Details

sample144.0ms

Algorithm

intervals

Results

36.0ms	254×	body	80	valid
27.0ms	46×	body	640	valid
19.0ms	26×	body	1280	valid
12.0ms	28×	body	320	valid
3.0ms	8×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
5	1878
4	761
3	231
2	72
1	34
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
1.6b	(cos (/ (+ phi2 phi1) 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
19.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
9.0ms	(cos (/ (+ phi2 phi1) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

559.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
723.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
171.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
47.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify2.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	4293
2	1093
1	359
0	142

prune709.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2))))
1.6b	(cos (* 0.5 (+ phi1 phi2)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `hypot-udef` `distribute-lft-in` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 65

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2))
12.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2)) R)
63.0ms	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2))))
8.0ms	(cos (* 0.5 (+ phi1 phi2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

572.0ms	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2))
754.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2)) R)
130.0ms	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2))))
49.0ms	(cos (* 0.5 (+ phi1 phi2)))

simplify2.5s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	4332
2	1095
1	375
0	155

prune749.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))) (- phi1 phi2)) R)
0.1b	(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
0.1b	(* (- lambda1 lambda2) (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
0.2b	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`flip3--` `associate-r` `flip--` `sin-mult`
8×	`frac-times` `cos-mult`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `frac-sub` `log1p-expm1-u` `sub-div`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*l/`
1×	`fma-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 101

Calls

4 calls:

9.0ms	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))) (- phi1 phi2)) R)
80.0ms	(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
274.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
23.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

series24.3s

Counts

4 → 12

Calls

4 calls:

23.7s	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))) (- phi1 phi2)) R)
160.0ms	(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
347.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
91.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

simplify4.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	3855
1	911
0	314

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (- phi1 phi2)) R)
0.1b	(fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
0.1b	(* (- lambda1 lambda2) (fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
0.2b	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
2×	`associate-*l/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--` `sin-mult` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 77

Calls

4 calls:

11.0ms	(* (hypot (* (- lambda1 lambda2) (fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (- phi1 phi2)) R)
0.0ms	(fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
35.0ms	(* (- lambda1 lambda2) (fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
29.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

series23.2s

Counts

4 → 12

Calls

4 calls:

22.6s	(* (hypot (* (- lambda1 lambda2) (fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (- phi1 phi2)) R)
203.0ms	(fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
355.0ms	(* (- lambda1 lambda2) (fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
98.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

simplify4.5s

Counts

89 → 89

Iterations

Iter	Nodes
done	5009
2	2946
1	744
0	264

prune919.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes661.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	31
2	31
1	29
0	20

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	8430×	body	80	valid
1.0s	1221×	body	640	valid
708.0ms	785×	body	1280	valid
279.0ms	740×	body	320	valid
113.0ms	350×	body	160	valid