Details

sample144.0ms

Algorithm

intervals

Results

86.0ms	99×	body	1280	valid
32.0ms	77×	body	640	valid
10.0ms	49×	body	320	valid
4.0ms	256×	pre	80	true
3.0ms	24×	body	160	valid
0.0ms	7×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.4b	(log (+ 1.0 x))
6.5b	(log (- 1.0 x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 75

Calls

3 calls:

8.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
2.0ms	(log (+ 1.0 x))
4.0ms	(log (- 1.0 x))

series223.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
40.0ms	(log (+ 1.0 x))
48.0ms	(log (- 1.0 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	452	686
1	1669	638
2	5001	623

prune234.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 57.9b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.5b	(log (- 1.0 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
83×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`pow1` `div-exp` `prod-exp` `add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
5×	`log-prod` `log-pow`
4×	`log-div` `associate-/l*`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `div-sub` `flip--` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 165

Calls

3 calls:

30.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
8.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
3.0ms	(log (- 1.0 x))

series241.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
145.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
42.0ms	(log (- 1.0 x))

simplify95.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	928	1453
1	3837	1286
2	5001	1286

prune519.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
158×	`add-sqr-sqrt`
136×	`associate-r`
112×	`unpow-prod-down`
94×	`*-un-lft-identity`
82×	`add-cube-cbrt`
51×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*`
4×	`log-pow` `cbrt-unprod` `difference-of-squares`
3×	`cbrt-undiv` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `clear-num` `flip--`

Counts

3 → 268

Calls

3 calls:

29.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
29.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series232.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
125.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	753	2429
1	3174	2138
2	5001	2135

prune813.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(expm1 (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0b	(log1p (expm1 (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
91×	`add-sqr-sqrt`
68×	`associate-r`
61×	`*-un-lft-identity`
56×	`unpow-prod-down`
49×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
11×	`add-cbrt-cube`
10×	`pow1` `div-exp` `prod-exp`
8×	`distribute-lft-out--`
6×	`pow-to-exp` `pow-exp` `associate-/l*`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `log-pow` `add-log-exp` `difference-of-squares`
3×	`associate-l` `associate-/r*`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `div-sub` `log1p-expm1` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--` `expm1-udef`

Counts

4 → 178

Calls

4 calls:

30.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0ms	(expm1 (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0ms	(log1p (expm1 (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))))
25.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
183.0ms	(expm1 (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
257.0ms	(log1p (expm1 (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))))
121.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify93.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	830	2356
1	3879	2036
2	5001	2033

prune634.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	16
1	18	16

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.9s	3378×	body	1280	valid
1.0s	2570×	body	640	valid
248.0ms	1242×	body	320	valid
105.0ms	8000×	pre	80	true
73.0ms	618×	body	160	valid
9.0ms	192×	body	80	valid