Details

Time bar (total: 12.2s)

sample91.0ms

Algorithm
intervals
Results
19.0ms50×body1280valid
17.0ms273×body80nan
10.0ms171×body80valid
8.0ms13×body2560valid
7.0ms27×body640valid
3.0ms17×body320valid
1.0ms9×body160valid

simplify56.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01819
13319
25719
38119
49619
510319
610519
done10519

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* z t) 3.0)
0.3b
(/ a (* b 3.0))
0.3b
(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
23.4b
(cos (- y (/ (* z t) 3.0)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×prod-diff
19×add-exp-log add-cbrt-cube
15×times-frac
9×pow1
5×prod-exp cbrt-unprod div-inv
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u associate-/l* add-log-exp
3×cos-diff associate-*r* pow-prod-down
2×frac-2neg clear-num
1×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
Counts
4 → 101
Calls
4 calls:
3.0ms
(/ (* z t) 3.0)
3.0ms
(/ a (* b 3.0))
14.0ms
(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
13.0ms
(cos (- y (/ (* z t) 3.0)))

series158.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (* z t) 3.0)
17.0ms
(/ a (* b 3.0))
88.0ms
(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
36.0ms
(cos (- y (/ (* z t) 3.0)))

simplify879.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (225.0ms)

IterNodesCost
03272847
16992377
222541875
done50001875

prune584.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 16.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
0.3b
(/ a (* b 3.0))
26.3b
(cos (/ (* z t) 3.0))
26.4b
(sin (/ (* z t) 3.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
9×pow1
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×times-frac associate-*r/ associate-*r* pow-prod-down associate-/l*
2×cbrt-undiv div-exp
1×distribute-rgt-in frac-2neg distribute-lft-in flip3-+ associate-*l* frac-add clear-num associate-/r* cos-mult *-commutative flip-+ div-inv sin-mult
Counts
4 → 66
Calls
4 calls:
16.0ms
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
5.0ms
(/ a (* b 3.0))
1.0ms
(cos (/ (* z t) 3.0))
1.0ms
(sin (/ (* z t) 3.0))

series236.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
18.0ms
(/ a (* b 3.0))
9.0ms
(cos (/ (* z t) 3.0))
16.0ms
(sin (/ (* z t) 3.0))

simplify596.0ms

Counts
78 → 78
Iterations

Useful iterations: done (593.0ms)

IterNodesCost
01701336
14501281
218341094
done50001092

prune435.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 14.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ a (* b 3.0))
0.3b
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
26.4b
(cos (* 0.3333333333333333 (* t z)))
26.4b
(sin (/ (* z t) 3.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
9×pow1
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×times-frac associate-*r/ associate-*r* pow-prod-down associate-/l*
2×cbrt-undiv div-exp
1×distribute-rgt-in frac-2neg distribute-lft-in flip3-+ associate-*l* frac-add clear-num associate-/r* cos-mult *-commutative flip-+ div-inv sin-mult
Counts
4 → 66
Calls
4 calls:
3.0ms
(/ a (* b 3.0))
25.0ms
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
4.0ms
(cos (* 0.3333333333333333 (* t z)))
1.0ms
(sin (/ (* z t) 3.0))

series256.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ a (* b 3.0))
215.0ms
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
9.0ms
(cos (* 0.3333333333333333 (* t z)))
15.0ms
(sin (/ (* z t) 3.0))

simplify606.0ms

Counts
78 → 78
Iterations

Useful iterations: done (604.0ms)

IterNodesCost
01731336
14591281
218531093
done50011091

prune469.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 14.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
0.3b
(* (/ 1 b) (/ a 3.0))
26.4b
(cos (* 0.3333333333333333 (* t z)))
26.4b
(sin (/ (* z t) 3.0))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
31×add-exp-log
25×times-frac
21×*-un-lft-identity add-cbrt-cube
19×add-cube-cbrt
16×associate-*r*
14×associate-*l*
11×pow1 prod-exp
8×div-exp
7×cbrt-unprod
6×unswap-sqr
4×cbrt-undiv expm1-log1p-u associate-*r/ pow-prod-down log1p-expm1-u add-log-exp
2×rec-exp 1-exp *-commutative div-inv
1×distribute-rgt-in frac-times distribute-lft-in flip3-+ associate-*l/ frac-add cos-mult flip-+ sin-mult
Counts
4 → 101
Calls
4 calls:
25.0ms
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
16.0ms
(* (/ 1 b) (/ a 3.0))
4.0ms
(cos (* 0.3333333333333333 (* t z)))
1.0ms
(sin (/ (* z t) 3.0))

series229.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
15.0ms
(* (/ 1 b) (/ a 3.0))
9.0ms
(cos (* 0.3333333333333333 (* t z)))
15.0ms
(sin (/ (* z t) 3.0))

simplify1.1s

Counts
113 → 113
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02421788
16911628
228161364
done50001362

prune537.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 14.8b

regimes2.9s

Accuracy

44.6% (2.5b remaining)

Error of 18.2b against oracle of 15.7b and baseline of 20.2b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
042106
15576
25676
done5676

end0.0ms

sample2.8s

Algorithm
intervals
Results
598.0ms1557×body1280valid
592.0ms9074×body80nan
346.0ms5663×body80valid
252.0ms924×body640valid
249.0ms373×body2560valid
84.0ms430×body320valid
27.0ms195×body160valid