Details

sample237.0ms

Algorithm

intervals

Results

79.0ms	72×	body	2560	valid
67.0ms	133×	body	1280	valid
56.0ms	63×	body	10240	exit
10.0ms	33×	body	640	valid
6.0ms	319×	pre	80	true
1.0ms	5×	body	320	valid
1.0ms	9×	body	80	valid
1.0ms	4×	body	160	valid

simplify100.0ms

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

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: 61.8b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
2.4b	(- (exp (* a eps)) 1.0)
3.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite31.0ms

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)

series164.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
35.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (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

prune392.0ms

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: 50.5b

Counts

151 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
3.5b	(- (exp (* (+ a b) eps)) 1.0)
11.6b	(* (pow eps 2) (pow b 2))
12.1b	(* (pow eps 3) (pow b 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
27×	`*-un-lft-identity`
25×	`associate-l`
23×	`add-cube-cbrt` `associate-r`
20×	`sqr-pow`
19×	`prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`add-cbrt-cube` `unpow2`
9×	`prod-diff`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `pow-prod-down` `*-commutative` `cbrt-unprod`
2×	`cube-mult` `flip3--` `unpow3` `associate-*l/` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log`

Counts

4 → 168

Calls

4 calls:

7.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series360.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow eps 2) (pow b 2))
67.0ms	(* (pow eps 3) (pow b 3))

simplify114.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	623	1364
1	2997	1148
2	5002	1102

prune647.0ms

Filtered

180 candidates to 98 candidates (54.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	175	5	180
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	176	9	185

Merged error: 49.7b

Counts

185 → 9

localize41.0ms

Local error

Found 4 expressions with local error:

11.6b	(* (pow eps 2) (pow b 2))
12.1b	(* (pow eps 3) (pow b 3))
12.1b	(* (pow eps 3) (pow b 3))
12.1b	(* (pow eps 3) (pow b 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

114×	`add-sqr-sqrt`
64×	`unswap-sqr`
56×	`unpow-prod-down`
52×	`add-exp-log`
44×	`associate-r` `associate-l`
42×	`cube-prod`
40×	`sqr-pow`
36×	`prod-exp`
26×	`add-cube-cbrt` `*-un-lft-identity`
24×	`pow-to-exp` `pow-exp`
12×	`add-cbrt-cube`
10×	`unpow2`
6×	`cube-mult` `unpow3`
4×	`pow1` `expm1-log1p-u` `pow-prod-down` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

4 → 236

Calls

4 calls:

8.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))
10.0ms	(* (pow eps 3) (pow b 3))
10.0ms	(* (pow eps 3) (pow b 3))

series417.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (pow eps 2) (pow b 2))
58.0ms	(* (pow eps 3) (pow b 3))
260.0ms	(* (pow eps 3) (pow b 3))
65.0ms	(* (pow eps 3) (pow b 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	326	1294
1	1830	1146
2	5001	1139

prune939.0ms

Filtered

248 candidates to 118 candidates (47.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	248	9	257

Merged error: 49.7b

Counts

257 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (exp (* a eps)) 1.0)
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))))
3.5b	(- (exp (* (+ a b) eps)) 1.0)
11.6b	(* (pow eps 2) (pow b 2))

rewrite31.0ms

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:

5.0ms	(- (exp (* a eps)) 1.0)
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 b) eps)) 1.0)
10.0ms	(* (pow eps 2) (pow b 2))

series309.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (exp (* a eps)) 1.0)
197.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
47.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))

simplify79.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (65.0ms)

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

prune496.0ms

Filtered

147 candidates to 87 candidates (59.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	5	147
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	146	10	156

Merged error: 49.1b

Counts

156 → 10

regimes240.0ms

Accuracy

44% (4.8b remaining)

Error of 53.3b against oracle of 48.5b and baseline of 57.1b

bsearch267.0ms

Steps

Iters	Range		Point
9	2.797292414147033e+40	1.5507233175302914e+47	8.895710189523327e+43
5	-3688053911496.1914	-937727910791.0848	-2942943340030.655

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	86
1	65	86

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.5s	2595×	body	2560	valid
1.8s	2073×	body	10240	exit
1.7s	3407×	body	1280	valid
307.0ms	1082×	body	640	valid
183.0ms	10075×	pre	80	true
71.0ms	365×	body	320	valid
24.0ms	424×	body	80	valid
16.0ms	129×	body	160	valid