Details

analyze1.7s (16.2%)

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

sample204.0ms (1.9%)

Algorithm

1×

intervals

Results

85.0ms	79×	body	2560	valid
59.0ms	103×	body	1280	valid
15.0ms	43×	body	640	valid
6.0ms	308×	pre	80	true
6.0ms	15×	body	1280	overflowed
5.0ms	9×	body	80	overflowed
4.0ms	16×	body	640	overflowed
3.0ms	14×	body	320	valid
2.0ms	5×	body	2560	overflowed
1.0ms	6×	body	320	overflowed
1.0ms	13×	body	80	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	160	overflowed

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	24

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 60.5b

Counts

2 → 1

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* b eps)) 1.0)
3.1b	(- (exp (* a eps)) 1.0)
4.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite23.0ms (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))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)

series42.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

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

prune146.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Merged error: 49.3b

Counts

84 → 3

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.7b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (* b (+ eps (* b (* 1/2 (* eps eps))))))))
4.1b	(- (exp (* (+ a b) eps)) 1.0)
7.2b	(* b (* 1/2 (* eps eps)))
16.5b	(* (pow eps 3) (pow b 3))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log` `add-sqr-sqrt`
27×	`add-cbrt-cube`
19×	`prod-exp`
16×	`unswap-sqr`
15×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
13×	`pow1` `-un-lft-identity` `associate-r*`
11×	`add-cube-cbrt` `cbrt-unprod`
10×	`sqr-pow`
8×	`associate-/r/`
7×	`pow-prod-down`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 124

Calls

4 calls:

19.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (* b (+ eps (* b (* 1/2 (* eps eps))))))))
9.0ms	(* (pow eps 3) (pow b 3))
7.0ms	(* b (* 1/2 (* eps eps)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series672.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

638.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (* b (+ eps (* b (* 1/2 (* eps eps))))))))
17.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (pow eps 3) (pow b 3))
7.0ms	(* b (* 1/2 (* eps eps)))

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5169	2567

prune390.0ms (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	133	6	139

Merged error: 0.0b

Counts

139 → 6

localize4.0ms (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))

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4881	196
1	4881	196

prune54.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	22	6	28

Merged error: 0.0b

Counts

28 → 6

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.3b	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

rewrite78.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`*-un-lft-identity`
106×	`sqrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`add-sqr-sqrt` `times-frac`
35×	`swap-sqr`
30×	`sqrt-div`
28×	`add-cube-cbrt`
21×	`pow1`
13×	`associate-r` `associate-l`
11×	`flip3-+` `frac-add` `flip-+`
10×	`sqrt-pow1` `pow1/2`
9×	`frac-times`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 170

Calls

4 calls:

31.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))
14.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
12.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
12.0ms	(+ (/ 1 b) (/ 1 a))

series25.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
9.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
5.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))
2.0ms	(+ (/ 1 b) (/ 1 a))

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5074	2012

prune309.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	182	6	188

Merged error: 0.0b

Counts

188 → 6

regimes190.0ms (1.8%)

Accuracy

Total 3.4b remaining (96.9%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

end0.0ms (0%)

sample6.3s (59.8%)

Algorithm

1×

intervals

Results

2.7s	2523×	body	2560	valid
2.0s	3458×	body	1280	valid
363.0ms	1052×	body	640	valid
271.0ms	626×	body	1280	overflowed
204.0ms	9695×	pre	80	true
119.0ms	179×	body	2560	overflowed
112.0ms	383×	body	640	overflowed
82.0ms	352×	body	320	valid
36.0ms	175×	body	320	overflowed
34.0ms	467×	body	80	valid
23.0ms	148×	body	160	valid
18.0ms	247×	body	80	overflowed
13.0ms	83×	body	160	overflowed
1.0ms	1×	body	2560	invalid
0.0ms	1×	body	1280	invalid

Details

analyze1.7s (16.2%)

sample204.0ms (1.9%)

simplify44.0ms (0.4%)

prune9.0ms (0.1%)

localize16.0ms (0.2%)

rewrite23.0ms (0.2%)

series42.0ms (0.4%)

simplify34.0ms (0.3%)

prune146.0ms (1.4%)

localize28.0ms (0.3%)

rewrite45.0ms (0.4%)

series672.0ms (6.4%)

simplify57.0ms (0.5%)

prune390.0ms (3.7%)

localize4.0ms (0%)

rewrite13.0ms (0.1%)

series3.0ms (0%)

simplify76.0ms (0.7%)

prune54.0ms (0.5%)

localize7.0ms (0.1%)

rewrite78.0ms (0.7%)

series25.0ms (0.2%)

simplify46.0ms (0.4%)

prune309.0ms (2.9%)

regimes190.0ms (1.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample6.3s (59.8%)

Profiling