Details

sample265.0ms

Algorithm

intervals

Results

190.0ms	161×	body	1280	valid
42.0ms	65×	body	640	valid
7.0ms	2×	body	2560	valid
6.0ms	14×	body	320	valid
3.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	12

prune5.0ms

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: 17.6b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b	(cos (- lambda1 lambda2))

rewrite20.0ms

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`
9×	`prod-diff`
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×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

8.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
6.0ms	(cos (- lambda1 lambda2))

series177.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
50.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify42.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	388	1113
1	1250	911
2	5001	909

prune337.0ms

Filtered

86 candidates to 59 candidates (68.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	71	15	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	15	87

Merged error: 2.7b

Counts

87 → 15

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin lambda1) (sin lambda2))
189.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	494	1387
1	2248	1185
2	5002	1184

prune445.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	80	12	92
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	92	15	107

Merged error: 2.6b

Counts

107 → 15

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.3b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

10.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
70.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
46.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	423	1492
1	1873	1256
2	5002	1247

prune480.0ms

Filtered

85 candidates to 62 candidates (72.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	85	15	100

Merged error: 2.6b

Counts

100 → 15

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `fma-udef` `sin-mult`

Counts

4 → 61

Calls

4 calls:

1.0ms	(fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))
5.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))
46.0ms	(* (sin phi1) (sin phi2))
52.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	202	940
1	636	816
2	2097	815
3	5001	814

prune318.0ms

Filtered

73 candidates to 56 candidates (76.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	63	10	73
Fresh	10	3	13
Picked	1	0	1
Done	0	1	1
Total	74	14	88

Merged error: 2.6b

Counts

88 → 14

regimes1.0s

Accuracy

0% (0.3b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	19
1	32	19

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.9s	4784×	body	1280	valid
1.4s	2106×	body	640	valid
313.0ms	687×	body	320	valid
77.0ms	268×	body	160	valid
23.0ms	151×	body	80	valid
20.0ms	6×	body	2560	valid