Details

sample240.0ms

Algorithm

intervals

Results

94.0ms	98×	body	2560	valid
64.0ms	60×	body	10240	exit
47.0ms	97×	body	1280	valid
9.0ms	34×	body	640	valid
5.0ms	317×	pre	80	true
3.0ms	16×	body	320	valid
1.0ms	10×	body	80	valid
0.0ms	2×	body	160	valid

simplify98.0ms

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

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.1b	(- (exp (* b eps)) 1.0)
3.2b	(- (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))
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series167.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
38.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (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

prune385.0ms

Filtered

150 candidates to 91 candidates (60.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	144	6	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	6	151

Merged error: 52.4b

Counts

151 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (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)))))
5.8b	(- (exp (* (+ a b) eps)) 1.0)
13.0b	(* (pow eps 2) (pow b 2))
14.5b	(* (pow eps 3) (pow b 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
23×	`*-un-lft-identity`
22×	`prod-exp`
21×	`add-cube-cbrt`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
9×	`prod-diff`
6×	`cbrt-unprod` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `*-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

13.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (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))
12.0ms	(* (pow eps 3) (pow b 3))

series1.5s

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 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
49.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))
66.0ms	(* (pow eps 3) (pow b 3))

simplify147.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	785	1762
1	4542	1404
2	5001	1399

prune636.0ms

Filtered

181 candidates to 103 candidates (56.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	184	3	187

Merged error: 0.2b

Counts

187 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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:

13.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify71.0ms

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

prune65.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0.2b

Counts

40 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
0.6b	(cbrt (/ 1 b))
0.6b	(cbrt (/ 1 b))
0.6b	(cbrt (/ 1 b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 161

Calls

4 calls:

16.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
3.0ms	(cbrt (/ 1 b))
2.0ms	(cbrt (/ 1 b))
3.0ms	(cbrt (/ 1 b))

series741.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
184.0ms	(cbrt (/ 1 b))
178.0ms	(cbrt (/ 1 b))
180.0ms	(cbrt (/ 1 b))

simplify44.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	223	1172
1	902	1064
2	5001	908

prune287.0ms

Filtered

173 candidates to 104 candidates (60.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	172	5	177

Merged error: 0.2b

Counts

177 → 5

regimes69.0ms

Accuracy

0% (2.6b remaining)

Error of 3.1b against oracle of 0.5b and baseline of 3.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	2554×	body	2560	valid
1.8s	2036×	body	10240	exit
1.8s	3505×	body	1280	valid
284.0ms	1017×	body	640	valid
174.0ms	10040×	pre	80	true
76.0ms	387×	body	320	valid
22.0ms	421×	body	80	valid
14.0ms	120×	body	160	valid

Details

sample240.0ms

simplify98.0ms

prune3.0ms

localize19.0ms

rewrite30.0ms

series167.0ms

simplify64.0ms

prune385.0ms

localize26.0ms

rewrite42.0ms

series1.5s

simplify147.0ms

prune636.0ms

localize5.0ms

rewrite14.0ms

series11.0ms

simplify71.0ms

prune65.0ms

localize8.0ms

rewrite31.0ms

series741.0ms

simplify44.0ms

prune287.0ms

regimes69.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.9s

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