Details

sample142.0ms

Algorithm

intervals

Results

49.0ms	46×	body	640	valid
34.0ms	269×	body	80	valid
20.0ms	24×	body	1280	valid
9.0ms	26×	body	320	valid
3.0ms	11×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	257	16
4	826	16
5	2355	16
done	5000	16

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize30.0ms

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)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite76.0ms

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 (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
17.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
42.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

521.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
689.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
150.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
36.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.3s

Counts

75 → 75

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	139	1279
1	327	1271
2	960	1077
3	3194	1060
done	5000	1059

prune419.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize31.0ms

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)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite81.0ms

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)
48.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

601.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
708.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
156.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
42.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.7s

Counts

75 → 75

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	139	1279
1	327	1271
2	960	1077
3	3194	1060
done	5000	1059

prune380.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.0b

localize39.0ms

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)
2.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite100.0ms

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:

64.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
5.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
6.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
21.0ms	(cos (/ (+ phi1 phi2) 2.0))

series344.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
43.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
99.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
38.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.2s

Counts

109 → 109

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	131	1572
1	267	1275
2	862	1143
done	5000	1138

prune598.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3))
0.5b	(pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3)
0.6b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod` `log-pow`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`exp-prod`
14×	`unpow-prod-down` `cube-prod`
10×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 90

Calls

4 calls:

5.0ms	(cbrt (pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3))
27.0ms	(pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3)
35.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series206.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cbrt (pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3))
83.0ms	(pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3)
34.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.9s

Counts

102 → 102

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	113	1527
1	208	1063
2	438	959
3	2232	943
done	5001	939

prune496.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.0b

regimes501.0ms

Accuracy

0% (0.1b remaining)

Error of 3.6b against oracle of 3.4b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	22	16
done	22	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.7s	8426×	body	80	valid
1.0s	1319×	body	640	valid
786.0ms	778×	body	1280	valid
443.0ms	713×	body	320	valid
148.0ms	355×	body	160	valid