Details

sample201.0ms

Algorithm

intervals

Results

91.0ms	83×	body	2560	valid
66.0ms	119×	body	1280	valid
10.0ms	31×	body	640	valid
10.0ms	330×	pre	80	true
5.0ms	74×	body	80	overflowed
2.0ms	9×	body	320	valid
1.0ms	10×	body	80	valid
1.0ms	4×	body	160	valid

simplify100.0ms

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: 61.6b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.4b	(- (exp (* b eps)) 1.0)
5.4b	(- (exp (* a eps)) 1.0)
6.5b	(- (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:

10.0ms	(* (- (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)

series161.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
30.0ms	(- (exp (* b eps)) 1.0)
36.0ms	(- (exp (* a eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

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

prune389.0ms

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: 49.5b

Counts

151 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (exp (* a eps)) 1.0)
6.5b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow eps 2) (pow b 2))
15.3b	(* (pow eps 3) (pow b 3))

rewrite35.0ms

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:

4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
12.0ms	(* (pow eps 3) (pow b 3))

series186.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (exp (* a eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)
30.0ms	(* (pow eps 2) (pow b 2))
64.0ms	(* (pow eps 3) (pow b 3))

simplify89.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	554	1168
1	2622	884
2	5001	872

prune620.0ms

Filtered

182 candidates to 96 candidates (52.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	180	7	187

Merged error: 48.8b

Counts

187 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
5.4b	(- (exp (* a eps)) 1.0)
6.5b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow eps 2) (pow b 2))

rewrite35.0ms

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:

13.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* eps b) 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))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
32.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow eps 2) (pow b 2))

simplify98.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	714	1696
1	3610	1258
2	5001	1247

prune514.0ms

Filtered

148 candidates to 87 candidates (58.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	152	3	155

Merged error: 0.0b

Counts

155 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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:

12.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify70.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	107	112
1	368	101
2	1274	98
3	3144	98
4	5001	98

prune57.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0.0b

Counts

40 → 4

regimes71.0ms

Accuracy

0% (3.1b remaining)

Error of 3.5b against oracle of 0.4b 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

sample5.7s

Algorithm

intervals

Results

2.7s	2580×	body	2560	valid
1.9s	3399×	body	1280	valid
371.0ms	1099×	body	640	valid
206.0ms	10024×	pre	80	true
136.0ms	2022×	body	80	overflowed
73.0ms	324×	body	320	valid
32.0ms	468×	body	80	valid
19.0ms	132×	body	160	valid