Details

sample266.0ms

Algorithm

intervals

Results

193.0ms	150×	body	1280	valid
49.0ms	70×	body	640	valid
5.0ms	12×	body	320	valid
3.0ms	20×	body	80	valid
1.0ms	4×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(sin (- lambda1 lambda2))
2.9b	(cos (- lambda1 lambda2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
16.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series174.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify105.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372

prune307.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(cos (- lambda1 lambda2))

rewrite27.0ms

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`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 68

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (sin phi1) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series198.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos lambda1) (sin lambda2))
42.0ms	(* (sin phi1) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	299	481
1	1250	409
2	5002	409

prune410.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
5×	`sin-cos-mult`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin phi1) (cos phi2))
100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
45.0ms	(* (sin lambda1) (sin lambda2))
117.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	388	782
1	1793	604
2	5002	604

prune461.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (* (sin phi1) (cos phi2)))) (* (sin lambda1) (sin lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
3.2b	(log (exp (* (sin phi1) (cos phi2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
23×	`add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`log-pow` `add-log-exp`
5×	`associate-r`
3×	`log-prod` `*-commutative`
2×	`exp-prod` `exp-to-pow` `associate-*r/` `cos-mult` `sin-cos-mult` `sin-mult`
1×	`frac-times` `rem-log-exp` `associate-*l/` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

9.0ms	(* (log (exp (* (sin phi1) (cos phi2)))) (* (sin lambda1) (sin lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
1.0ms	(log (exp (* (sin phi1) (cos phi2))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (log (exp (* (sin phi1) (cos phi2)))) (* (sin lambda1) (sin lambda2)))
45.0ms	(* (sin lambda1) (sin lambda2))
116.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
49.0ms	(log (exp (* (sin phi1) (cos phi2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	362	744
1	1601	584
2	5001	581

prune453.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes377.0ms

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	37	31
1	37	31

end0.0ms

sample8.7s

Algorithm

intervals

Results

6.5s	4635×	body	1280	valid
1.5s	1990×	body	640	valid
257.0ms	544×	body	320	valid
95.0ms	613×	body	80	valid
63.0ms	218×	body	160	valid