Details

sample232.0ms

Algorithm

intervals

Results

87.0ms	85×	body	2560	valid
55.0ms	112×	body	1280	valid
54.0ms	61×	body	10240	exit
11.0ms	40×	body	640	valid
6.0ms	317×	pre	80	true
1.0ms	7×	body	320	valid
1.0ms	10×	body	80	valid
0.0ms	2×	body	160	valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 61.5b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.5b	(- (exp (* b eps)) 1.0)
3.5b	(- (exp (* a eps)) 1.0)
6.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

285×	`add-sqr-sqrt`
224×	`times-frac`
221×	`*-un-lft-identity`
160×	`associate-r`
126×	`associate-l`
121×	`add-cube-cbrt`
50×	`distribute-lft-out--` `difference-of-squares`
32×	`*-commutative` `unswap-sqr`
27×	`prod-diff`
16×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
14×	`associate-/l*`
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`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 368

Calls

4 calls:

40.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
8.0ms	(- (exp (* b eps)) 1.0)
8.0ms	(- (exp (* a eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)

series338.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
37.0ms	(- (exp (* b eps)) 1.0)
35.0ms	(- (exp (* a eps)) 1.0)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify100.0ms

Algorithm

egg-herbie

Counts

380 → 380

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1587	6913
1	5002	6541

prune1.1s

Filtered

380 candidates to 236 candidates (62.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	376	4	380
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	377	4	381

Merged error: 0.1b

Counts

381 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-add`
56×	`*-un-lft-identity`
54×	`associate-/r` `associate-/l`
46×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`frac-2neg` `clear-num`
15×	`times-frac`
13×	`fma-def`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 114

Calls

1 calls:

19.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify79.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	774	754
1	3125	693
2	5002	597

prune112.0ms

Filtered

117 candidates to 50 candidates (42.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	115	6	121

Merged error: 0.1b

Counts

121 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)
9.2b	(/ (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)) (* (cbrt a) b))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
64×	`add-sqr-sqrt` `times-frac`
44×	`add-cube-cbrt`
30×	`associate-l`
29×	`cbrt-prod`
17×	`distribute-lft-out`
16×	`associate-/r*`
15×	`associate-r`
11×	`add-cbrt-cube`
10×	`unswap-sqr`
9×	`add-exp-log`
5×	`*-commutative`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `pow1/3`
2×	`div-exp` `cbrt-unprod` `associate-/l/`
1×	`frac-2neg` `flip3-+` `prod-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 142

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)
53.0ms	(/ (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)) (* (cbrt a) b))

series770.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt a)
175.0ms	(cbrt a)
181.0ms	(cbrt a)
235.0ms	(/ (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)) (* (cbrt a) b))

simplify56.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	395	1796
1	1650	1713
2	5001	1703

prune259.0ms

Filtered

154 candidates to 113 candidates (73.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	154	6	160

Merged error: 0.1b

Counts

160 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (/ (* (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a))) (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))) (* (cbrt (cbrt a)) (cbrt (cbrt a)))) (/ (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a))) (* (cbrt (cbrt a)) b)))
5.8b	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))
5.8b	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))
5.8b	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

11421×	`add-sqr-sqrt`
10936×	`cbrt-prod`
4466×	`unswap-sqr`
3755×	`times-frac`
3443×	`*-un-lft-identity`
3247×	`associate-l`
3053×	`associate-/r*`
2820×	`frac-times`
2190×	`add-cube-cbrt`
1764×	`swap-sqr`
1652×	`associate-/l*`
1523×	`associate-r`
673×	`add-cbrt-cube`
572×	`cbrt-div`
566×	`cbrt-unprod`
552×	`distribute-lft-out`
448×	`*-commutative`
434×	`associate-/l/`
331×	`cbrt-undiv`
286×	`flip3-+` `flip-+`
150×	`associate-*l/`
119×	`clear-num`
118×	`frac-2neg`
98×	`associate-*r/`
73×	`add-exp-log`
32×	`prod-exp`
22×	`div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`un-div-inv` `div-inv`
1×	`pow-prod-down`

Counts

4 → 5746

Calls

4 calls:

2.4s	(* (/ (* (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a))) (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))) (* (cbrt (cbrt a)) (cbrt (cbrt a)))) (/ (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a))) (* (cbrt (cbrt a)) b)))
46.0ms	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))
46.0ms	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))
43.0ms	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))

series2.0s

Counts

4 → 12

Calls

4 calls:

244.0ms	(* (/ (* (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a))) (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))) (* (cbrt (cbrt a)) (cbrt (cbrt a)))) (/ (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a))) (* (cbrt (cbrt a)) b)))
596.0ms	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))
595.0ms	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))
595.0ms	(cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))

simplify2.2s

Algorithm

egg-herbie

Counts

5758 → 5758

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5001	276733

prune15.5s

Filtered

5758 candidates to 3636 candidates (63.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	5758	0	5758
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	5758	6	5764

Merged error: 0.1b

Counts

5764 → 6

regimes107.0ms

Accuracy

0% (3.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.6s	2572×	body	2560	valid
1.8s	1942×	body	10240	exit
1.7s	3488×	body	1280	valid
288.0ms	1007×	body	640	valid
177.0ms	9945×	pre	80	true
69.0ms	356×	body	320	valid
25.0ms	465×	body	80	valid
15.0ms	115×	body	160	valid