Details

analyze1.1s (19.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample89.0ms (1.7%)

Algorithm

1×

intervals

Results

41.0ms	87×	body	1280	valid
27.0ms	76×	body	640	valid
5.0ms	68×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	5×	body	160	valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune7.0ms (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: 16.5b

Counts

2 → 1

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.6b	(cos (+ a b))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

7.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series45.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

27.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5018	783

prune121.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.2b

Counts

77 → 8

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 105

Calls

4 calls:

12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
4.0ms	(* (cos a) (cos b))

series97.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
8.0ms	(* (cos a) (cos b))

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5806	1575

prune189.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	114	11	125

Merged error: 0.0b

Counts

125 → 11

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (sin b) r)
0.1b	(* (cos a) (cos b))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 81

Calls

4 calls:

11.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
4.0ms	(* (cos a) (cos b))
4.0ms	(* (sin b) r)

series79.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin b) r)
9.0ms	(* (sin a) (sin b))
8.0ms	(* (cos a) (cos b))

simplify39.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5067	909

prune146.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 0.0b

Counts

104 → 10

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
0.1b	(* (cos a) (cos b))
0.2b	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
0.2b	(/ (* (cos a) (cos b)) (sin b))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cos-mult` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

9.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
7.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
6.0ms	(* (cos a) (cos b))
6.0ms	(/ (* (cos a) (cos b)) (sin b))

series90.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
21.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
16.0ms	(/ (* (cos a) (cos b)) (sin b))
8.0ms	(* (cos a) (cos b))

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4923	1426
1	4923	1426

prune117.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	103	10	113

Merged error: 0b

Counts

113 → 10

regimes230.0ms (4.3%)

Accuracy

Total 0.3b remaining (87.1%)

Threshold costs 0.3b (87.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms (0%)

sample2.7s (50.2%)

Algorithm

1×

intervals

Results

1.6s	2954×	body	1280	valid
533.0ms	1828×	body	640	valid
152.0ms	755×	body	320	valid
142.0ms	2121×	body	80	valid
51.0ms	342×	body	160	valid
0.0ms	1×	body	160	invalid

Details

analyze1.1s (19.9%)

sample89.0ms (1.7%)

simplify3.0ms (0.1%)

prune7.0ms (0.1%)

localize10.0ms (0.2%)

rewrite17.0ms (0.3%)

series45.0ms (0.8%)

simplify62.0ms (1.2%)

prune121.0ms (2.3%)

localize16.0ms (0.3%)

rewrite35.0ms (0.6%)

series97.0ms (1.8%)

simplify57.0ms (1.1%)

prune189.0ms (3.5%)

localize16.0ms (0.3%)

rewrite26.0ms (0.5%)

series79.0ms (1.5%)

simplify39.0ms (0.7%)

prune146.0ms (2.7%)

localize15.0ms (0.3%)

rewrite31.0ms (0.6%)

series90.0ms (1.7%)

simplify66.0ms (1.2%)

prune117.0ms (2.2%)

regimes230.0ms (4.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.7s (50.2%)

Profiling