Details

sample219.0ms

Algorithm

intervals

Results

70.0ms	73×	body	2560	valid
56.0ms	110×	body	1280	valid
56.0ms	69×	body	10240	exit
11.0ms	37×	body	640	valid
5.0ms	325×	pre	80	true
2.0ms	13×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	7×	body	160	valid

simplify93.0ms

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: 60.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.6b	(- (exp (* b eps)) 1.0)
3.3b	(- (exp (* a eps)) 1.0)
3.8b	(- (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)

series168.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
36.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune307.0ms

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: 49.2b

Counts

89 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
15.2b	(* (pow eps 2) (pow b 2))
17.5b	(* (pow eps 3) (pow b 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 (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series179.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow eps 2) (pow b 2))
65.0ms	(* (pow eps 3) (pow b 3))

simplify78.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	460	826
1	2259	690
2	5002	683

prune501.0ms

Filtered

150 candidates to 78 candidates (52.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	147	8	155

Merged error: 48.3b

Counts

155 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
3.3b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
15.2b	(* (pow eps 2) (pow b 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
18×	`add-exp-log`
17×	`unswap-sqr`
16×	`*-un-lft-identity`
14×	`unpow-prod-down`
13×	`associate-l`
11×	`associate-r`
10×	`add-cube-cbrt` `prod-exp` `unpow2` `sqr-pow`
8×	`add-cbrt-cube` `add-log-exp`
6×	`pow1` `pow-to-exp` `pow-exp`
5×	`flip3--` `flip--`
4×	`frac-times`
3×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `cbrt-unprod`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 109

Calls

4 calls:

14.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 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)
7.0ms	(* (pow eps 2) (pow b 2))

series328.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
38.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow eps 2) (pow b 2))

simplify100.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	612	1201
1	3063	1069
2	5002	1065

prune479.0ms

Filtered

121 candidates to 75 candidates (62.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	8	121
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	118	11	129

Merged error: 48.0b

Counts

129 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))))
3.2b	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b))))
3.3b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))))
12.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b))))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series1.7s

Counts

4 → 12

Calls

4 calls:

1.4s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))))
212.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b))))
34.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	753	1944
1	4310	1667
2	5002	1667

prune419.0ms

Filtered

101 candidates to 73 candidates (72.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Merged error: 0.0b

Counts

112 → 5

regimes106.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

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	2589×	body	2560	valid
1.8s	2045×	body	10240	exit
1.7s	3430×	body	1280	valid
304.0ms	1065×	body	640	valid
168.0ms	10049×	pre	80	true
62.0ms	320×	body	320	valid
25.0ms	454×	body	80	valid
18.0ms	146×	body	160	valid