Details

Time bar (total: 1.2m)

sample540.0ms

Algorithm
intervals
Results
339.0ms94×body1280valid
66.0ms50×body640valid
22.0ms83×body80valid
17.0ms17×body320valid
7.0ms12×body160valid

simplify897.0ms

Calls
1 calls:
Slowest
896.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.1b

localize52.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
0.1b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b
(hypot (sin kx) (sin ky))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
19×times-frac
13×associate-*r*
10×add-cbrt-cube add-exp-log
9×associate-*r/
7×associate-/l*
6×associate-/r*
5×pow1
3×expm1-log1p-u clear-num associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp prod-exp un-div-inv cbrt-unprod div-inv unswap-sqr
1×hypot-udef pow-prod-down *-commutative
Calls
3 calls:
Slowest
39.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
17.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series790.0ms

Calls
3 calls:
Slowest
389.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
241.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
160.0ms
(hypot (sin kx) (sin ky))

simplify3.7s

Calls
69 calls:
Slowest
488.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
412.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky)))))
347.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
320.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
285.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

localize6.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.2b
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
0.1b
(hypot (sin kx) (sin ky))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-/r*
10×add-cbrt-cube add-exp-log
9×associate-/r/ associate-/l*
6×div-inv
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×hypot-udef
Calls
3 calls:
Slowest
25.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
11.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series715.0ms

Calls
3 calls:
Slowest
300.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
271.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
144.0ms
(hypot (sin kx) (sin ky))

simplify7.9s

Calls
140 calls:
Slowest
576.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
436.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
430.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
419.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
406.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))

prune1.8s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.9b

localize9.0ms

Local error

Found 4 expressions with local error:

1.1b
(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.2b
(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
0.1b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b
(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
9×times-frac
8×add-cbrt-cube add-exp-log
6×pow1
5×expm1-log1p-u log1p-expm1-u
4×insert-posit16 add-log-exp
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×expm1-log1p
1×cbrt-undiv log1p-udef clear-num frac-2neg div-exp pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod div-inv expm1-udef unswap-sqr
Calls
4 calls:
Slowest
14.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
10.0ms
(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
1.0ms
(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms
(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))

series1.3s

Calls
4 calls:
Slowest
375.0ms
(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
335.0ms
(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
317.0ms
(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))
224.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify4.1s

Calls
50 calls:
Slowest
526.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
357.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
322.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
306.0ms
(log (+ (* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky)) 1))
300.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.4s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 8.9b

localize10.0ms

Local error

Found 4 expressions with local error:

5.8b
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))
5.8b
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))
5.8b
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))
0.5b
(* (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
297×cbrt-div
254×associate-*r/
216×add-sqr-sqrt
189×cbrt-prod
156×*-un-lft-identity
125×add-cube-cbrt
121×frac-times
117×associate-*r*
108×associate-/l*
81×associate-/r*
78×times-frac
54×clear-num un-div-inv
49×associate-*l*
46×unswap-sqr
28×swap-sqr
27×frac-2neg
11×pow1 associate-*l/
9×pow1/3
8×add-cbrt-cube *-commutative
7×div-inv
6×add-exp-log
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp
Calls
4 calls:
Slowest
133.0ms
(* (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))))
26.0ms
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))
23.0ms
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))
21.0ms
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))

series1.8s

Calls
4 calls:
Slowest
455.0ms
(* (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))))
455.0ms
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))
429.0ms
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))
426.0ms
(cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))

simplify27.6s

Calls
533 calls:
Slowest
540.0ms
(* (* (* (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))) (* (* (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))))
529.0ms
(* (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))) (* (* (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))))
505.0ms
(* (cbrt (* (sin th) (sqrt (sin ky)))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))))
483.0ms
(* (* (* (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))) (cbrt (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))) (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))
444.0ms
(* (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))) (* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky)))))

prune6.7s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 8.9b

regimes984.0ms

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.7b and baseline of 8.9b

bsearch1.0ms

end0.0ms

sample11.9s

Algorithm
intervals
Results
6.0s2785×body1280valid
2.9s1783×body640valid
1.7s739×body320valid
730.0ms2321×body80valid
331.0ms372×body160valid