Details

Time bar (total: 35.0s)

sample188.0ms

Algorithm
intervals
Results
64.0ms42×body640valid
56.0ms49×body1280valid
29.0ms132×body80valid
16.0ms25×body320valid
3.0ms8×body160valid

simplify232.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
232.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.3b

localize44.0ms

Local error

Found 4 expressions with local error:

9.3b
(* (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)))

rewrite154.0ms

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
62.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
34.0ms
(* J (* (cos (/ K 2)) 2))
29.0ms
(* (cos (/ K 2)) (* -2 J))
27.0ms
(/ U (* J (* (cos (/ K 2)) 2)))

series537.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
109.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
68.0ms
(* J (* (cos (/ K 2)) 2))
68.0ms
(* (cos (/ K 2)) (* -2 J))

simplify6.8s

Counts
55 → 104
Calls
55 calls:
Slowest
487.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
464.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
418.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
382.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
355.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize31.0ms

Local error

Found 4 expressions with local error:

9.3b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.3b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
0.2b
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
0.1b
(* J (* (cos (/ K 2)) 2))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1
18×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
9×*-un-lft-identity associate-*l* pow-prod-down prod-exp add-cube-cbrt sqrt-prod cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 80
Calls
4 calls:
Slowest
60.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
14.0ms
(* J (* (cos (/ K 2)) 2))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series847.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
298.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
192.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
55.0ms
(* J (* (cos (/ K 2)) 2))

simplify4.1s

Counts
45 → 92
Calls
45 calls:
Slowest
473.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
438.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
341.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J))))
303.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J))))
291.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J))))

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.5b

localize104.0ms

Local error

Found 4 expressions with local error:

9.5b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.5b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.5b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.3b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
Slowest
2.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
370.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
351.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
347.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
256.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify2.9s

Counts
26 → 70
Calls
26 calls:
Slowest
463.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
450.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
410.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
276.0ms
(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))
261.0ms
(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.5b

localize106.0ms

Local error

Found 4 expressions with local error:

9.5b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.5b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.5b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.5b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
Slowest
1.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
362.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
353.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
349.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
326.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify3.3s

Counts
24 → 68
Calls
24 calls:
Slowest
439.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
402.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
393.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
387.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
292.0ms
(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))

prune1.6s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 4.5b

regimes584.0ms

Accuracy

-18.4% (4.7b remaining)

Error of 8.3b against oracle of 3.5b and baseline of 7.5b

bsearch158.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.3s1530×body1280valid
1.8s1175×body640valid
1.6s4363×body80valid
581.0ms649×body320valid
139.0ms285×body160valid