Details

sample245.0ms

Algorithm

intervals

Results

112.0ms	89×	body	2560	valid
75.0ms	103×	body	1280	valid
18.0ms	31×	body	640	valid
9.0ms	83×	body	80	overflowed
7.0ms	340×	pre	80	true
4.0ms	13×	body	320	valid
2.0ms	19×	body	80	valid
0.0ms	2×	body	160	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	13
5	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
1.4b	(- (exp (* b eps)) 1.0)
2.9b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `flip--` `add-log-exp`
9×	`fma-neg`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 117

Calls

4 calls:

22.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
7.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
6.0ms	(- (exp (* (+ a b) eps)) 1.0)

series308.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
31.0ms	(- (exp (* b eps)) 1.0)
37.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	608	1462
1	2778	1079
2	5002	1072

prune430.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

20.0ms

(+ (/ 1 b) (/ 1 a))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(+ (/ 1 b) (/ 1 a))

simplify69.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	107	112
1	368	101
2	1274	98
3	3144	98
4	5001	98

prune92.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 167

Calls

4 calls:

117.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
14.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
82.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
82.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
77.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify67.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	402	1859
1	1619	1609
2	5002	1449

prune358.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 b) b)
0.1b	(/ (- (/ 1 a)) a)
4.7b	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
31.3b	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

rewrite817.0ms

Algorithm

rewrite-expression-head

Rules

1384×	`times-frac`
1234×	`*-un-lft-identity`
653×	`add-sqr-sqrt`
317×	`add-cube-cbrt`
238×	`distribute-rgt-neg-in`
210×	`distribute-lft-out`
183×	`div-inv`
126×	`difference-of-squares`
98×	`distribute-lft-out--`
94×	`fma-def`
91×	`distribute-lft-neg-in`
56×	`associate-/l*`
25×	`associate-/r*`
17×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1` `neg-mul-1`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/l/`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u`
3×	`neg-sub0` `frac-2neg` `clear-num` `associate-/r/`
2×	`associate-+l-` `flip3-+` `frac-add` `flip-+` `pow-div`
1×	`+-commutative` `rec-exp` `flip3--` `pow-flip` `1-exp` `distribute-frac-neg` `sum-log` `frac-sub` `flip--` `distribute-neg-frac` `inv-pow`

Counts

4 → 635

Calls

4 calls:

6.0ms	(/ (/ 1 b) b)
12.0ms	(/ (- (/ 1 a)) a)
189.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
544.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (/ 1 b) b)
28.0ms	(/ (- (/ 1 a)) a)
23.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
36.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

simplify93.0ms

Algorithm

egg-herbie

Counts

647 → 647

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1357	6869
1	5001	5916

prune874.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes109.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.4s	2624×	body	2560	valid
2.5s	3392×	body	1280	valid
531.0ms	1088×	body	640	valid
212.0ms	9887×	pre	80	true
206.0ms	1884×	body	80	overflowed
119.0ms	352×	body	320	valid
49.0ms	425×	body	80	valid
29.0ms	122×	body	160	valid