Details

sample249.0ms

Algorithm

intervals

Results

84.0ms	89×	body	2560	valid
77.0ms	83×	body	10240	exit
48.0ms	103×	body	1280	valid
9.0ms	31×	body	640	valid
6.0ms	340×	pre	80	true
2.0ms	13×	body	320	valid
1.0ms	19×	body	80	valid
0.0ms	2×	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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 59.4b

Counts

2 → 1

localize15.0ms

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)

rewrite37.0ms

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:

19.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series313.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
38.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (62.0ms)

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

prune591.0ms

Filtered

129 candidates to 86 candidates (66.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	4	130

Merged error: 0.3b

Counts

130 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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:

13.0ms

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

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify68.0ms

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

prune84.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	33	8	41

Merged error: 0.2b

Counts

41 → 8

localize10.0ms

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)

rewrite11.0ms

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)

series720.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (cbrt b) (cbrt b))
173.0ms	(cbrt b)
171.0ms	(cbrt b)
175.0ms	(cbrt b)

simplify90.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (85.0ms)

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

prune235.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 0.2b

Counts

101 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt b))
0.6b	(cbrt (cbrt b))
0.6b	(cbrt (cbrt b))
0.9b	(pow (cbrt (cbrt b)) 4)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

5.0ms	(cbrt (cbrt b))
2.0ms	(cbrt (cbrt b))
2.0ms	(cbrt (cbrt b))
4.0ms	(pow (cbrt (cbrt b)) 4)

series1.0s

Counts

4 → 12

Calls

4 calls:

254.0ms	(cbrt (cbrt b))
247.0ms	(cbrt (cbrt b))
241.0ms	(cbrt (cbrt b))
296.0ms	(pow (cbrt (cbrt b)) 4)

simplify69.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	142	385
1	424	359
2	1551	337
3	5002	331

prune247.0ms

Filtered

86 candidates to 64 candidates (74.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	86	8	94

Merged error: 0.2b

Counts

94 → 8

regimes126.0ms

Accuracy

0% (3.0b 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

sample6.8s

Algorithm

intervals

Results

2.6s	2624×	body	2560	valid
1.7s	3392×	body	1280	valid
1.6s	1884×	body	10240	exit
306.0ms	1088×	body	640	valid
170.0ms	9887×	pre	80	true
65.0ms	352×	body	320	valid
23.0ms	425×	body	80	valid
15.0ms	122×	body	160	valid