Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample96.0ms (2.3%)

Algorithm

1×

intervals

Results

44.0ms	96×	body	1280	valid
18.0ms	19×	body	2560	valid
16.0ms	61×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	41×	body	80	valid
2.0ms	15×	body	160	valid

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune6.0ms (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: 36.7b

Counts

2 → 1

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.5b	(- (sin (+ x eps)) (sin x))
3.4b	(sin (+ x eps))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 23

Calls

2 calls:

6.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series18.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

10.0ms	(sin (+ x eps))
8.0ms	(- (sin (+ x eps)) (sin x))

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5348	268

prune50.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.5b

Counts

30 → 3

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

6.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(+ x (+ x eps))
5.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))

series19.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
4.0ms	(+ x (+ x eps))

simplify55.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5169	541

prune127.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Merged error: 0.5b

Counts

53 → 7

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
4.4b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`sin-cos-mult`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `associate-+r+` `flip3-+` `flip-+`

Counts

4 → 64

Calls

4 calls:

8.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
4.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))

series49.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
12.0ms	(- (* (cos x) (sin eps)) (sin x))
8.0ms	(* (cos x) (sin eps))
8.0ms	(* (sin x) (cos eps))

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5002	860

prune146.0ms (3.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	70	13	83

Merged error: 0.4b

Counts

83 → 13

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(+ (cos eps) 1)
0.4b	(+ (cos eps) 1)
2.8b	(+ (cos eps) -1)
5.8b	(/ (* (+ (* (cos x) (sin eps)) (* (sin x) (+ (cos eps) -1))) (- (* (sin x) (+ (cos eps) 1)) (* (cos x) (sin eps)))) (- (* (sin x) (+ (cos eps) 1)) (* (cos x) (sin eps))))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

21.0ms	(/ (* (+ (* (cos x) (sin eps)) (* (sin x) (+ (cos eps) -1))) (- (* (sin x) (+ (cos eps) 1)) (* (cos x) (sin eps)))) (- (* (sin x) (+ (cos eps) 1)) (* (cos x) (sin eps))))
4.0ms	(+ (cos eps) -1)
4.0ms	(+ (cos eps) 1)
4.0ms	(+ (cos eps) 1)

series30.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (* (+ (* (cos x) (sin eps)) (* (sin x) (+ (cos eps) -1))) (- (* (sin x) (+ (cos eps) 1)) (* (cos x) (sin eps)))) (- (* (sin x) (+ (cos eps) 1)) (* (cos x) (sin eps))))
3.0ms	(+ (cos eps) -1)
2.0ms	(+ (cos eps) 1)
2.0ms	(+ (cos eps) 1)

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4974	1318
1	4974	1318

prune136.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	6	5	11
Picked	1	0	1
Done	1	0	1
Total	83	10	93

Merged error: 0.1b

Counts

93 → 10

regimes156.0ms (3.7%)

Accuracy

Total 1.5b remaining (95.2%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	72
1	52	72

end0.0ms (0%)

sample3.1s (72.6%)

Algorithm

1×

intervals

Results

1.5s	3318×	body	1280	valid
619.0ms	631×	body	2560	valid
499.0ms	1816×	body	640	valid
151.0ms	785×	body	320	valid
67.0ms	1108×	body	80	valid
42.0ms	342×	body	160	valid

Details

analyze1.0ms (0%)

sample96.0ms (2.3%)

simplify4.0ms (0.1%)

prune6.0ms (0.1%)

localize8.0ms (0.2%)

rewrite10.0ms (0.2%)

series18.0ms (0.4%)

simplify42.0ms (1%)

prune50.0ms (1.2%)

localize12.0ms (0.3%)

rewrite18.0ms (0.4%)

series19.0ms (0.5%)

simplify55.0ms (1.3%)

prune127.0ms (3%)

localize13.0ms (0.3%)

rewrite24.0ms (0.6%)

series49.0ms (1.1%)

simplify43.0ms (1%)

prune146.0ms (3.4%)

localize20.0ms (0.5%)

rewrite33.0ms (0.8%)

series30.0ms (0.7%)

simplify45.0ms (1.1%)

prune136.0ms (3.2%)

regimes156.0ms (3.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (72.6%)

Profiling