Details

Time bar (total: 4.2m)

sample1.3s

Algorithm
intervals
Results
225.0ms92×body1280valid
214.0ms75×body80valid
76.0ms54×body640valid
23.0ms25×body320valid
6.0ms10×body160valid

simplify473.0ms

Calls
1 calls:
Slowest
472.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize49.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.2b
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.2b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))

rewrite408.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
48×add-sqr-sqrt
46×associate-*r*
41×sqrt-prod
35×times-frac add-cube-cbrt
29×associate-*l*
25×distribute-lft-out
21×pow1
17×associate-*r/
16×swap-sqr
13×add-cbrt-cube add-exp-log
11×associate-/r*
6×sqrt-div sin-mult
5×unswap-sqr
4×prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×pow-prod-down associate-/r/ *-commutative
2×pow2 clear-num flip3-+ pow-plus frac-add pow-sqr un-div-inv pow-prod-up flip-+ sqr-sin
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Calls
4 calls:
Slowest
295.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
73.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
21.0ms
(* (sin kx) (sin kx))
14.0ms
(* (sin ky) (sin ky))

series348.0ms

Calls
4 calls:
Slowest
185.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
116.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
26.0ms
(* (sin ky) (sin ky))
21.0ms
(* (sin kx) (sin kx))

simplify5.4s

Calls
143 calls:
Slowest
424.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
339.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
326.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
311.0ms
(sqrt (+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
293.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))

prune2.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.6b

localize37.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.2b
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.2b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
48×add-sqr-sqrt
46×associate-*r*
41×sqrt-prod
35×times-frac add-cube-cbrt
29×associate-*l*
25×distribute-lft-out
21×pow1
17×associate-*r/
16×swap-sqr
13×add-cbrt-cube add-exp-log
11×associate-/r*
6×sqrt-div sin-mult
5×unswap-sqr
4×prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×pow-prod-down associate-/r/ *-commutative
2×pow2 clear-num flip3-+ pow-plus frac-add pow-sqr un-div-inv pow-prod-up flip-+ sqr-sin
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Calls
4 calls:
Slowest
234.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
48.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
21.0ms
(* (sin ky) (sin ky))
12.0ms
(* (sin kx) (sin kx))

series384.0ms

Calls
4 calls:
Slowest
209.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
109.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
33.0ms
(* (sin kx) (sin kx))
33.0ms
(* (sin ky) (sin ky))

simplify5.3s

Calls
143 calls:
Slowest
381.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
322.0ms
(sqrt (+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
308.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
282.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
274.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune2.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.6b

localize38.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.1b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.7b
(/ (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.4b
(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite940.0ms

Algorithm
rewrite-expression-head
Rules
2189×sqrt-prod
1982×*-un-lft-identity
1571×times-frac
780×add-sqr-sqrt
735×associate-*r*
613×add-cube-cbrt
570×distribute-lft-out
501×associate-*l*
228×swap-sqr
108×sqrt-div
68×associate-/l*
60×unswap-sqr
51×associate-/r/
42×associate-/r*
38×sin-mult
22×associate-/l/
20×associate-*r/
19×flip3-+ frac-add flip-+
17×div-inv
15×add-cbrt-cube add-exp-log *-commutative
6×pow1
5×cbrt-undiv div-exp
4×clear-num insert-posit16 add-log-exp
3×frac-2neg
2×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp un-div-inv cbrt-unprod
Calls
4 calls:
Slowest
642.0ms
(/ (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
88.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
85.0ms
(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
64.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series580.0ms

Calls
4 calls:
Slowest
210.0ms
(/ (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
174.0ms
(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
105.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
91.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.9m

Calls
1955 calls:
Slowest
724.0ms
(/ (* (sin th) (/ (sin ky) (sqrt (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))))) (sqrt (sqrt 1)))
703.0ms
(/ (* (sin th) (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (sqrt (sqrt 1)))) (sqrt (sqrt (* (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))
670.0ms
(/ (* (sin th) (/ 1 (* (cbrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (cbrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))) (sqrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
602.0ms
(/ (* (sin th) (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (sqrt (sqrt 1)))) (* (cbrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (cbrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))
585.0ms
(/ (* (sin th) (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (* (cbrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (cbrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))) 1)

prune16.8s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.6b

localize56.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
0.2b
(/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)))
0.2b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
294×*-un-lft-identity
243×times-frac
131×add-sqr-sqrt
126×add-cube-cbrt
112×sqrt-prod
70×distribute-lft-out
62×associate-*l*
40×associate-/r*
34×swap-sqr
20×associate-/r/
19×pow1
14×associate-/l*
13×add-cbrt-cube add-exp-log
6×sqrt-div associate-*r* sin-mult
5×div-inv
4×insert-posit16 add-log-exp
3×cbrt-undiv div-exp associate-/l/
2×pow2 clear-num frac-2neg flip3-+ pow-plus pow-prod-down frac-add prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ sqr-sin unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
96.0ms
(/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)))
79.0ms
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
19.0ms
(* (sin kx) (sin kx))
11.0ms
(* (sin ky) (sin ky))

series414.0ms

Calls
4 calls:
Slowest
216.0ms
(/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)))
134.0ms
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
39.0ms
(* (sin kx) (sin kx))
24.0ms
(* (sin ky) (sin ky))

simplify18.5s

Calls
356 calls:
Slowest
719.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
497.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))))
332.0ms
(sqrt (+ (pow (* (sin ky) (sin ky)) 3) (pow (* (sin kx) (sin kx)) 3)))
318.0ms
(sqrt (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx)))))
313.0ms
(* (sin ky) (sqrt (+ (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))))

prune3.6s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.7b

regimes1.4s

Accuracy

0% (2.0b remaining)

Error of 12.4b against oracle of 10.4b and baseline of 12.4b

bsearch5.0ms

end0.0ms

sample12.0s

Algorithm
intervals
Results
6.6s2808×body1280valid
2.8s1816×body640valid
1.3s2259×body80valid
846.0ms754×body320valid
195.0ms363×body160valid