Details

analyze1.7s

Algorithm: search

sample205.0ms

Algorithm

intervals

Results

91.0ms	81×	body	2560	valid
68.0ms	116×	body	1280	valid
11.0ms	33×	body	640	valid
6.0ms	289×	pre	80	true
5.0ms	11×	body	1280	overflowed
4.0ms	5×	body	2560	overflowed
3.0ms	10×	body	640	overflowed
2.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	10×	body	80	valid
0.0ms	2×	body	320	overflowed
0.0ms	4×	body	80	overflowed
0.0ms	1×	body	160	overflowed

simplify96.0ms

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: 61.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (+ a b) eps))
2.5b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* b eps)) 1.0)
3.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
10×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`exp-to-pow`
1×	`exp-prod` `sum-log` `rem-exp-log`

Counts

4 → 53

Calls

4 calls:

3.0ms	(exp (* (+ a b) eps))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
6.0ms	(- (exp (* (+ a b) eps)) 1.0)

series34.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify70.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	246	363
1	713	333
2	2393	329
3	5001	327

prune106.0ms

Filtered

47 candidates to 65 candidates (-38.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Merged error: 49.3b

Counts

66 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (* b (+ (+ (* (* 1/2 (pow eps 2)) b) (* (* 1/6 (pow eps 3)) (pow b 2))) eps))))
3.9b	(- (exp (* (+ a b) eps)) 1.0)
5.9b	(* (* 1/2 (pow eps 2)) b)
12.6b	(* (* 1/6 (pow eps 3)) (pow b 2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
37×	`prod-exp`
35×	`add-cbrt-cube`
15×	`cbrt-unprod`
11×	`associate-r`
10×	`associate-*r/`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`pow-to-exp` `pow-exp` `associate-/r/`
7×	`add-cube-cbrt`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
5×	`flip3--` `flip--`
4×	`frac-times`
3×	`unpow-prod-down` `flip3-+` `flip-+`
2×	`associate-l` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`

Counts

4 → 99

Calls

4 calls:

22.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (* b (+ (+ (* (* 1/2 (pow eps 2)) b) (* (* 1/6 (pow eps 3)) (pow b 2))) eps))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (* 1/2 (pow eps 2)) b)
8.0ms	(* (* 1/6 (pow eps 3)) (pow b 2))

series603.0ms

Counts

4 → 12

Calls

4 calls:

577.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (* b (+ (+ (* (* 1/2 (pow eps 2)) b) (* (* 1/6 (pow eps 3)) (pow b 2))) eps))))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
4.0ms	(* (* 1/2 (pow eps 2)) b)
8.0ms	(* (* 1/6 (pow eps 3)) (pow b 2))

simplify39.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	832	1639
1	5001	1296

prune226.0ms

Filtered

64 candidates to 111 candidates (-73.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	113	3	116

Merged error: 0.0b

Counts

116 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

11.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify64.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2755	90
4	5001	90

prune42.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	19	6	25

Merged error: 0.0b

Counts

25 → 6

localize4.0ms

Local error

Found 1 expressions with local error:

15.3b

(/ (+ b a) (* b a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 25

Calls

1 calls:

6.0ms

(/ (+ b a) (* b a))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(/ (+ b a) (* b a))

simplify45.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	145	134
1	519	113
2	2023	113
3	5001	113

prune25.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	4	4
Picked	1	0	1
Done	1	0	1
Total	28	6	34

Merged error: 0.0b

Counts

34 → 6

regimes216.0ms

Accuracy

67.9% (3.4b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 10.7b

bsearch1.3s

Steps

Iters	Range		Point
7	7.952001139533124e-45	4.0647337626834936e-43	3.984657991412354e-43
9	-1.3674432792361776e-41	-1.8337304692099022e-47	-2.9507540274357845e-43

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	7
1	22	7

end0.0ms

analyze1.7s

Algorithm: search

sample6.2s

Algorithm

intervals

Results

2.7s	2551×	body	2560	valid
1.9s	3434×	body	1280	valid
356.0ms	1071×	body	640	valid
273.0ms	639×	body	1280	overflowed
198.0ms	9687×	pre	80	true
113.0ms	382×	body	640	overflowed
108.0ms	158×	body	2560	overflowed
85.0ms	369×	body	320	valid
40.0ms	192×	body	320	overflowed
33.0ms	445×	body	80	valid
23.0ms	130×	body	160	valid
15.0ms	220×	body	80	overflowed
13.0ms	95×	body	160	overflowed
2.0ms	1×	body	2560	invalid

Details

analyze1.7s

sample205.0ms

simplify96.0ms

prune4.0ms

localize17.0ms

rewrite17.0ms

series34.0ms

simplify70.0ms

prune106.0ms

localize26.0ms

rewrite43.0ms

series603.0ms

simplify39.0ms

prune226.0ms

localize5.0ms

rewrite12.0ms

series3.0ms

simplify64.0ms

prune42.0ms

localize4.0ms

rewrite7.0ms

series6.0ms

simplify45.0ms

prune25.0ms

regimes216.0ms

bsearch1.3s

simplify1.0ms

end0.0ms

analyze1.7s

sample6.2s

Profiling