Details

sample231.0ms

Algorithm

intervals

Results

74.0ms	292×	body	80	valid
51.0ms	48×	body	640	valid
33.0ms	15×	body	160	valid
27.0ms	20×	body	1280	valid
14.0ms	18×	body	320	valid

simplify1.6s

Counts: 1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize43.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (/ (+ phi2 phi1) 2))
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

rewrite43.0ms

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` `insert-posit16` `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 → 67

Calls

4 calls:

Slowest

23.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
10.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
9.0ms	(cos (/ (+ phi2 phi1) 2))
0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

641.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
477.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
135.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
31.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.3s

Counts: 79 → 79

prune1000.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize67.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (/ (+ phi2 phi1) 2))
0.5b	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.2b	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
0.1b	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`associate-l` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `expm1-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

Slowest

32.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
14.0ms	(cos (/ (+ phi2 phi1) 2))
1.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
89.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
73.0ms	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
39.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.8s

Counts: 71 → 71

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize40.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (* 1/2 (+ phi1 phi2)))
0.1b	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.0b	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))

rewrite46.0ms

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` `insert-posit16` `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 → 69

Calls

4 calls:

Slowest

28.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
8.0ms	(cos (* 1/2 (+ phi1 phi2)))
6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.0ms	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

608.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
530.0ms	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
110.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
24.0ms	(cos (* 1/2 (+ phi1 phi2)))

simplify1.5s

Counts: 81 → 81

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
0.2b	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
0.1b	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
0.1b	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))) (- phi1 phi2)) R)

rewrite411.0ms

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` `insert-posit16` `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 → 105

Calls

4 calls:

Slowest

287.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
77.0ms	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
40.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
6.0ms	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))) (- phi1 phi2)) R)

series22.4s

Counts

4 → 12

Calls

4 calls:

Slowest

21.8s	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))) (- phi1 phi2)) R)
342.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
151.0ms	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
91.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

simplify3.4s

Counts: 117 → 117

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes622.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch6.0ms

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.3s	8433×	body	80	valid
1.6s	1311×	body	640	valid
1.2s	784×	body	1280	valid
905.0ms	723×	body	320	valid
198.0ms	329×	body	160	valid