Details

sample240.0ms

Algorithm

intervals

Results

90.0ms	89×	body	2560	valid
65.0ms	72×	body	10240	exit
50.0ms	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

simplify92.0ms

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: 59.6b

Counts

2 → 1

localize20.0ms

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)

rewrite24.0ms

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

series160.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
35.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune283.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 50.4b

Counts

89 → 5

localize31.0ms

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))

rewrite30.0ms

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 (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

series183.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))
68.0ms	(* (pow eps 3) (pow b 3))

simplify86.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	460	772
1	2092	679
2	5001	636

prune512.0ms

Filtered

150 candidates to 78 candidates (52.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	146	9	155

Merged error: 49.9b

Counts

155 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

3.3b	(+ (* 1/6 (pow (* b eps) 3)) (+ (* 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))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`add-exp-log` `unswap-sqr`
14×	`unpow-prod-down`
13×	`add-log-exp`
12×	`*-un-lft-identity`
10×	`unpow2` `sqr-pow`
9×	`prod-exp`
8×	`add-cube-cbrt` `associate-r` `associate-l`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
4×	`pow1`
3×	`sum-log`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 92

Calls

4 calls:

10.0ms	(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow eps 2) (pow b 2))

series204.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
37.0ms	(- (exp (* a eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow eps 2) (pow b 2))

simplify64.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	445	695
1	1845	602
2	5002	598

prune418.0ms

Filtered

104 candidates to 62 candidates (59.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Merged error: 49.8b

Counts

113 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 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))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
12×	`*-un-lft-identity`
10×	`unpow2` `sqr-pow`
8×	`add-cube-cbrt` `associate-r` `associate-l` `associate-/r/` `add-log-exp`
6×	`pow-to-exp` `flip3--` `pow-exp` `flip--`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `associate-*l/` `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 → 110

Calls

4 calls:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(* (pow eps 2) (pow b 2))

series998.0ms

Counts

4 → 12

Calls

4 calls:

882.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
34.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))

simplify116.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	738	1419
1	4138	1141
2	5001	1141

prune380.0ms

Filtered

122 candidates to 76 candidates (62.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	128	3	131

Merged error: 0.1b

Counts

131 → 3

regimes67.0ms

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

sample6.6s

Algorithm

intervals

Results

2.5s	2585×	body	2560	valid
1.6s	3417×	body	1280	valid
1.6s	1910×	body	10240	exit
293.0ms	1079×	body	640	valid
171.0ms	9913×	pre	80	true
57.0ms	312×	body	320	valid
24.0ms	471×	body	80	valid
16.0ms	139×	body	160	valid