Details

sample674.0ms

Algorithm

intervals

Results

378.0ms	154×	body	1280	valid
138.0ms	71×	body	640	valid
15.0ms	20×	body	320	valid
6.0ms	1×	body	2560	valid
3.0ms	7×	body	160	valid
1.0ms	3×	body	80	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	19
1	26	19
2	33	19
3	35	19
done	35	19

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.4b	(cos (- lambda1 lambda2))

rewrite75.0ms

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:

15.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
26.0ms	(* (sin phi1) (sin phi2))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
26.0ms	(cos (- lambda1 lambda2))

series233.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
92.0ms	(* (sin phi1) (sin phi2))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
50.0ms	(cos (- lambda1 lambda2))

simplify4.0s

Counts

67 → 67

Iterations

Useful iterations: 3 (349.0ms)

Iter	Nodes	Cost
0	111	1035
1	198	1027
2	439	889
3	727	887
4	962	887
5	1591	887
6	3482	887
done	5000	887

prune455.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.5b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

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*` `cos-mult`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`frac-times` `associate-*r/` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/`

Counts

4 → 76

Calls

4 calls:

158.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
17.0ms	(* (sin phi1) (sin phi2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
104.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
64.0ms	(* (sin phi1) (sin phi2))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	195	2211
1	472	2178
2	1673	1781
done	5000	1748

prune808.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (exp (log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.6b	(log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))
0.7b	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-prod`
6×	`associate-r`
4×	`exp-sum` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`acos-asin` `rem-log-exp` `log-pow` `sin-mult`

Counts

4 → 61

Calls

4 calls:

48.0ms	(* (exp (log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))) R)
26.0ms	(* (sin phi1) (sin phi2))
2.0ms	(log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))
5.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (exp (log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))) R)
69.0ms	(* (sin phi1) (sin phi2))
104.0ms	(log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))
37.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))

simplify4.6s

Counts

73 → 73

Iterations

Useful iterations: 4 (760.0ms)

Iter	Nodes	Cost
0	128	1973
1	230	1910
2	533	1588
3	900	1588
4	1138	1586
5	1825	1586
6	4052	1586
done	5000	1586

prune672.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin lambda2) (sin lambda2))
0.3b	(/ (* (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda2)) (* (sin lambda1) (sin lambda1))))) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda2)) (* (sin lambda1) (sin lambda1))))) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
27×	`add-exp-log` `associate-r/` `associate-l/` `add-cbrt-cube`
23×	`cos-mult`
20×	`sin-mult`
18×	`pow-prod-down`
16×	`associate-/l/`
12×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`frac-times` `frac-sub`
5×	`pow-sqr` `pow-prod-up` `sub-div`
4×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `pow-plus` `div-exp` `associate-/r*` `associate-/r/`
2×	`pow2` `*-commutative`
1×	`acos-asin` `flip3--` `frac-2neg` `flip3-+` `frac-add` `clear-num` `flip--` `flip-+` `sqr-sin` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

27.0ms	(* (sin lambda2) (sin lambda2))
971.0ms	(/ (* (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda2)) (* (sin lambda1) (sin lambda1))))) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
72.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda2)) (* (sin lambda1) (sin lambda1))))) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series889.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (sin lambda2) (sin lambda2))
699.0ms	(/ (* (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda2)) (* (sin lambda1) (sin lambda1))))) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
101.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
64.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda2)) (* (sin lambda1) (sin lambda1))))) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.7s

Counts

126 → 126

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	247	3429
1	623	2967
2	2461	2465
done	5000	2420

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.3b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	54
1	45	54
done	45	54

end0.0ms

sample18.7s

Algorithm

intervals

Results

14.0s	4713×	body	1280	valid
3.0s	2154×	body	640	valid
668.0ms	695×	body	320	valid
146.0ms	290×	body	160	valid
71.0ms	13×	body	2560	valid
35.0ms	136×	body	80	valid