Details

sample23.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
4.0ms	96×	body	80	overflowed

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	5
1	7	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.5b	(/ (exp a) (+ (exp a) (exp b)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-def` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 52

Calls

2 calls:

4.0ms	(+ (exp a) (exp b))
9.0ms	(/ (exp a) (+ (exp a) (exp b)))

series54.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (exp a) (exp b))
36.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify96.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	171	405
1	513	376
2	1324	374
3	4489	373
4	5001	373

prune125.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (exp a) (exp b))
0.5b	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
1.0b	(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
4.7b	(- (* (exp b) (exp b)) (* (exp a) (exp b)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
55×	`times-frac`
41×	`add-sqr-sqrt`
36×	`associate-l`
35×	`distribute-lft-out`
34×	`add-cube-cbrt`
28×	`unpow-prod-down` `cube-prod`
13×	`add-cbrt-cube`
9×	`add-exp-log` `associate-/r*`
8×	`pow1`
7×	`sum-cubes`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `exp-prod` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `distribute-lft-in` `fma-neg` `diff-log` `prod-diff` `associate-*l/` `clear-num` `pow-prod-up` `flip--`

Counts

4 → 153

Calls

4 calls:

8.0ms	(* (exp a) (exp b))
32.0ms	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
163.0ms	(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
7.0ms	(- (* (exp b) (exp b)) (* (exp a) (exp b)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (exp a) (exp b))
58.0ms	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
140.0ms	(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
41.0ms	(- (* (exp b) (exp b)) (* (exp a) (exp b)))

simplify99.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	684	2183
1	3843	1943
2	5001	1937

prune462.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp b) 3)
0.5b	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
0.7b	(pow (exp (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))) (fma (exp b) (- (exp b) (exp a)) (pow (exp a) 2)))
4.3b	(- (exp b) (exp a))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
54×	`times-frac`
46×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
38×	`pow-pow`
36×	`exp-prod`
35×	`distribute-lft-out`
34×	`unpow-prod-down`
31×	`cube-prod`
9×	`prod-diff` `associate-/r*`
7×	`sum-cubes` `add-cbrt-cube`
6×	`pow1` `pow-unpow` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`fma-neg` `associate-/l*`
2×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+` `div-inv` `sqr-pow`
1×	`cbrt-undiv` `unpow-prod-up` `cube-mult` `sub-neg` `flip3--` `frac-2neg` `diff-log` `unpow3` `div-exp` `clear-num` `flip--` `fma-udef` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 164

Calls

4 calls:

2.0ms	(pow (exp b) 3)
31.0ms	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
82.0ms	(pow (exp (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))) (fma (exp b) (- (exp b) (exp a)) (pow (exp a) 2)))
6.0ms	(- (exp b) (exp a))

series292.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (exp b) 3)
61.0ms	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
183.0ms	(pow (exp (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))) (fma (exp b) (- (exp b) (exp a)) (pow (exp a) 2)))
24.0ms	(- (exp b) (exp a))

simplify98.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	531	1940
1	2874	1767
2	5001	1762

prune543.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (fma (exp 1/2) (- (* 1/4 a) (* 1/4 b)) (exp 1/2)))
0.1b	(fma (exp 1/2) (- (* 1/4 a) (* 1/4 b)) (exp 1/2))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-log-exp` `log-pow` `fma-udef`

Counts

2 → 24

Calls

2 calls:

1.0ms	(log (fma (exp 1/2) (- (* 1/4 a) (* 1/4 b)) (exp 1/2)))
0.0ms	(fma (exp 1/2) (- (* 1/4 a) (* 1/4 b)) (exp 1/2))

series198.0ms

Counts

2 → 6

Calls

2 calls:

127.0ms	(log (fma (exp 1/2) (- (* 1/4 a) (* 1/4 b)) (exp 1/2)))
71.0ms	(fma (exp 1/2) (- (* 1/4 a) (* 1/4 b)) (exp 1/2))

simplify41.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	138	294
1	351	239
2	1343	222
3	5001	216

prune71.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes97.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	7	5

end0.0ms

sample667.0ms

Algorithm

intervals

Results

325.0ms	8000×	body	80	valid
143.0ms	3438×	body	80	overflowed