Details

Time bar (total: 37.2s)Debug log

sample138.0ms

Algorithm
intervals
Results
44.0ms51×body1280valid
41.0ms139×body80valid
27.0ms42×body640valid
7.0ms16×body320valid
2.0ms8×body160valid

simplify272.0ms

Calls
1 calls:
Slowest
272.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize49.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
4.2b
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
0.2b
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
0.1b
(* (* -2 J) (cos (/ K 2)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×add-exp-log
12×pow1
11×add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt
9×associate-*r*
9×*-un-lft-identity
6×sqrt-prod
4×add-log-exp
4×cbrt-unprod
4×prod-exp
4×pow-prod-down
4×sqrt-div
4×unpow-prod-down
2×flip-+
2×*-commutative
2×associate-*r/
2×associate-*l*
2×flip3-+
1×unpow2
1×div-inv
1×pow-exp
1×pow1/2
1×pow-pow
1×rem-sqrt-square
1×pow-to-exp
Calls
4 calls:
Slowest
16.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
8.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
4.0ms
(* (* -2 J) (cos (/ K 2)))
3.0ms
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)

series370.0ms

Calls
4 calls:
Slowest
109.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
105.0ms
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
104.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
52.0ms
(* (* -2 J) (cos (/ K 2)))

simplify5.9s

Calls
45 calls:
Slowest
612.0ms
(sqrt (+ (pow 1 3) (pow (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) 3)))
433.0ms
(sqrt (+ (* 1 1) (- (* (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)) (* 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
373.0ms
(sqrt (- 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
269.0ms
(+ (+ (log (* -2 J)) (log (cos (/ K 2)))) (log (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
265.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune921.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.9b

localize19.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
9.4b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
4.3b
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
4.3b
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×add-cube-cbrt
10×*-un-lft-identity
6×rem-sqrt-square
4×add-log-exp
4×flip-+
4×add-exp-log
4×pow1/2
4×add-cbrt-cube
4×flip3-+
4×pow1
Calls
4 calls:
Slowest
18.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
12.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
12.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
7.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

series558.0ms

Calls
4 calls:
Slowest
206.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
184.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
90.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
78.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify6.3s

Calls
44 calls:
Slowest
257.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
257.0ms
(sqrt (sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
256.0ms
(sqrt (+ (pow 1 3) (pow (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) 3)))
245.0ms
(sqrt (sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
245.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) 3))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.9b

localize17.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
4.2b
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
18×pow1
13×add-cbrt-cube
10×cbrt-unprod
10×prod-exp
10×pow-prod-down
10×add-sqr-sqrt
9×add-cube-cbrt
9×*-un-lft-identity
6×sqrt-prod
6×associate-*r*
6×cbrt-prod
4×add-log-exp
4×sqrt-div
2×flip-+
2×associate-*r/
2×pow1/3
2×flip3-+
1×*-commutative
1×associate-*l*
1×pow1/2
1×rem-sqrt-square
Calls
4 calls:
Slowest
104.0ms
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
12.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))

series457.0ms

Calls
4 calls:
Slowest
128.0ms
(cbrt (cos (/ K 2)))
119.0ms
(cbrt (cos (/ K 2)))
114.0ms
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
97.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify5.0s

Calls
45 calls:
Slowest
376.0ms
(sqrt (+ (* 1 1) (- (* (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)) (* 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
346.0ms
(sqrt (- 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
249.0ms
(cbrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
232.0ms
(sqrt (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
226.0ms
(sqrt (* (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.9b

localize35.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
4.2b
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (log (exp (cbrt (cos (/ K 2))))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
18×pow1
14×add-cbrt-cube
10×cbrt-unprod
10×prod-exp
10×pow-prod-down
10×add-sqr-sqrt
9×add-cube-cbrt
9×*-un-lft-identity
6×sqrt-prod
6×associate-*r*
6×cbrt-prod
4×add-log-exp
4×sqrt-div
2×flip-+
2×associate-*r/
2×pow1/3
2×flip3-+
1×*-commutative
1×associate-*l*
1×pow1/2
1×rem-sqrt-square
Calls
4 calls:
Slowest
111.0ms
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (log (exp (cbrt (cos (/ K 2))))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
10.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))

series421.0ms

Calls
4 calls:
Slowest
123.0ms
(cbrt (cos (/ K 2)))
119.0ms
(cbrt (cos (/ K 2)))
104.0ms
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (log (exp (cbrt (cos (/ K 2))))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
76.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify6.0s

Calls
45 calls:
Slowest
593.0ms
(sqrt (+ (pow 1 3) (pow (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) 3)))
468.0ms
(sqrt (+ (* 1 1) (- (* (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)) (* 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
436.0ms
(sqrt (- 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
277.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
257.0ms
(sqrt (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.9b

regimes759.0ms

Accuracy

80.7% (1.0b remaining)

Error of 13.6b against oracle of 12.6b and baseline of 17.8b

bsearch8.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.1s1537×body1280valid
1.7s1250×body640valid
1.4s4276×body80valid
463.0ms613×body320valid
209.0ms325×body160valid