Details

sample273.0ms

Algorithm

intervals

Results

205.0ms	157×	body	1280	valid
37.0ms	53×	body	640	valid
6.0ms	24×	body	80	valid
6.0ms	13×	body	320	valid
2.0ms	9×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 13.7b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(sin (- lambda1 lambda2))
2.1b	(cos (- lambda1 lambda2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

7.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
9.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series194.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune426.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	81	17	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	17	99

Merged error: 7.1b

Counts

99 → 17

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.1b	(cos (- lambda1 lambda2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
10×	`prod-diff`
6×	`associate-r` `add-log-exp`
5×	`cos-diff`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-*l/`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `*-commutative` `flip--` `associate--r+`
1×	`fma-neg` `diff-log` `sin-cos-mult` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

4.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series374.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
124.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify57.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	493	1137
1	1784	957
2	5001	955

prune503.0ms

Filtered

96 candidates to 64 candidates (66.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	9	7	16
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Merged error: 0.1b

Counts

113 → 12

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 92

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos lambda1) (sin lambda2))
49.0ms	(* (sin lambda1) (sin lambda2))
124.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
171.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify72.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	524	989
1	2555	869
2	5001	869

prune574.0ms

Filtered

104 candidates to 75 candidates (72.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	93	11	104
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	99	17	116

Merged error: 0.0b

Counts

116 → 17

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`associate-*l/`
1×	`flip3--` `flip--` `sin-mult`

Counts

4 → 83

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (sin phi1) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos lambda1) (sin lambda2))
47.0ms	(* (sin lambda1) (sin lambda2))
124.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
192.0ms	(* (sin phi1) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)))

simplify46.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	363	810
1	1541	687
2	5002	687

prune418.0ms

Filtered

95 candidates to 68 candidates (71.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	96	16	112

Merged error: 0.0b

Counts

112 → 16

regimes620.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	24
1	30	24

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.3s	4596×	body	1280	valid
1.5s	1927×	body	640	valid
283.0ms	574×	body	320	valid
97.0ms	685×	body	80	valid
67.0ms	218×	body	160	valid