Details

sample53.0ms

Algorithm

intervals

Results

36.0ms	107×	body	10240	exit
6.0ms	256×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	5
1	7	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.8b	(/ (exp a) (+ (exp a) (exp b)))

rewrite19.0ms

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:

5.0ms	(+ (exp a) (exp b))
9.0ms	(/ (exp a) (+ (exp a) (exp b)))

series52.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (exp a) (exp b))
33.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify95.0ms

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

prune127.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (exp a) (+ (exp a) (exp b))))
0.0b	(log (exp (/ (exp a) (+ (exp a) (exp b)))))
0.0b	(+ (exp a) (exp b))
0.8b	(/ (exp a) (+ (exp a) (exp b)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
36×	`exp-prod` `times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`log-pow`
11×	`distribute-lft-out`
7×	`add-log-exp`
6×	`associate-/r/` `add-cbrt-cube`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `flip3-+` `associate-/r*` `flip-+` `log1p-expm1-u`
3×	`log-prod` `fma-def` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `sum-log` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

20.0ms	(exp (/ (exp a) (+ (exp a) (exp b))))
18.0ms	(log (exp (/ (exp a) (+ (exp a) (exp b)))))
5.0ms	(+ (exp a) (exp b))
9.0ms	(/ (exp a) (+ (exp a) (exp b)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(exp (/ (exp a) (+ (exp a) (exp b))))
36.0ms	(log (exp (/ (exp a) (+ (exp a) (exp b)))))
17.0ms	(+ (exp a) (exp b))
31.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify47.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	249	881
1	649	815
2	1531	808
3	5001	805

prune301.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.0b	(exp (exp a))
0.0b	(/ 1 (+ (exp a) (exp b)))
0.5b	(pow (exp (exp a)) (/ 1 (+ (exp a) (exp b))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`times-frac`
18×	`pow-unpow`
8×	`add-exp-log` `distribute-lft-out`
7×	`add-log-exp`
6×	`pow1` `exp-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-pow` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`unpow-prod-down` `fma-def` `flip3-+` `flip-+` `associate-/l*`
2×	`div-exp` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `pow-exp` `clear-num` `sum-log` `rem-exp-log` `inv-pow` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

4.0ms	(+ (exp a) (exp b))
1.0ms	(exp (exp a))
8.0ms	(/ 1 (+ (exp a) (exp b)))
7.0ms	(pow (exp (exp a)) (/ 1 (+ (exp a) (exp b))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (exp a) (exp b))
23.0ms	(exp (exp a))
23.0ms	(/ 1 (+ (exp a) (exp b)))
73.0ms	(pow (exp (exp a)) (/ 1 (+ (exp a) (exp b))))

simplify125.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	339	761
1	1244	697
2	4913	657
3	5001	657

prune290.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`pow1`
6×	`distribute-rgt-in` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in` `prod-diff`
5×	`add-exp-log`
4×	`associate-*r/` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `sub-neg` `log-div` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `associate--l+` `log-pow` `flip--` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`log-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 50

Calls

2 calls:

7.0ms	(log (* (exp 1/2) (- (fma a 1/4 1) (* 1/4 b))))
15.0ms	(* (exp 1/2) (- (fma a 1/4 1) (* 1/4 b)))

series158.0ms

Counts

2 → 6

Calls

2 calls:

102.0ms	(log (* (exp 1/2) (- (fma a 1/4 1) (* 1/4 b))))
56.0ms	(* (exp 1/2) (- (fma a 1/4 1) (* 1/4 b)))

simplify43.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	280	471
1	1106	408
2	5001	399

prune115.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes75.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.7b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	8
1	13	8

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s	3486×	body	10240	exit
179.0ms	8000×	body	80	valid