Details

sample216.0ms

Algorithm

intervals

Results

85.0ms	84×	body	2560	valid
50.0ms	105×	body	1280	valid
46.0ms	48×	body	10240	exit
9.0ms	32×	body	640	valid
5.0ms	304×	pre	80	true
3.0ms	17×	body	320	valid
1.0ms	14×	body	80	valid
1.0ms	4×	body	160	valid

simplify99.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.1b	(- (exp (* a eps)) 1.0)
4.9b	(- (exp (* b eps)) 1.0)
5.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite44.0ms

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:

24.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* b eps)) 1.0)
6.0ms	(- (exp (* (+ a b) eps)) 1.0)

series471.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
34.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* b eps)) 1.0)
53.0ms	(- (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

prune440.0ms

Filtered

129 candidates to 86 candidates (66.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

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:

18.0ms

(+ (/ 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

prune85.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt b) (cbrt b))
0.6b	(cbrt b)
0.6b	(cbrt b)
0.6b	(cbrt b)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt b) (cbrt b))
1.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(cbrt b)

series746.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (cbrt b) (cbrt b))
179.0ms	(cbrt b)
183.0ms	(cbrt b)
178.0ms	(cbrt b)

simplify93.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune272.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite185.0ms

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:

127.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
15.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
18.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
15.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
84.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
84.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
86.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (45.0ms)

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

prune356.0ms

Filtered

179 candidates to 95 candidates (53.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes78.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.6s	2608×	body	2560	valid
1.8s	1980×	body	10240	exit
1.7s	3394×	body	1280	valid
300.0ms	1079×	body	640	valid
168.0ms	9980×	pre	80	true
62.0ms	342×	body	320	valid
25.0ms	465×	body	80	valid
13.0ms	112×	body	160	valid