Details

sample214.0ms

Algorithm

intervals

Results

71.0ms	73×	body	2560	valid
54.0ms	69×	body	10240	exit
51.0ms	110×	body	1280	valid
10.0ms	37×	body	640	valid
6.0ms	325×	pre	80	true
2.0ms	13×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	7×	body	160	valid

simplify97.0ms

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

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: 60.0b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.6b	(- (exp (* b eps)) 1.0)
3.3b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

11.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series186.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
35.0ms	(- (exp (* b eps)) 1.0)
49.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	488	1660
1	2051	1241
2	5003	1216

prune411.0ms

Filtered

150 candidates to 91 candidates (60.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	5	151

Merged error: 49.2b

Counts

151 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
15.2b	(* (pow eps 2) (pow b 2))
17.5b	(* (pow eps 3) (pow b 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `unswap-sqr`
28×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-diff` `prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series183.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))
67.0ms	(* (pow eps 3) (pow b 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	554	1114
1	2456	873
2	5002	825

prune629.0ms

Filtered

182 candidates to 96 candidates (52.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	179	8	187

Merged error: 48.3b

Counts

187 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
3.3b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
15.2b	(* (pow eps 2) (pow b 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`add-exp-log` `prod-diff`
17×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`associate-l`
11×	`associate-r`
10×	`prod-exp` `unpow2` `sqr-pow`
8×	`add-cbrt-cube` `add-log-exp`
6×	`pow1` `pow-to-exp` `fma-neg` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `cbrt-unprod` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 135

Calls

4 calls:

7.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow eps 2) (pow b 2))

series334.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
39.0ms	(- (exp (* a eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)
37.0ms	(* (pow eps 2) (pow b 2))

simplify79.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	545	1268
1	2255	1000
2	5002	991

prune577.0ms

Filtered

147 candidates to 87 candidates (59.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	144	11	155

Merged error: 48.0b

Counts

155 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (pow (* b eps) 2) (* eps b)))))
3.2b	(* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (pow (* b eps) 2) (* eps b))))
3.3b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-neg`
5×	`flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u`
3×	`associate-r` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `diff-log` `associate-*r/` `associate-/r/` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

14.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (pow (* b eps) 2) (* eps b)))))
7.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (pow (* b eps) 2) (* eps b))))
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series1.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (pow (* b eps) 2) (* eps b)))))
208.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (pow (* b eps) 2) (* eps b))))
35.0ms	(- (exp (* a eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify99.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	657	1814
1	3410	1418
2	5001	1409

prune450.0ms

Filtered

121 candidates to 80 candidates (66.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	127	5	132

Merged error: 0.0b

Counts

132 → 5

regimes111.0ms

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

sample6.8s

Algorithm

intervals

Results

2.5s	2589×	body	2560	valid
1.8s	2045×	body	10240	exit
1.7s	3430×	body	1280	valid
295.0ms	1065×	body	640	valid
173.0ms	10049×	pre	80	true
57.0ms	320×	body	320	valid
24.0ms	454×	body	80	valid
17.0ms	146×	body	160	valid