Details

analyze1.1s (20.3%)

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

46.0ms	87×	body	1280	valid
22.0ms	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:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.6b	(cos (+ a b))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

5.0ms	(/ (* r (sin b)) (cos (+ a b)))
4.0ms	(cos (+ a b))
4.0ms	(* r (sin b))

series38.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(* r (sin b))
6.0ms	(cos (+ a b))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5357	439

prune105.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	10	57

Merged error: 0.1b

Counts

57 → 10

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
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))))

rewrite24.0ms (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:

9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
4.0ms	(* (cos a) (cos b))
4.0ms	(* r (sin b))

series82.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (cos a) (cos b))
10.0ms	(* (sin a) (sin b))
8.0ms	(* r (sin b))

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4976	875
1	4976	875

prune164.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	91	12	103

Merged error: 0.0b

Counts

103 → 12

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))

rewrite27.0ms (0.5%)

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:

8.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
7.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
5.0ms	(/ (* (cos a) (cos b)) (sin b))
4.0ms	(* (cos a) (cos b))

series96.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
20.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
17.0ms	(/ (* (cos a) (cos b)) (sin b))
9.0ms	(* (cos a) (cos b))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4923	1426
1	4923	1426

prune162.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 0b

Counts

115 → 12

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite32.0ms (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 b) (sin a)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
5.0ms	(* (sin b) (sin a))
4.0ms	(* (cos a) (cos b))

series105.0ms (2%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
32.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
10.0ms	(* (cos a) (cos b))
10.0ms	(* (sin b) (sin a))

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6041	1616

prune120.0ms (2.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	117	12	129

Merged error: 0b

Counts

129 → 12

regimes257.0ms (4.9%)

Accuracy

Total 0.3b remaining (85.3%)

Threshold costs 0.3b (85.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	16
1	41	16

end0.0ms (0%)

sample2.5s (48.7%)

Algorithm

1×

intervals

Results

1.4s	2954×	body	1280	valid
526.0ms	1828×	body	640	valid
153.0ms	755×	body	320	valid
148.0ms	2121×	body	80	valid
53.0ms	342×	body	160	valid
0.0ms	1×	body	160	invalid

Details

analyze1.1s (20.3%)

sample89.0ms (1.7%)

simplify3.0ms (0.1%)

prune7.0ms (0.1%)

localize10.0ms (0.2%)

rewrite14.0ms (0.3%)

series38.0ms (0.7%)

simplify66.0ms (1.3%)

prune105.0ms (2%)

localize19.0ms (0.4%)

rewrite24.0ms (0.5%)

series82.0ms (1.6%)

simplify39.0ms (0.8%)

prune164.0ms (3.1%)

localize15.0ms (0.3%)

rewrite27.0ms (0.5%)

series96.0ms (1.8%)

simplify66.0ms (1.3%)

prune162.0ms (3.1%)

localize17.0ms (0.3%)

rewrite32.0ms (0.6%)

series105.0ms (2%)

simplify57.0ms (1.1%)

prune120.0ms (2.3%)

regimes257.0ms (4.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.5s (48.7%)

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