Details

sample270.0ms

Algorithm

intervals

Results

187.0ms	139×	body	1280	valid
52.0ms	75×	body	640	valid
8.0ms	17×	body	320	valid
2.0ms	8×	body	160	valid
2.0ms	17×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 13.9b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(sin (- lambda1 lambda2))
4.0b	(cos (- lambda1 lambda2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-l` `prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
9×	`associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sub-neg` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff`

Counts

4 → 99

Calls

4 calls:

8.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(sin (- lambda1 lambda2))
6.0ms	(cos (- lambda1 lambda2))

series197.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
93.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify53.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	450	1132
1	1340	897
2	5002	871

prune466.0ms

Filtered

111 candidates to 75 candidates (67.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	11	112

Merged error: 7.7b

Counts

112 → 11

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.1b	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(cos (- lambda1 lambda2))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
153×	`prod-diff`
99×	`*-un-lft-identity`
97×	`associate-l`
91×	`add-cube-cbrt`
84×	`associate-r`
34×	`unswap-sqr`
28×	`*-commutative`
12×	`fma-neg`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`cos-diff`
2×	`sub-neg`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `diff-log` `associate-*l/` `sin-cos-mult` `flip--`

Counts

4 → 255

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin lambda2))
21.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(cos (- lambda1 lambda2))

series255.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos lambda1) (sin lambda2))
94.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
95.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify100.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	891	5175
1	2701	3689
2	5001	3496

prune757.0ms

Filtered

267 candidates to 100 candidates (37.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	260	7	267
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	270	8	278

Merged error: 0.1b

Counts

278 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.1b	(+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-sqr-sqrt`
144×	`prod-diff`
112×	`*-un-lft-identity`
108×	`associate-l`
91×	`associate-r`
88×	`add-cube-cbrt`
35×	`unswap-sqr`
29×	`*-commutative`
12×	`fma-def` `fma-neg`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod` `log1p-expm1-u` `sin-mult` `distribute-lft-out--` `difference-of-squares`
3×	`+-commutative` `frac-times` `flip3-+` `associate-*r/` `frac-add` `cos-mult` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`sub-neg` `flip3--` `diff-log` `associate-*l/` `sum-log` `flip--`

Counts

4 → 277

Calls

4 calls:

21.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
20.0ms	(+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
5.0ms	(* (sin lambda1) (sin lambda2))
25.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
83.0ms	(+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
46.0ms	(* (sin lambda1) (sin lambda2))
185.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify335.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	973	5409
1	3634	3969
2	5001	3968

prune958.0ms

Filtered

289 candidates to 127 candidates (43.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	281	8	289
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	288	9	297

Merged error: 0.0b

Counts

297 → 9

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 84

Calls

4 calls:

7.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))

series415.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
99.0ms	(cbrt (sin lambda2))
100.0ms	(cbrt (sin lambda2))
101.0ms	(cbrt (sin lambda2))

simplify101.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	168	520
1	612	447
2	3597	404
3	5001	398

prune522.0ms

Filtered

96 candidates to 68 candidates (70.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	96	9	105

Merged error: 0.0b

Counts

105 → 9

regimes377.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	32
1	37	32

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.9s	4529×	body	1280	valid
1.4s	1989×	body	640	valid
267.0ms	578×	body	320	valid
101.0ms	705×	body	80	valid
64.0ms	199×	body	160	valid