Details

sample273.0ms

Algorithm

intervals

Results

164.0ms	97×	body	1280	valid
54.0ms	56×	body	640	valid
18.0ms	75×	body	80	valid
14.0ms	21×	body	320	valid
3.0ms	7×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	22
1	61	22
2	71	22
3	72	22
4	72	22

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 72

Calls

4 calls:

4.0ms	(* (sin theta) (sin delta))
4.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin theta) (sin delta))
155.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
182.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify102.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	322	1198
1	1021	1064
2	4124	1059
3	5001	1054

prune479.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.8b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`log-prod`
7×	`pow1`
6×	`add-exp-log` `prod-diff` `add-cbrt-cube` `add-log-exp`
5×	`exp-sum`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-r` `associate-l`
2×	`sub-neg`
1×	`log-div` `asin-acos` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

4.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
5.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
180.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
180.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify102.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	294	1664
1	894	1453
2	3493	1344
3	5001	1338

prune506.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
1.2b	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
1.2b	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`log-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
12×	`prod-diff` `log-pow`
10×	`exp-sum`
8×	`pow1` `sqrt-pow1` `add-log-exp`
6×	`add-exp-log` `exp-prod` `fma-neg`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 96

Calls

4 calls:

3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.0ms	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
6.0ms	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

177.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
180.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
393.0ms	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
371.0ms	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	253	2712
1	607	2446
2	2215	2272
3	5003	2132

prune767.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
1.2b	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`prod-diff`
11×	`log-prod`
10×	`add-log-exp`
9×	`fma-neg`
8×	`sqrt-prod`
6×	`pow1` `log-pow`
5×	`add-exp-log` `exp-sum`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod` `flip3--` `diff-log` `flip--`
1×	`log-div` `pow1/2` `exp-diff` `sqrt-div` `rem-log-exp`

Counts

4 → 88

Calls

4 calls:

3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.0ms	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

series891.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
177.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
178.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
359.0ms	(log (sqrt (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	253	2446
1	607	2169
2	2215	2076
3	5003	1896

prune733.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes342.0ms

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	32	24
1	32	24

end0.0ms

sample8.8s

Algorithm

intervals

Results

5.5s	3145×	body	1280	valid
1.9s	1827×	body	640	valid
499.0ms	2022×	body	80	valid
471.0ms	698×	body	320	valid
141.0ms	308×	body	160	valid