Details

sample128.0ms

Algorithm

intervals

Results

37.0ms	52×	body	640	valid
28.0ms	257×	body	80	valid
18.0ms	26×	body	1280	valid
10.0ms	29×	body	320	valid
2.0ms	10×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	259	16
4	1055	16
done	5001	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
1.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
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 (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
8.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
45.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

565.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
752.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
151.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
44.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.0s

Counts

75 → 75

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	139	1279
1	335	1271
2	1431	1079
done	5002	1069

prune371.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (pow (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) 1) (- phi1 phi2))
0.1b	(* (hypot (pow (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) 1) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
1.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
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:

1.0ms	(hypot (pow (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) 1) (- phi1 phi2))
15.0ms	(* (hypot (pow (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) 1) (- phi1 phi2)) R)
49.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
21.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

575.0ms	(hypot (pow (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) 1) (- phi1 phi2))
667.0ms	(* (hypot (pow (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) 1) (- phi1 phi2)) R)
147.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
58.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify803.0ms

Counts

75 → 75

Iterations

Useful iterations: done (800.0ms)

Iter	Nodes	Cost
0	141	1357
1	347	1254
2	1523	1070
done	5000	1060

prune448.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
1.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`associate-*l/`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

78.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
4.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
6.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
13.0ms	(cos (/ (+ phi1 phi2) 2.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
39.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
87.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
53.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.2s

Counts

109 → 109

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	131	1572
1	323	1287
2	1951	1143
done	5001	1141

prune555.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
0.5b	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
1.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

84×	`cbrt-prod`
45×	`unpow-prod-down` `cube-prod`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`cube-mult` `unpow3` `sqr-pow`
6×	`pow1` `add-exp-log` `pow-unpow`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`pow-to-exp` `pow1/3` `pow-exp` `rem-cube-cbrt`
1×	`rem-cbrt-cube`

Counts

4 → 131

Calls

4 calls:

8.0ms	(cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3))
3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
7.0ms	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series206.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3))
74.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
62.0ms	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
29.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify788.0ms

Counts

143 → 143

Iterations

Useful iterations: done (782.0ms)

Iter	Nodes	Cost
0	126	2637
1	373	1747
2	1250	1548
done	5000	1544

prune489.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

regimes468.0ms

Accuracy

0% (0.2b remaining)

Error of 4.0b against oracle of 3.8b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	16	18
1	21	16
done	21	16

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.8s	800×	body	1280	valid
1.4s	8249×	body	80	valid
1.1s	1306×	body	640	valid
353.0ms	726×	body	320	valid
154.0ms	334×	body	160	valid