Details

sample299.0ms

Algorithm

intervals

Results

11.0ms	47×	body	1280	valid
8.0ms	46×	body	640	valid
5.0ms	141×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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:

0.2b	(- 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))

rewrite26.0ms

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))
8.0ms	(* (tan x) (tan x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

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

prune282.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 0.0b

Counts

132 → 11

localize9.0ms

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

rewrite139.0ms

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))
50.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))
7.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
82.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
175.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))
114.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))

simplify322.0ms

Algorithm

egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2457	44315
1	5001	35123

prune1.9s

Filtered

795 candidates to 508 candidates (63.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	791	4	795
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	795	11	806

Merged error: 0.0b

Counts

806 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

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))
0.3b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

10.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
8.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
95.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	373	1261
1	1240	1156
2	5001	1132

prune307.0ms

Filtered

143 candidates to 103 candidates (72.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	144	10	154

Merged error: 0.0b

Counts

154 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
0.3b	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
0.4b	(pow (/ 1.0 (fma (tan x) (tan x) 1.0)) 3)
0.4b	(pow (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))) 3)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

312×	`times-frac`
178×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
60×	`unpow-prod-down` `cube-prod`
28×	`associate-/r*`
23×	`add-exp-log` `add-cbrt-cube`
20×	`div-inv`
18×	`associate-/r/`
16×	`tan-quot`
10×	`cbrt-undiv` `div-exp`
6×	`pow1` `pow-unpow` `associate-/l*`
5×	`pow-exp` `rem-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `clear-num` `associate-/l/` `sqr-pow`

Counts

4 → 320

Calls

4 calls:

7.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
7.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
5.0ms	(pow (/ 1.0 (fma (tan x) (tan x) 1.0)) 3)
12.0ms	(pow (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))) 3)

series486.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
105.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
117.0ms	(pow (/ 1.0 (fma (tan x) (tan x) 1.0)) 3)
158.0ms	(pow (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))) 3)

simplify72.0ms

Algorithm

egg-herbie

Counts

332 → 332

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1305	4643
1	5001	4181

prune833.0ms

Filtered

332 candidates to 198 candidates (59.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	332	10	342

Merged error: 0.0b

Counts

342 → 10

regimes218.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	11
1	14	11

end0.0ms

sample909.0ms

Algorithm

intervals

Results

356.0ms	1465×	body	1280	valid
201.0ms	1264×	body	640	valid
148.0ms	4355×	body	80	valid
66.0ms	600×	body	320	valid
24.0ms	316×	body	160	valid