Details

sample248.0ms

Algorithm

intervals

Results

89.0ms	84×	body	2560	valid
67.0ms	70×	body	10240	exit
61.0ms	125×	body	1280	valid
6.0ms	326×	pre	80	true
5.0ms	18×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	10×	body	80	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	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: 61.5b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* a eps)) 1.0)
4.6b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

10.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series168.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
39.0ms	(- (exp (* a eps)) 1.0)
31.0ms	(- (exp (* b eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673

prune341.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 49.3b

Counts

89 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)
13.4b	(* (pow a 2) (pow eps 2))
15.0b	(* (pow a 3) (pow eps 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))
9.0ms	(* (pow a 3) (pow eps 3))

series182.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (exp (* b eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
69.0ms	(* (pow a 3) (pow eps 3))

simplify82.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	470	772
1	2119	679
2	5002	636

prune582.0ms

Filtered

150 candidates to 80 candidates (53.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	147	7	154

Merged error: 49.1b

Counts

154 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (exp (* eps b)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)
13.4b	(* (pow a 2) (pow eps 2))
15.0b	(* (pow a 3) (pow eps 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

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

series181.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (exp (* eps b)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow a 2) (pow eps 2))
61.0ms	(* (pow a 3) (pow eps 3))

simplify79.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	465	826
1	2251	690
2	5001	683

prune612.0ms

Filtered

150 candidates to 78 candidates (52.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	150	7	157

Merged error: 49.1b

Counts

157 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.8b	(- (exp (* (+ a b) eps)) 1.0)
14.1b	(* (pow eps 2) (pow b 2))
15.6b	(* (pow eps 3) (pow b 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
22×	`prod-exp`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`associate-/r/`
6×	`cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `pow-prod-down` `associate-l/` `-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 → 155

Calls

4 calls:

22.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
11.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (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) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
30.0ms	(* (pow eps 2) (pow b 2))
66.0ms	(* (pow eps 3) (pow b 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	848	1789
1	5001	1488

prune677.0ms

Filtered

167 candidates to 96 candidates (57.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	2	2	4
Picked	1	0	1
Done	2	0	2
Total	170	4	174

Merged error: 0.0b

Counts

174 → 4

regimes86.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b 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

sample6.9s

Algorithm

intervals

Results

2.6s	2572×	body	2560	valid
1.7s	3484×	body	1280	valid
1.7s	1979×	body	10240	exit
287.0ms	1019×	body	640	valid
169.0ms	9981×	pre	80	true
64.0ms	332×	body	320	valid
26.0ms	466×	body	80	valid
16.0ms	129×	body	160	valid