Details

analyze1.1s

Algorithm

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

sample87.0ms

Algorithm

intervals

Results

47.0ms	92×	body	1280	valid
16.0ms	57×	body	640	valid
6.0ms	29×	body	320	valid
4.0ms	67×	body	80	valid
2.0ms	11×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 16.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.7b	(cos (+ a b))

rewrite16.0ms

Algorithm

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))

series40.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify54.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5145	783

prune112.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 0.2b

Counts

77 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin 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))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 99

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
50.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5157	1671

prune183.0ms

Filtered

89 candidates to 111 candidates (-24.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	96	15	111
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	106	15	121

Merged error: 0.0b

Counts

121 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
0.3b	(pow (* (sin b) (sin a)) 3)
22.5b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

13.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
10.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
5.0ms	(pow (* (sin b) (sin a)) 3)
3.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series105.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
18.0ms	(pow (* (sin b) (sin a)) 3)
9.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5005	1662

prune184.0ms

Filtered

84 candidates to 118 candidates (-40.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	117	16	133

Merged error: 0.0b

Counts

133 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a))))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a))))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a)))))
3.7b	(log (pow (exp (sin b)) (sin a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
14×	`log-prod`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`associate--r+`
6×	`pow1` `unpow-prod-down`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `rem-log-exp` `associate-l` `associate-/r` `flip--` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `-commutative`

Counts

4 → 99

Calls

4 calls:

7.0ms	(- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a))))
10.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a))))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a)))))
3.0ms	(log (pow (exp (sin b)) (sin a)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a))))
60.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a))))))
38.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin b)) (sin a)))))
24.0ms	(log (pow (exp (sin b)) (sin a)))

simplify38.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5053	1743

prune93.0ms

Filtered

82 candidates to 111 candidates (-35.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	110	17	127

Merged error: 0.0b

Counts

127 → 17

regimes345.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	19
1	18	19

end0.0ms

analyze1.0s

Algorithm

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

sample2.7s

Algorithm

intervals

Results

1.6s	2952×	body	1280	valid
524.0ms	1790×	body	640	valid
158.0ms	767×	body	320	valid
154.0ms	2168×	body	80	valid
48.0ms	323×	body	160	valid
0.0ms	1×	body	640	invalid

Details

analyze1.1s

sample87.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite16.0ms

series40.0ms

simplify54.0ms

prune112.0ms

localize15.0ms

rewrite30.0ms

series102.0ms

simplify55.0ms

prune183.0ms

localize19.0ms

rewrite33.0ms

series105.0ms

simplify49.0ms

prune184.0ms

localize20.0ms

rewrite31.0ms

series148.0ms

simplify38.0ms

prune93.0ms

regimes345.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0s

sample2.7s

Profiling