Details

Time bar (total: 48.3s)

sample243.0ms

Algorithm
intervals
Results
103.0ms48×body1280valid
51.0ms45×body640valid
36.0ms127×body80valid
24.0ms27×body320valid
5.0ms9×body160valid

simplify244.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
244.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize28.0ms

Local error

Found 4 expressions with local error:

8.7b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
0.1b
(* J (* (cos (/ K 2)) 2))
0.1b
(* (cos (/ K 2)) (* -2 J))
0.1b
(/ U (* J (* (cos (/ K 2)) 2)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
9×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-*r* *-commutative associate-/l*
1×clear-num associate-/r* frac-2neg div-inv
Counts
4 → 92
Calls
4 calls:
Slowest
60.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
23.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
20.0ms
(* (cos (/ K 2)) (* -2 J))
16.0ms
(* J (* (cos (/ K 2)) 2))

series570.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
311.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
113.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
87.0ms
(* (cos (/ K 2)) (* -2 J))
59.0ms
(* J (* (cos (/ K 2)) 2))

simplify7.0s

Counts
55 → 104
Calls
55 calls:
Slowest
530.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
463.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
451.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
451.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
386.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J))))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize72.0ms

Local error

Found 4 expressions with local error:

8.7b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1 add-exp-log
23×add-cbrt-cube
22×pow-prod-down prod-exp cbrt-unprod
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
1×associate-*r* *-commutative
Counts
4 → 78
Calls
4 calls:
Slowest
194.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
2.0ms
(cbrt (cos (/ K 2)))
2.0ms
(cbrt (cos (/ K 2)))
2.0ms
(cbrt (cos (/ K 2)))

series819.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
170.0ms
(cbrt (cos (/ K 2)))
142.0ms
(cbrt (cos (/ K 2)))
136.0ms
(cbrt (cos (/ K 2)))

simplify11.6s

Counts
45 → 90
Calls
45 calls:
Slowest
859.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
778.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
734.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
556.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (cos (/ K 2)) (cos (/ K 2))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
554.0ms
(+ (log (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (+ (+ (log (cbrt (cos (/ K 2)))) (log (cbrt (cos (/ K 2))))) (+ (log (cbrt (cos (/ K 2)))) (+ (log -2) (log J)))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize49.0ms

Local error

Found 4 expressions with local error:

8.7b
(* J (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
0.1b
(* (* -2 (cos (/ K 2))) (* J (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))))
0.1b
(/ (/ U J) (* 2 (cos (/ K 2))))
0.0b
(hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-cbrt-cube add-exp-log
22×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×pow1
13×associate-/l*
11×prod-exp cbrt-unprod
9×pow-prod-down
6×cbrt-undiv div-exp
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×*-commutative
1×hypot-udef clear-num associate-/r* frac-2neg unswap-sqr associate-/l/
Counts
4 → 106
Calls
4 calls:
Slowest
39.0ms
(* (* -2 (cos (/ K 2))) (* J (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))))
21.0ms
(/ (/ U J) (* 2 (cos (/ K 2))))
6.0ms
(* J (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
0.0ms
(hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
306.0ms
(* (* -2 (cos (/ K 2))) (* J (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))))
288.0ms
(* J (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
283.0ms
(hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))
146.0ms
(/ (/ U J) (* 2 (cos (/ K 2))))

simplify7.5s

Counts
81 → 118
Calls
81 calls:
Slowest
521.0ms
(* (* (* J J) J) (* (* (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))) (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))))
368.0ms
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
349.0ms
(* (* (* (* -2 (cos (/ K 2))) (* -2 (cos (/ K 2)))) (* -2 (cos (/ K 2)))) (* (* (* J J) J) (* (* (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))) (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))))
343.0ms
(* (* (* (* -2 -2) -2) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2)))) (* (* (* J J) J) (* (* (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))) (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))))
330.0ms
(- (- (log U) (log J)) (+ (log 2) (log (cos (/ K 2)))))

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize66.0ms

Local error

Found 4 expressions with local error:

9.0b
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
9.0b
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
9.0b
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
2.1b
(* J (* (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt pow1 add-exp-log
8×*-un-lft-identity add-cube-cbrt
7×add-cbrt-cube
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l* pow-prod-down prod-exp cbrt-unprod
1×associate-*r* *-commutative unswap-sqr
Counts
4 → 64
Calls
4 calls:
Slowest
29.0ms
(* J (* (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))))
1.0ms
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
1.0ms
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
1.0ms
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
407.0ms
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
397.0ms
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
377.0ms
(cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))
329.0ms
(* J (* (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))))

simplify4.2s

Counts
32 → 76
Calls
32 calls:
Slowest
450.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
438.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
385.0ms
(* J (exp (* 1/3 (- (+ (log 1/4) (* 2 (log U))) (* 2 (log J))))))
365.0ms
(* (* (* J J) J) (* (* (* (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2))))))) (* (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))))) (* (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))) (cbrt (hypot 1 (/ (/ U J) (* 2 (cos (/ K 2)))))))))
321.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.2b

regimes620.0ms

Accuracy

-22.7% (4.9b remaining)

Error of 8.5b against oracle of 3.6b and baseline of 7.6b

bsearch140.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.4s1516×body1280valid
1.7s1233×body640valid
1.2s4297×body80valid
488.0ms619×body320valid
145.0ms335×body160valid