Details

sample332.0ms

Algorithm

intervals

Results

85.0ms	147×	body	80	valid
72.0ms	47×	body	1280	valid
39.0ms	36×	body	640	valid
11.0ms	13×	body	320	valid
7.0ms	13×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	39
3	31
2	24
1	15
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 128

Calls

4 calls:

26.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms	(- 1 (* (tan x) (tan x)))
27.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

series533.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
61.0ms	(- 1 (* (tan x) (tan x)))
97.0ms	(* (tan x) (tan x))
170.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

140 → 140

Iterations

Iter	Nodes
done	2016
3	2016
2	1102
1	401
0	157

prune592.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
89×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
72×	`add-cube-cbrt`
26×	`difference-of-squares`
21×	`associate-/r*`
19×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `prod-diff` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 196

Calls

4 calls:

21.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
5.0ms	(- 1 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))

series251.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
47.0ms	(- 1 (* (tan x) (tan x)))
40.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

208 → 208

Iterations

Iter	Nodes
done	2006
3	2006
2	1729
1	735
0	283

prune941.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1)
0.1b	(/ (* 1 (- 1 (* (tan x) (tan x)))) (fma (tan x) (tan x) 1))
0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-exp-log`
12×	`add-cube-cbrt`
11×	`pow1` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `tan-quot` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `times-frac` `fma-neg` `swap-sqr` `div-exp` `associate-r` `associate-l` `prod-diff` `prod-exp` `associate-r/`
2×	`cbrt-undiv` `flip3--` `cbrt-unprod` `flip--` `difference-of-squares` `associate-/l/`
1×	`pow2` `frac-times` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `pow-sqr` `-commutative` `pow-prod-up` `fma-udef` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1)
21.0ms	(/ (* 1 (- 1 (* (tan x) (tan x)))) (fma (tan x) (tan x) 1))
15.0ms	(- 1 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma (tan x) (tan x) 1)
91.0ms	(/ (* 1 (- 1 (* (tan x) (tan x)))) (fma (tan x) (tan x) 1))
52.0ms	(- 1 (* (tan x) (tan x)))
37.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

104 → 104

Iterations

Iter	Nodes
done	2003
3	2003
2	1037
1	384
0	149

prune516.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (fma (tan x) (tan x) 1))
0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.4b	(log1p (/ (- 1 (* (tan x) (tan x))) (fma (tan x) (tan x) 1)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
20×	`add-cube-cbrt`
15×	`times-frac`
11×	`pow1`
10×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`expm1-log1p-u` `associate-/l*`
4×	`tan-quot` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-neg` `swap-sqr` `associate-r` `associate-l*` `prod-diff`
2×	`flip3--` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `cbrt-undiv` `log1p-udef` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `log1p-expm1` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

18.0ms	(/ (- 1 (* (tan x) (tan x))) (fma (tan x) (tan x) 1))
10.0ms	(- 1 (* (tan x) (tan x)))
29.0ms	(* (tan x) (tan x))
1.0ms	(log1p (/ (- 1 (* (tan x) (tan x))) (fma (tan x) (tan x) 1)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- 1 (* (tan x) (tan x))) (fma (tan x) (tan x) 1))
34.0ms	(- 1 (* (tan x) (tan x)))
40.0ms	(* (tan x) (tan x))
252.0ms	(log1p (/ (- 1 (* (tan x) (tan x))) (fma (tan x) (tan x) 1)))

simplify1.2s

Counts

119 → 119

Iterations

Iter	Nodes
done	2018
3	2018
2	1221
1	428
0	178

prune655.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes224.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.8s	1492×	body	1280	valid
1.5s	1274×	body	640	valid
1.1s	4311×	body	80	valid
487.0ms	595×	body	320	valid
176.0ms	328×	body	160	valid