Details

sample158.0ms

Algorithm

intervals

Results

101.0ms	113×	body	1280	valid
34.0ms	89×	body	640	valid
7.0ms	33×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	15×	body	160	valid
0.0ms	6×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 62.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.1b	(log (+ 1.0 x))
5.1b	(log (- 1.0 x))

rewrite28.0ms

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:

16.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.0ms	(log (+ 1.0 x))
6.0ms	(log (- 1.0 x))

series216.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (+ 1.0 x))
48.0ms	(log (- 1.0 x))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

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

prune205.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 60.0b

localize13.0ms

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))))))
5.1b	(log (- 1.0 x))

rewrite66.0ms

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:

37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
15.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.0ms	(log (- 1.0 x))

series241.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
136.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
48.0ms	(log (- 1.0 x))

simplify92.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (20.0ms)

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

prune695.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

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))))))

rewrite144.0ms

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:

35.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
55.0ms	(/ (- (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))))))

series236.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
57.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
127.0ms	(/ (- (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))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	753	2567
1	3636	2134
2	5002	2133

prune761.0ms

Pruning

4 alts after pruning (2 fresh and 2 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))))))

rewrite101.0ms

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:

36.0ms	(* 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))))))))
56.0ms	(/ (- (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))))))

series613.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
180.0ms	(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)))))))
252.0ms	(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))))))))
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

190 → 190

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	829	2287
1	3415	2038
2	5001	2035

prune585.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

0% (0.4b 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	18	16
1	18	16

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.8s	3346×	body	1280	valid
997.0ms	2520×	body	640	valid
250.0ms	1304×	body	320	valid
91.0ms	8000×	pre	80	true
67.0ms	626×	body	160	valid
9.0ms	204×	body	80	valid