Details

sample5.9s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 51.857636%

Guaranteed chance to sample good point: 4.428816%

Results

79.0ms	70×	body	2560	valid
73.0ms	117×	body	1280	valid
12.0ms	33×	body	640	valid
9.0ms	20×	body	1280	overflowed
7.0ms	318×	pre	80	true
6.0ms	19×	body	640	overflowed
4.0ms	5×	body	2560	overflowed
3.0ms	12×	body	320	valid
2.0ms	9×	body	320	overflowed
2.0ms	22×	body	80	valid
1.0ms	6×	body	160	overflowed
0.0ms	2×	body	160	valid
0.0ms	3×	body	80	overflowed

simplify97.0ms

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

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: 58.7b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.1b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* b eps)) 1.0)
4.4b	(- (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)

series44.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* a eps)) 1.0)
9.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune134.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

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: 50.7b

Counts

89 → 5

localize33.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (exp (* b eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)
11.1b	(* (pow a 2) (pow eps 2))
13.6b	(* (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))

series38.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow a 2) (pow eps 2))
10.0ms	(* (pow a 3) (pow eps 3))

simplify85.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (70.0ms)

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

prune271.0ms

Filtered

80 candidates to 150 candidates (-87.5%)

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: 49.9b

Counts

155 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

2.8b	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
3.0b	(- (exp (* b eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)
11.1b	(* (pow a 2) (pow eps 2))

rewrite27.0ms

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:

9.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))

series46.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
7.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	452	695
1	1920	602
2	5001	598

prune210.0ms

Filtered

64 candidates to 104 candidates (-62.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	105	7	112

Merged error: 49.4b

Counts

112 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (pow (* eps a) 2)) (* a eps))) (- (exp (* b eps)) 1.0))
2.8b	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (pow (* eps a) 2)) (* a eps)))
3.0b	(- (exp (* b eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

12.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (pow (* eps a) 2)) (* a eps))) (- (exp (* b eps)) 1.0))
7.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (pow (* eps a) 2)) (* a eps)))
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series72.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (pow (* eps a) 2)) (* a eps))) (- (exp (* b eps)) 1.0))
18.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (pow (* eps a) 2)) (* a eps)))
7.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	465	1171
1	2356	1064
2	5001	1064

prune172.0ms

Filtered

63 candidates to 85 candidates (-34.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	84	8	92

Merged error: 49.3b

Counts

92 → 8

regimes265.0ms

Accuracy

51% (4.2b remaining)

Error of 52.7b against oracle of 48.5b and baseline of 57.1b

bsearch203.0ms

Steps

Iters	Range		Point
7	81876485944005.34	4416180672567909.0	891284059327835.8
10	-3.2692071683296207e+44	-9.549029158899558e+33	-1.4721383257472567e+38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	40
1	69	40
2	69	40

end0.0ms

sample12.1s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 51.857636%

Guaranteed chance to sample good point: 4.428816%

Results

2.7s	2531×	body	2560	valid
2.0s	3445×	body	1280	valid
389.0ms	1137×	body	640	valid
291.0ms	671×	body	1280	overflowed
216.0ms	9602×	pre	80	true
109.0ms	378×	body	640	overflowed
88.0ms	133×	body	2560	overflowed
81.0ms	334×	body	320	valid
36.0ms	176×	body	320	overflowed
34.0ms	432×	body	80	valid
19.0ms	121×	body	160	valid
16.0ms	114×	body	160	overflowed
9.0ms	123×	body	80	overflowed
6.0ms	5×	body	2560	invalid
1.0ms	2×	body	1280	invalid

Details

sample5.9s

simplify97.0ms

prune4.0ms

localize17.0ms

rewrite23.0ms

series44.0ms

simplify41.0ms

prune134.0ms

localize33.0ms

rewrite29.0ms

series38.0ms

simplify85.0ms

prune271.0ms

localize32.0ms

rewrite27.0ms

series46.0ms

simplify67.0ms

prune210.0ms

localize29.0ms

rewrite29.0ms

series72.0ms

simplify73.0ms

prune172.0ms

regimes265.0ms

bsearch203.0ms

simplify2.0ms

end0.0ms

sample12.1s

Profiling