) (tan x) 1.0)

series354.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
83.0ms	(* (sin x) (tan x))
93.0ms	(/ (* (sin x) (tan x)) (cos x))
85.0ms	(fma (tan x) (tan x) 1.0)

simplify1.6s

Counts

107 → 107

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	183	2078
1	407	1730
2	1286	1407
done	5001	1165

prune421.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (fma (tan x) (tan x) 1.0))
0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
0.2b	(* (tan x) (tan x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
16×	`associate-r`
14×	`pow1`
13×	`add-cbrt-cube`
7×	`associate-l`
5×	`prod-exp`
4×	`tan-quot` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`frac-times` `swap-sqr` `associate-l/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`pow2` `pow-flip` `frac-2neg` `pow-plus` `clear-num` `pow-sqr` `un-div-inv` `pow-prod-up` `fma-udef` `inv-pow` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

5.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
0.0ms	(fma (tan x) (tan x) 1.0)
40.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
16.0ms	(* (tan x) (tan x))

series413.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
63.0ms	(fma (tan x) (tan x) 1.0)
180.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
61.0ms	(* (tan x) (tan x))

simplify3.1s

Counts

128 → 128

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	177	1836
1	379	1612
2	1049	1438
3	3476	1416
done	5002	1413

prune343.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes131.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	12	16
done	12	16

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.9s	1258×	body	640	valid
1.6s	1546×	body	1280	valid
624.0ms	4253×	body	80	valid
293.0ms	634×	body	320	valid
84.0ms	309×	body	160	valid