Details

Time bar (total: 26.2s)

sample191.0ms

Algorithm
intervals
Results
74.0ms267×body80valid
38.0ms40×body640valid
37.0ms28×body1280valid
15.0ms25×body320valid
5.0ms9×body160valid

simplify393.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
393.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize36.0ms

Local error

Found 4 expressions with local error:

2.3b
(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))

rewrite40.0ms

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
24.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms
(cos (/ (+ phi2 phi1) 2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
703.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
561.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
140.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
38.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.5s

Counts
34 → 79
Calls
34 calls:
Slowest
497.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
447.0ms
(* (* (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (* R R) R))
398.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
304.0ms
(- (+ (* 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))))))
246.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.3b

localize54.0ms

Local error

Found 4 expressions with local error:

2.3b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

rewrite38.0ms

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
19.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
11.0ms
(cos (/ (+ phi2 phi1) 2))
6.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
756.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
477.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
129.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
34.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.4s

Counts
35 → 79
Calls
35 calls:
Slowest
422.0ms
(* (* (* R R) R) (* (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))))
415.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
353.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
294.0ms
(- (+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* R (* lambda2 (* phi1 phi2))) (* (cos (* 1/2 (+ phi1 phi2))) (pow lambda1 2))) (/ (* R (* phi1 phi2)) (* (cos (* 1/2 (+ phi1 phi2))) lambda1)))))
255.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.3b

localize35.0ms

Local error

Found 4 expressions with local error:

2.3b
(cos (/ (+ phi2 phi1) 2))
2.3b
(cos (/ (+ phi2 phi1) 2))
2.3b
(cos (/ (+ phi2 phi1) 2))
0.5b
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))

rewrite42.0ms

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 cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Counts
4 → 44
Calls
4 calls:
Slowest
18.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
8.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(cos (/ (+ phi2 phi1) 2))

series96.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
28.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
23.0ms
(cos (/ (+ phi2 phi1) 2))
23.0ms
(cos (/ (+ phi2 phi1) 2))
23.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.8s

Counts
15 → 56
Calls
15 calls:
Slowest
393.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
364.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
359.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
336.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
101.0ms
(cbrt (* (+ (cos (+ (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2))) (cos (- (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2)))) (cos (/ (+ phi2 phi1) 2))))

prune1.1s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.3b

localize65.0ms

Local error

Found 4 expressions with local error:

2.3b
(cos (/ (+ phi1 phi2) 2))
2.3b
(cos (/ (+ phi1 phi2) 2))
2.3b
(cos (+ (/ (+ phi1 phi2) 2) (/ (+ phi1 phi2) 2)))
1.0b
(cbrt 2)

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
1×cos-sum pow1/3
Counts
4 → 45
Calls
4 calls:
Slowest
92.0ms
(cos (+ (/ (+ phi1 phi2) 2) (/ (+ phi1 phi2) 2)))
8.0ms
(cos (/ (+ phi1 phi2) 2))
8.0ms
(cos (/ (+ phi1 phi2) 2))
1.0ms
(cbrt 2)

series77.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
32.0ms
(cos (/ (+ phi1 phi2) 2))
28.0ms
(cos (/ (+ phi1 phi2) 2))
17.0ms
(cos (+ (/ (+ phi1 phi2) 2) (/ (+ phi1 phi2) 2)))
0.0ms
(cbrt 2)

simplify1.3s

Counts
14 → 55
Calls
14 calls:
Slowest
402.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
347.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
225.0ms
(* R (hypot (* (- lambda1 lambda2) (/ (cbrt (fma (cos (/ (+ phi1 phi2) 2)) (cos (+ (/ (+ phi1 phi2) 2) (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))) (cbrt 2))) (- phi1 phi2)))
192.0ms
(- 1 (+ (* phi1 phi2) (* 1/2 (pow phi1 2))))
35.0ms
(cos (* 1/2 (+ phi1 phi2)))

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.3b

regimes922.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.5s8356×body80valid
2.1s1350×body640valid
1.1s780×body1280valid
542.0ms749×body320valid
146.0ms346×body160valid