Details

Time bar (total: 31.8s)

sample206.0ms

Algorithm
intervals
Results
65.0ms48×body640valid
58.0ms262×body80valid
35.0ms27×body1280valid
24.0ms34×body320valid
3.0ms6×body160valid

simplify676.0ms

Calls
1 calls:
Slowest
676.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize31.0ms

Local error

Found 4 expressions with local error:

3.4b
(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))

rewrite88.0ms

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
Calls
4 calls:
Slowest
60.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
18.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.3s

Calls
4 calls:
Slowest
638.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
514.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
95.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
23.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.4s

Calls
34 calls:
Slowest
492.0ms
(* (* (* (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))
482.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
310.0ms
(- (+ (* 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))))))
280.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
276.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.1b

localize48.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (* (+ phi1 phi2) 1/2))
0.1b
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
0.0b
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))

rewrite69.0ms

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
Calls
4 calls:
Slowest
33.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
23.0ms
(cos (* (+ phi1 phi2) 1/2))
12.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))

series1.3s

Calls
4 calls:
Slowest
636.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
488.0ms
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))
119.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
37.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify3.8s

Calls
34 calls:
Slowest
543.0ms
(* (* (* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (* (* R R) R))
492.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
356.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
292.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (* (+ phi1 phi2) 1/2)))
276.0ms
(- (+ (* 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))))))

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize40.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (* (+ phi1 phi2) 1/2))
3.4b
(cos (* (+ phi1 phi2) 1/2))
3.4b
(cos (* (+ phi1 phi2) 1/2))
0.4b
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
23×add-sqr-sqrt
18×associate-*l*
11×*-un-lft-identity add-cube-cbrt
7×unswap-sqr
6×associate-*r*
4×expm1-log1p-u pow1 add-cbrt-cube swap-sqr add-exp-log *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×pow3 rem-cbrt-cube
1×cbrt-div pow1/3 associate-*l/ cos-mult
Calls
4 calls:
Slowest
100.0ms
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
49.0ms
(cos (* (+ phi1 phi2) 1/2))
36.0ms
(cos (* (+ phi1 phi2) 1/2))
25.0ms
(cos (* (+ phi1 phi2) 1/2))

series129.0ms

Calls
4 calls:
Slowest
37.0ms
(cos (* (+ phi1 phi2) 1/2))
34.0ms
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
34.0ms
(cos (* (+ phi1 phi2) 1/2))
23.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify3.1s

Calls
43 calls:
Slowest
402.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
400.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
347.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
314.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
245.0ms
(cbrt (* (+ (cos (+ (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2))) (cos (- (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2)))) (cos (* (+ phi1 phi2) 1/2))))

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

localize46.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (* (+ phi1 phi2) 1/2))
0.6b
(cbrt (- lambda1 lambda2))
0.6b
(cbrt (- lambda1 lambda2))
0.6b
(cbrt (- lambda1 lambda2))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
49.0ms
(cos (* (+ phi1 phi2) 1/2))
6.0ms
(cbrt (- lambda1 lambda2))
5.0ms
(cbrt (- lambda1 lambda2))
5.0ms
(cbrt (- lambda1 lambda2))

series564.0ms

Calls
4 calls:
Slowest
193.0ms
(cbrt (- lambda1 lambda2))
182.0ms
(cbrt (- lambda1 lambda2))
164.0ms
(cbrt (- lambda1 lambda2))
26.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify4.2s

Calls
33 calls:
Slowest
595.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 lambda1)))))
577.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 lambda1)))))
561.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 lambda1)))))
437.0ms
(- (exp (* 1/3 (+ (log -1) (log lambda2)))) (+ (* 1/9 (* (exp (* 1/3 (- (log -1) (* 5 (log lambda2))))) (pow lambda1 2))) (* 1/3 (* (exp (* 1/3 (- (log -1) (* 2 (log lambda2))))) lambda1))))
436.0ms
(- (exp (* 1/3 (+ (log -1) (log lambda2)))) (+ (* 1/9 (* (exp (* 1/3 (- (log -1) (* 5 (log lambda2))))) (pow lambda1 2))) (* 1/3 (* (exp (* 1/3 (- (log -1) (* 2 (log lambda2))))) lambda1))))

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.1b

regimes981.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch4.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.5s8311×body80valid
1.8s1273×body640valid
1.1s814×body1280valid
557.0ms729×body320valid
194.0ms381×body160valid