Details

sample249.0ms

Algorithm

intervals

Results

94.0ms	89×	body	2560	valid
67.0ms	72×	body	10240	exit
53.0ms	104×	body	1280	valid
9.0ms	34×	body	640	valid
6.0ms	329×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	17×	body	80	valid
0.0ms	3×	body	160	valid

simplify104.0ms

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: 59.6b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* b eps)) 1.0)
3.9b	(- (exp (* a eps)) 1.0)
5.8b	(- (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)

series170.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (51.0ms)

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

prune407.0ms

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: 50.4b

Counts

151 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (exp (* a eps)) 1.0)
5.8b	(- (exp (* (+ a b) eps)) 1.0)
13.8b	(* (pow eps 2) (pow b 2))
15.9b	(* (pow eps 3) (pow b 3))

rewrite38.0ms

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)
8.0ms	(* (pow eps 2) (pow b 2))
14.0ms	(* (pow eps 3) (pow b 3))

series186.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))
68.0ms	(* (pow eps 3) (pow b 3))

simplify99.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (85.0ms)

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

prune656.0ms

Filtered

182 candidates to 96 candidates (52.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	177	5	182
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	178	9	187

Merged error: 49.9b

Counts

187 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

3.3b	(fma 1/6 (pow (* b eps) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))
3.9b	(- (exp (* a eps)) 1.0)
5.8b	(- (exp (* (+ a b) eps)) 1.0)
13.8b	(* (pow eps 2) (pow b 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
16×	`add-exp-log` `unswap-sqr`
14×	`unpow-prod-down`
10×	`unpow2` `sqr-pow`
9×	`prod-exp`
8×	`associate-r` `associate-l` `add-log-exp`
6×	`pow-to-exp` `fma-neg` `pow-exp` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 119

Calls

4 calls:

1.0ms	(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)
7.0ms	(* (pow eps 2) (pow b 2))

series203.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma 1/6 (pow (* b eps) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))
34.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow eps 2) (pow b 2))

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	448	928
1	1637	697
2	5001	688

prune512.0ms

Filtered

131 candidates to 77 candidates (58.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	125	6	131
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	131	9	140

Merged error: 49.8b

Counts

140 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
3.9b	(- (exp (* a eps)) 1.0)
5.8b	(- (exp (* (+ a b) eps)) 1.0)
13.8b	(* (pow eps 2) (pow b 2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
28×	`add-exp-log`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff` `add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
10×	`unpow2` `sqr-pow`
8×	`associate-r` `associate-l` `add-log-exp`
6×	`pow-to-exp` `fma-neg` `pow-exp`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

18.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (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)
7.0ms	(* (pow eps 2) (pow b 2))

series980.0ms

Counts

4 → 12

Calls

4 calls:

860.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
41.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow eps 2) (pow b 2))

simplify110.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	706	1575
1	3575	1200
2	5002	1191

prune416.0ms

Filtered

148 candidates to 87 candidates (58.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	154	3	157

Merged error: 0.1b

Counts

157 → 3

regimes65.0ms

Accuracy

0% (3.2b remaining)

Error of 3.5b against oracle of 0.2b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	2585×	body	2560	valid
1.7s	3417×	body	1280	valid
1.7s	1910×	body	10240	exit
302.0ms	1079×	body	640	valid
168.0ms	9913×	pre	80	true
57.0ms	312×	body	320	valid
25.0ms	471×	body	80	valid
17.0ms	139×	body	160	valid