Details

analyze2.8s

Algorithm: search

sample289.0ms

Algorithm

intervals

Results

197.0ms	148×	body	1280	valid
58.0ms	80×	body	640	valid
8.0ms	16×	body	320	valid
4.0ms	1×	body	2560	valid
2.0ms	7×	body	160	valid
1.0ms	4×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

prune10.0ms

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: 16.7b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.4b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.1b	(cos (- lambda1 lambda2))

rewrite14.0ms

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×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

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

series47.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
25.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	200	661
1	565	569
2	1790	569
3	5001	569

prune158.0ms

Filtered

49 candidates to 67 candidates (-36.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	54	13	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	13	68

Merged error: 3.1b

Counts

68 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.4b	(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×	`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 → 72

Calls

4 calls:

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

series111.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
9.0ms	(* (sin phi1) (sin phi2))
43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	486	1308
1	2165	1096
2	5001	1095

prune341.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	71	13	84
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	81	16	97

Merged error: 2.9b

Counts

97 → 16

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.4b	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`associate-l`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
4×	`difference-of-squares`
2×	`asin-acos` `flip3--` `times-frac` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`sub-neg` `diff-log` `sin-mult` `associate--r-`

Counts

4 → 66

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
9.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
1.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
7.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
64.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
14.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
22.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify75.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	282	1489
1	845	1348
2	3043	1342
3	5001	1342

prune189.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	80	14	94

Merged error: 2.8b

Counts

94 → 14

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
0.4b	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.4b	(exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
12×	`exp-prod`
9×	`add-log-exp`
7×	`add-cube-cbrt` `log-pow`
6×	`log-prod` `exp-sum` `difference-of-squares`
5×	`pow1`
4×	`add-exp-log` `asin-acos` `add-cbrt-cube`
3×	`sub-neg` `times-frac` `distribute-lft-out--` `associate--r-`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `flip3--` `rem-log-exp` `flip--`

Counts

4 → 65

Calls

4 calls:

7.0ms	(log (exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
1.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
7.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
9.0ms	(exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(log (exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
12.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
24.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
45.0ms	(exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify82.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	216	1747
1	491	1603
2	1032	1573
3	2811	1567
4	5002	1567

prune101.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	78	13	91

Merged error: 2.8b

Counts

91 → 13

regimes1.3s

Accuracy

0% (0.7b remaining)

Error of 4.0b against oracle of 3.2b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	57
1	39	57

end0.0ms

analyze2.8s

Algorithm: search

sample8.8s

Algorithm

intervals

Results

6.3s	4789×	body	1280	valid
1.6s	2167×	body	640	valid
317.0ms	635×	body	320	valid
94.0ms	270×	body	160	valid
29.0ms	9×	body	2560	valid
22.0ms	130×	body	80	valid
1.0ms	1×	body	640	invalid

Details

analyze2.8s

sample289.0ms

simplify6.0ms

prune10.0ms

localize25.0ms

rewrite14.0ms

series47.0ms

simplify49.0ms

prune158.0ms

localize34.0ms

rewrite21.0ms

series111.0ms

simplify65.0ms

prune341.0ms

localize34.0ms

rewrite23.0ms

series109.0ms

simplify75.0ms

prune189.0ms

localize38.0ms

rewrite26.0ms

series104.0ms

simplify82.0ms

prune101.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.8s

sample8.8s

Profiling