Details

analyze1.7s (15.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

sample218.0ms (2%)

Algorithm

1×

intervals

Results

87.0ms	77×	body	2560	valid
65.0ms	103×	body	1280	valid
16.0ms	44×	body	640	valid
13.0ms	26×	body	1280	overflowed
7.0ms	317×	pre	80	true
5.0ms	16×	body	640	overflowed
4.0ms	6×	body	2560	overflowed
3.0ms	10×	body	320	valid
2.0ms	19×	body	80	valid
1.0ms	3×	body	320	overflowed
1.0ms	3×	body	160	valid
1.0ms	4×	body	160	overflowed
0.0ms	6×	body	80	overflowed

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	24

prune14.0ms (0.1%)

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 → 2

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.0b	(- (exp (* b eps)) 1.0)
2.8b	(- (exp (* a eps)) 1.0)
4.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite24.0ms (0.2%)

Algorithm

1×	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×	`associate-r/` `associate-l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

10.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)

series43.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
9.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)

simplify34.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4887	1142
1	4887	1142

prune163.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Merged error: 47.5b

Counts

85 → 6

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(* b (* 1/6 (pow eps 3)))
4.0b	(- (exp (* (+ a b) eps)) 1.0)
4.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b eps) (* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2)))))))
12.6b	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

14.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b eps) (* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2)))))))
11.0ms	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))
6.0ms	(* b (* 1/6 (pow eps 3)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series690.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

641.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b eps) (* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2)))))))
25.0ms	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* b (* 1/6 (pow eps 3)))

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4972	2426
1	4972	2426

prune263.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	101	3	104

Merged error: 0.0b

Counts

104 → 3

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite13.0ms (0.1%)

Algorithm

1×	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:

12.0ms

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

series3.0ms (0%)

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4881	196
1	4881	196

prune43.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	20	5	25

Merged error: 0.0b

Counts

25 → 5

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))

rewrite81.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

35.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series93.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
20.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	6184	2287

prune456.0ms (4.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	170	6	176

Merged error: 0.0b

Counts

176 → 6

regimes264.0ms (2.5%)

Accuracy

Total 0.2b remaining (58.5%)

Threshold costs 0.2b (58.5%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	86
1	51	86

end0.0ms (0%)

sample6.3s (58.4%)

Algorithm

1×

intervals

Results

2.8s	2597×	body	2560	valid
1.9s	3401×	body	1280	valid
345.0ms	1042×	body	640	valid
277.0ms	650×	body	1280	overflowed
207.0ms	9712×	pre	80	true
109.0ms	166×	body	2560	overflowed
104.0ms	362×	body	640	overflowed
80.0ms	351×	body	320	valid
45.0ms	208×	body	320	overflowed
36.0ms	482×	body	80	valid
21.0ms	127×	body	160	valid
17.0ms	240×	body	80	overflowed
11.0ms	84×	body	160	overflowed
2.0ms	2×	body	2560	invalid

Details

analyze1.7s (15.9%)

sample218.0ms (2%)

simplify42.0ms (0.4%)

prune14.0ms (0.1%)

localize17.0ms (0.2%)

rewrite24.0ms (0.2%)

series43.0ms (0.4%)

simplify34.0ms (0.3%)

prune163.0ms (1.5%)

localize26.0ms (0.2%)

rewrite39.0ms (0.4%)

series690.0ms (6.4%)

simplify69.0ms (0.6%)

prune263.0ms (2.5%)

localize5.0ms (0%)

rewrite13.0ms (0.1%)

series3.0ms (0%)

simplify69.0ms (0.6%)

prune43.0ms (0.4%)

localize9.0ms (0.1%)

rewrite81.0ms (0.8%)

series93.0ms (0.9%)

simplify81.0ms (0.8%)

prune456.0ms (4.2%)

regimes264.0ms (2.5%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.3s (58.4%)

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