Details

sample270.0ms

Algorithm

intervals

Results

9.0ms	35×	body	1280	valid
7.0ms	41×	body	640	valid
6.0ms	145×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	17×	body	160	valid

simplify17.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 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))

rewrite25.0ms

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:

3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882

prune253.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Merged error: 0.0b

Counts

132 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 173

Calls

4 calls:

4.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
1.0ms	(fma (tan x) (tan x) 1.0)
7.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series281.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
40.0ms	(fma (tan x) (tan x) 1.0)
105.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))

simplify80.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	576	2372
1	2645	2169
2	5001	2069

prune271.0ms

Filtered

185 candidates to 110 candidates (59.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	187	8	195

Merged error: 0.0b

Counts

195 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
92×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
66×	`add-cube-cbrt`
24×	`associate-/r*`
22×	`add-exp-log`
16×	`add-cbrt-cube`
12×	`distribute-lft-out--` `difference-of-squares`
9×	`div-exp` `associate-/r/`
7×	`pow1`
6×	`div-inv`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`tan-quot` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `associate-/l/` `inv-pow` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
6.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
11.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (/ (* (tan x) (sin x)) (cos x)))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma (tan x) (tan x) 1.0)
60.0ms	(/ (* (tan x) (sin x)) (cos x))
41.0ms	(* (tan x) (sin x))
124.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (/ (* (tan x) (sin x)) (cos x)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	643	2615
1	3075	2409
2	5002	2297

prune312.0ms

Filtered

177 candidates to 99 candidates (55.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	176	9	185

Merged error: 0.0b

Counts

185 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.3b	(* (tan x) (tan x))
0.3b	(cbrt (/ 1 (pow (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))) 3)))
0.4b	(pow (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))) 3)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
145×	`add-sqr-sqrt`
131×	`cbrt-prod`
119×	`add-cube-cbrt` `*-un-lft-identity`
72×	`unpow-prod-down` `cube-prod`
24×	`difference-of-squares`
17×	`associate-/r/`
12×	`pow1`
9×	`add-exp-log` `add-cbrt-cube` `div-inv`
8×	`flip3--` `flip--`
4×	`tan-quot` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`cube-div` `pow-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-to-exp` `cbrt-div` `pow-pow` `pow-plus` `pow1/3` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 240

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
5.0ms	(* (tan x) (tan x))
18.0ms	(cbrt (/ 1 (pow (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))) 3)))
7.0ms	(pow (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))) 3)

series338.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (tan x) (tan x) 1.0)
31.0ms	(* (tan x) (tan x))
103.0ms	(cbrt (/ 1 (pow (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))) 3)))
161.0ms	(pow (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))) 3)

simplify116.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	874	4701
1	4401	4193
2	5001	4186

prune278.0ms

Filtered

252 candidates to 93 candidates (36.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	251	10	261

Merged error: 0.0b

Counts

261 → 10

regimes160.0ms

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	11
1	15	11

end0.0ms

sample938.0ms

Algorithm

intervals

Results

374.0ms	1518×	body	1280	valid
198.0ms	1239×	body	640	valid
151.0ms	4305×	body	80	valid
77.0ms	633×	body	320	valid
24.0ms	305×	body	160	valid