Details

Time bar (total: 7.8s)

sample21.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify474.0ms

Counts
1 → 1
Iterations

Useful iterations: done (473.0ms)

IterNodesCost
01317
12617
26117
314117
436417
588515
done500013

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- x (/ z (- (/ (* z z) y) (/ t 2.0))))
6.1b
(/ (* z z) y)
7.8b
(/ z (- (/ (* z z) y) (/ t 2.0)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
221×add-sqr-sqrt
152×times-frac
114×*-un-lft-identity
93×prod-diff
86×add-cube-cbrt
54×difference-of-squares
14×distribute-lft-out--
12×associate-/r/
11×associate-/r*
10×add-exp-log add-cbrt-cube
5×flip3-- flip-- div-inv add-log-exp
4×frac-sub associate-/l*
3×pow1 cbrt-undiv expm1-log1p-u fma-neg div-exp log1p-expm1-u
2×frac-2neg clear-num
1×sub-neg diff-log prod-exp cbrt-unprod
Counts
3 → 188
Calls
3 calls:
58.0ms
(- x (/ z (- (/ (* z z) y) (/ t 2.0))))
4.0ms
(/ (* z z) y)
26.0ms
(/ z (- (/ (* z z) y) (/ t 2.0)))

series105.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(- x (/ z (- (/ (* z z) y) (/ t 2.0))))
19.0ms
(/ (* z z) y)
41.0ms
(/ z (- (/ (* z z) y) (/ t 2.0)))

simplify1.1s

Counts
197 → 197
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03779707
19349097
230986904
done50016901

prune460.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- x (/ z (- (/ z (/ y z)) (/ t 2.0))))
0.1b
(/ z (/ y z))
7.8b
(/ z (- (/ z (/ y z)) (/ t 2.0)))

rewrite277.0ms

Algorithm
rewrite-expression-head
Rules
425×add-sqr-sqrt
351×times-frac
227×*-un-lft-identity
147×add-cube-cbrt
120×prod-diff
80×difference-of-squares
27×distribute-lft-out--
24×associate-/r*
13×associate-/r/
10×add-exp-log add-cbrt-cube
9×div-inv
6×associate-/l*
5×flip3-- flip-- add-log-exp
4×cbrt-undiv div-exp frac-sub
3×pow1 expm1-log1p-u fma-neg log1p-expm1-u
2×frac-2neg clear-num
1×sub-neg diff-log
Counts
3 → 276
Calls
3 calls:
166.0ms
(- x (/ z (- (/ z (/ y z)) (/ t 2.0))))
7.0ms
(/ z (/ y z))
79.0ms
(/ z (- (/ z (/ y z)) (/ t 2.0)))

series105.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(- x (/ z (- (/ z (/ y z)) (/ t 2.0))))
18.0ms
(/ z (/ y z))
41.0ms
(/ z (- (/ z (/ y z)) (/ t 2.0)))

simplify473.0ms

Counts
285 → 285
Iterations

Useful iterations: done (460.0ms)

IterNodesCost
054713650
1133912841
done50009601

prune637.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ y z) 2.0)
1.0b
(/ z (- (* z 2.0) (* (/ y z) t)))
5.1b
(* (/ y z) t)
11.3b
(* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
41×associate-*l*
38×times-frac
37×add-exp-log add-cbrt-cube
35×add-cube-cbrt *-un-lft-identity
14×prod-exp cbrt-unprod
13×pow1
8×cbrt-undiv div-exp
7×associate-*r*
5×pow-prod-down associate-*l/
4×expm1-log1p-u associate-/r/ log1p-expm1-u div-inv add-log-exp unswap-sqr
3×associate-/r* *-commutative associate-/l*
2×flip3-- flip--
1×frac-times frac-2neg associate-*r/ clear-num
Counts
4 → 142
Calls
4 calls:
8.0ms
(* (/ y z) 2.0)
5.0ms
(/ z (- (* z 2.0) (* (/ y z) t)))
11.0ms
(* (/ y z) t)
23.0ms
(* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0))

series127.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (/ y z) 2.0)
52.0ms
(/ z (- (* z 2.0) (* (/ y z) t)))
19.0ms
(* (/ y z) t)
38.0ms
(* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0))

simplify901.0ms

Counts
154 → 154
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
02062156
15682102
224951764
done50001764

prune596.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ z (- (* z 2.0) (* (/ y z) t)))
5.1b
(* (/ y z) t)
11.3b
(* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0))
27.7b
(cbrt (pow (* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0)) 3))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
32×add-exp-log add-cbrt-cube
28×add-cube-cbrt *-un-lft-identity times-frac associate-*l*
12×prod-exp cbrt-unprod
11×pow1
8×cbrt-prod
7×cbrt-undiv div-exp associate-*l/
4×expm1-log1p-u associate-*r* pow-prod-down associate-/r/ log1p-expm1-u add-log-exp
3×cube-div cbrt-div associate-/r* div-inv associate-/l*
2×frac-times flip3-- associate-*r/ *-commutative flip-- unswap-sqr
1×cube-mult unpow-prod-down frac-2neg pow1/3 unpow3 cube-prod clear-num rem-cbrt-cube sqr-pow
Counts
4 → 130
Calls
4 calls:
5.0ms
(/ z (- (* z 2.0) (* (/ y z) t)))
8.0ms
(* (/ y z) t)
26.0ms
(* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0))
2.0ms
(cbrt (pow (* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0)) 3))

series149.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ z (- (* z 2.0) (* (/ y z) t)))
19.0ms
(* (/ y z) t)
40.0ms
(* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0))
39.0ms
(cbrt (pow (* (/ z (- (* z 2.0) (* (/ y z) t))) (* (/ y z) 2.0)) 3))

simplify991.0ms

Counts
142 → 142
Iterations

Useful iterations: 2 (191.0ms)

IterNodesCost
02172527
15942121
227132055
done50002055

prune424.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes88.0ms

Accuracy

40.2% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 1.5b

bsearch50.0ms

Steps
ItersRangePoint
8
28159834.57455786
105325879555.74261
526596793.1128736

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02136
12536
done2536

end0.0ms

sample527.0ms

Algorithm
intervals
Results
319.0ms8000×body80valid