Details

sample79.0ms

Algorithm

intervals

Results

34.0ms	76×	body	1280	valid
16.0ms	61×	body	640	valid
5.0ms	85×	body	80	valid
5.0ms	26×	body	320	valid
1.0ms	8×	body	160	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

prune9.0ms

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: 13.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.2b	(cos (+ a b))

rewrite14.0ms

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))

series37.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify31.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

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

prune94.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

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: 0.2b

Counts

57 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))))

rewrite22.0ms

Algorithm

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:

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
51.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify46.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	367	682
1	1616	593
2	5001	592

prune140.0ms

Filtered

65 candidates to 93 candidates (-43.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	92	11	103

Merged error: 0.0b

Counts

103 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

4.0ms	(* r (sin b))
6.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
12.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
23.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))
51.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	474	1263
1	2419	1082
2	5001	1054

prune141.0ms

Filtered

75 candidates to 126 candidates (-68.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	124	13	137

Merged error: 0.0b

Counts

137 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(* (* r (sin b)) (* (/ 1 (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

96×	`pow1`
72×	`add-exp-log`
54×	`add-cbrt-cube`
43×	`pow-prod-down` `prod-exp`
35×	`associate-l`
31×	`cbrt-unprod`
26×	`cos-mult` `sin-mult`
25×	`associate-*r/`
20×	`add-sqr-sqrt`
16×	`frac-times` `associate-/r/`
14×	`-un-lft-identity` `times-frac` `associate-l/`
13×	`add-cube-cbrt`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
6×	`div-exp` `associate-r`
5×	`distribute-rgt-in` `distribute-lft-in` `sub-div`
4×	`flip3-+` `pow-plus` `frac-add` `*-commutative` `flip-+` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `difference-of-squares` `unswap-sqr`
2×	`pow2` `swap-sqr`
1×	`flip3--` `flip--` `div-inv`

Counts

4 → 177

Calls

4 calls:

24.0ms	(* (/ 1 (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
24.0ms	(* (* r (sin b)) (* (/ 1 (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ 1 (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
118.0ms	(* (* r (sin b)) (* (/ 1 (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify51.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1002	3521
1	5002	2767

prune191.0ms

Filtered

110 candidates to 189 candidates (-71.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	4	7	11
Picked	1	0	1
Done	1	0	1
Total	191	11	202

Merged error: 0b

Counts

202 → 11

regimes265.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	34
1	29	34

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2871×	body	1280	valid
488.0ms	1827×	body	640	valid
160.0ms	781×	body	320	valid
145.0ms	2191×	body	80	valid
50.0ms	331×	body	160	valid

Details

sample79.0ms

simplify6.0ms

prune9.0ms

localize11.0ms

rewrite14.0ms

series37.0ms

simplify31.0ms

prune94.0ms

localize14.0ms

rewrite22.0ms

series75.0ms

simplify46.0ms

prune140.0ms

localize16.0ms

rewrite29.0ms

series90.0ms

simplify62.0ms

prune141.0ms

localize21.0ms

rewrite73.0ms

series206.0ms

simplify51.0ms

prune191.0ms

regimes265.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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