Details

sample276.0ms

Algorithm

intervals

Results

12.0ms	50×	body	1280	valid
7.0ms	44×	body	640	valid
6.0ms	139×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series219.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	918
2	5001	882

prune312.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(* (tan x) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
54×	`prod-diff`
50×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow1`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`fma-def` `fma-neg`
5×	`frac-times`
4×	`tan-quot` `expm1-log1p-u` `flip3--` `flip3-+` `flip--` `flip-+` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 163

Calls

4 calls:

6.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(+ (sqrt 1.0) (tan x))
13.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (sqrt 1.0) (tan x))
34.0ms	(+ (sqrt 1.0) (tan x))
105.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
38.0ms	(* (tan x) (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	550	2052
1	2400	1381
2	5001	1360

prune352.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 184

Calls

4 calls:

5.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
8.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(* (tan x) (tan x))

series287.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
106.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))

simplify80.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	593	2482
1	2691	2268
2	5001	2158

prune420.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (fma (tan x) (tan x) 1.0))
0.2b	(/ (fma (tan x) (tan x) 1.0) (tan x))
0.3b	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
0.4b	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

1436×	`times-frac`
888×	`add-sqr-sqrt`
873×	`*-un-lft-identity`
867×	`add-cube-cbrt`
611×	`prod-diff`
107×	`div-inv`
58×	`associate-/r/`
45×	`tan-quot`
20×	`associate-/r*`
13×	`add-exp-log` `fma-neg` `add-cbrt-cube`
9×	`associate-/l*`
6×	`add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 783

Calls

4 calls:

3.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
4.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
7.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
51.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
83.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
106.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
186.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

simplify304.0ms

Algorithm

egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2457	44315
1	5001	35123

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	14
1	15	14

end0.0ms

sample923.0ms

Algorithm

intervals

Results

371.0ms	1528×	body	1280	valid
189.0ms	1219×	body	640	valid
153.0ms	4360×	body	80	valid
67.0ms	558×	body	320	valid
26.0ms	335×	body	160	valid