Details

Time bar (total: 22.4s)

sample248.0ms

Algorithm
intervals
Results
71.0ms60×body640valid
68.0ms262×body80valid
62.0ms18×body1280valid
15.0ms18×body320valid
8.0ms12×body160valid

simplify254.0ms

Calls
1 calls:
Slowest
254.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize47.0ms

Local error

Found 4 expressions with local error:

2.8b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- 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))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*l* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×associate-*l/ *-commutative
1×hypot-udef flip3-- pow-prod-down prod-exp cbrt-unprod flip--
Calls
4 calls:
Slowest
12.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
5.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.4s

Calls
4 calls:
Slowest
665.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
538.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
147.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
33.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.2s

Calls
24 calls:
Slowest
317.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
296.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
281.0ms
(- (+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* phi1 (* R phi2)) (* (cos (* 1/2 (+ phi1 phi2))) lambda1)) (/ (* phi1 (* lambda2 (* R phi2))) (* (cos (* 1/2 (+ phi1 phi2))) (pow lambda1 2))))))
236.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
192.0ms
(- (+ (/ (* lambda2 (* phi1 phi2)) (* (cos (* 1/2 (+ phi1 phi2))) (pow lambda1 2))) (+ (/ (* phi1 phi2) (* (cos (* 1/2 (+ phi1 phi2))) lambda1)) (* lambda2 (cos (* 1/2 (+ phi1 phi2)))))))

prune987.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.2b

localize14.0ms

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- expm1-udef
Calls
4 calls:
Slowest
10.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
4.0ms
(cos (/ (+ phi2 phi1) 2))
1.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

series350.0ms

Calls
4 calls:
Slowest
177.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
74.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
70.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
29.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.2s

Calls
24 calls:
Slowest
409.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
331.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))))
329.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
282.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
230.0ms
(- E (+ (* 1/8 (* E (pow phi2 2))) (+ (* 1/4 (* E (* phi1 phi2))) 1)))

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.2b

localize15.0ms

Local error

Found 4 expressions with local error:

2.8b
(cos (/ (+ phi2 phi1) 2))
0.5b
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.4b
(log1p (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.2b
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×expm1-log1p-u log1p-expm1-u
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
2×log1p-udef log1p-expm1
1×expm1-log1p expm1-udef
Calls
4 calls:
Slowest
2.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms
(log1p (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

series231.0ms

Calls
4 calls:
Slowest
89.0ms
(log1p (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
62.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
52.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
28.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.6s

Calls
15 calls:
Slowest
367.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
357.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
314.0ms
(- (log 2) (+ (* 1/8 (* phi1 phi2)) (* 1/16 (pow phi2 2))))
273.0ms
(- E (+ (* 1/8 (* E (pow phi2 2))) (+ (* 1/4 (* E (* phi1 phi2))) 1)))
48.0ms
(- (exp (cos (* 1/2 (+ phi1 phi2)))) 1)

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.2b

localize15.0ms

Local error

Found 4 expressions with local error:

2.8b
(cos (/ (+ phi2 phi1) 2))
2.8b
(cos (/ (+ phi2 phi1) 2))
2.8b
(cos (/ (+ phi2 phi1) 2))
0.5b
(cbrt (* (* (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
7.0ms
(cbrt (* (* (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))))
2.0ms
(cos (/ (+ phi2 phi1) 2))
2.0ms
(cos (/ (+ phi2 phi1) 2))
2.0ms
(cos (/ (+ phi2 phi1) 2))

series168.0ms

Calls
4 calls:
Slowest
80.0ms
(cbrt (* (* (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))))
40.0ms
(cos (/ (+ phi2 phi1) 2))
26.0ms
(cos (/ (+ phi2 phi1) 2))
22.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.5s

Calls
14 calls:
Slowest
342.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
340.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
326.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
312.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
31.0ms
(cos (* 1/2 (+ phi1 phi2)))

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.2b

regimes900.0ms

Accuracy

0% (0.2b remaining)

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

bsearch5.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.6s8309×body80valid
1.7s1311×body640valid
1.5s822×body1280valid
620.0ms770×body320valid
179.0ms353×body160valid