Details

sample94.0ms

Algorithm

intervals

Results

45.0ms	90×	body	1280	valid
16.0ms	49×	body	640	valid
7.0ms	16×	body	160	valid
5.0ms	24×	body	320	valid
5.0ms	77×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

prune3.0ms

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: 14.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.7b	(cos (+ a b))

rewrite13.0ms

Algorithm

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:

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

series39.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
27.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify30.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune84.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 0.1b

Counts

57 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
6.0ms	(* r (sin b))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
48.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune133.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (* (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 → 100

Calls

4 calls:

5.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
7.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
47.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
28.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5002	1178

prune163.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	111	12	123

Merged error: 0.0b

Counts

123 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `times-frac` `prod-exp` `associate-/r*` `log-pow` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`exp-prod` `flip3--` `exp-to-pow` `frac-2neg` `rem-log-exp` `clear-num` `flip--` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

4.0ms	(* r (sin b))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
47.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
9.0ms	(log (exp (* (sin a) (sin b))))

simplify38.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	301	698
1	1309	580
2	5001	574

prune74.0ms

Filtered

61 candidates to 86 candidates (-41.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	86	12	98

Merged error: 0.0b

Counts

98 → 12

regimes262.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2925×	body	1280	valid
494.0ms	1810×	body	640	valid
145.0ms	732×	body	320	valid
135.0ms	2182×	body	80	valid
51.0ms	352×	body	160	valid

Details

sample94.0ms

simplify6.0ms

prune3.0ms

localize9.0ms

rewrite13.0ms

series39.0ms

simplify30.0ms

prune84.0ms

localize16.0ms

rewrite25.0ms

series82.0ms

simplify45.0ms

prune133.0ms

localize15.0ms

rewrite30.0ms

series100.0ms

simplify52.0ms

prune163.0ms

localize18.0ms

rewrite21.0ms

series71.0ms

simplify38.0ms

prune74.0ms

regimes262.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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