Details

analyze1.2s (22.2%)

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 (1.6%)

Algorithm

1×

intervals

Results

45.0ms	98×	body	1280	valid
20.0ms	51×	body	640	valid
7.0ms	33×	body	320	valid
4.0ms	67×	body	80	valid
1.0ms	7×	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: 17.9b

Counts

2 → 1

localize11.0ms (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)))
3.2b	(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))

series49.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

24.0ms	(* r (/ (sin b) (cos (+ a b))))
13.0ms	(/ (sin b) (cos (+ a b)))
11.0ms	(cos (+ a b))

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5018	783

prune120.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 0.2b

Counts

77 → 7

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite33.0ms (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:

13.0ms	(* 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))

series102.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))
9.0ms	(* (cos a) (cos b))

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5806	1575

prune193.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	108	9	117
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	115	9	124

Merged error: 0.0b

Counts

124 → 9

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
0.3b	(pow (* (sin b) (sin a)) 3)
24.2b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`cbrt-prod`
4×	`sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `associate-r` `associate-l` `associate-/r` `associate-/r/` `associate-/l`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `div-exp` `clear-num` `cos-mult` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

10.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
5.0ms	(* (sin b) (sin a))
5.0ms	(pow (* (sin b) (sin a)) 3)
3.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series66.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
17.0ms	(pow (* (sin b) (sin a)) 3)
10.0ms	(cbrt (pow (* (sin b) (sin a)) 3))
10.0ms	(* (sin b) (sin a))

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5025	1152

prune186.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	102	9	111

Merged error: 0.0b

Counts

111 → 9

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 99

Calls

4 calls:

8.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
6.0ms	(* (/ (cos a) (sin b)) (cos b))
6.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
4.0ms	(/ (cos a) (sin b))

series97.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
20.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
17.0ms	(* (/ (cos a) (sin b)) (cos b))
11.0ms	(/ (cos a) (sin b))

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4937	1443
1	4937	1443

prune131.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	111	9	120

Merged error: 0b

Counts

120 → 9

regimes236.0ms (4.4%)

Accuracy

Total 0.3b remaining (84.4%)

Threshold costs 0.3b (84.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms (0%)

sample2.5s (47.1%)

Algorithm

1×

intervals

Results

1.4s	2883×	body	1280	valid
544.0ms	1859×	body	640	valid
168.0ms	792×	body	320	valid
144.0ms	2096×	body	80	valid
55.0ms	370×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze1.2s (22.2%)

sample89.0ms (1.6%)

simplify3.0ms (0.1%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

rewrite17.0ms (0.3%)

series49.0ms (0.9%)

simplify57.0ms (1.1%)

prune120.0ms (2.2%)

localize17.0ms (0.3%)

rewrite33.0ms (0.6%)

series102.0ms (1.9%)

simplify53.0ms (1%)

prune193.0ms (3.6%)

localize23.0ms (0.4%)

rewrite24.0ms (0.5%)

series66.0ms (1.2%)

simplify56.0ms (1%)

prune186.0ms (3.4%)

localize16.0ms (0.3%)

rewrite28.0ms (0.5%)

series97.0ms (1.8%)

simplify49.0ms (0.9%)

prune131.0ms (2.4%)

regimes236.0ms (4.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.5s (47.1%)

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