Details

Time bar (total: 15.7s)

sample81.0ms

Algorithm
intervals
Results
42.0ms510×body80valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (89.0ms)

IterNodesCost
01113
12113
25213
317113
449612
5188512
done500112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* z z) t)
0.0b
(- (* x x) (* (* y 4.0) (- (* z z) t)))
4.5b
(* (* y 4.0) (- (* z z) t))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
16×prod-diff
11×add-sqr-sqrt
10×distribute-rgt-in distribute-lft-in associate--r+
9×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
7×add-log-exp
6×sub-neg
4×associate-*r*
3×expm1-log1p-u flip3-- pow-prod-down prod-exp flip-- cbrt-unprod log1p-expm1-u
2×fma-neg diff-log associate-*r/ difference-of-squares
1×associate-*l* *-commutative
Counts
3 → 78
Calls
3 calls:
10.0ms
(- (* z z) t)
17.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
47.0ms
(* (* y 4.0) (- (* z z) t))

series281.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(- (* z z) t)
129.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
105.0ms
(* (* y 4.0) (- (* z z) t))

simplify2.3s

Counts
87 → 87
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01481288
14791145
229181000
done5001999

prune253.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.5b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* (- (- (* z z) t)) (* y 4.0)))
0.0b
(- (* z z) t)
4.5b
(* (- (- (* z z) t)) (* y 4.0))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*l*
10×add-sqr-sqrt
8×pow1 add-exp-log add-cbrt-cube
7×add-cube-cbrt *-un-lft-identity
5×add-log-exp
4×distribute-lft-neg-in distribute-rgt-neg-in
3×expm1-log1p-u prod-diff pow-prod-down prod-exp cbrt-unprod log1p-expm1-u difference-of-squares
2×flip3-- associate-*l/ flip-- distribute-neg-frac
1×distribute-lft-neg-out neg-mul-1 sub-neg fma-neg diff-log associate-*r* *-commutative fma-udef
Counts
3 → 61
Calls
3 calls:
1.0ms
(fma x x (* (- (- (* z z) t)) (* y 4.0)))
19.0ms
(- (* z z) t)
119.0ms
(* (- (- (* z z) t)) (* y 4.0))

series193.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(fma x x (* (- (- (* z z) t)) (* y 4.0)))
25.0ms
(- (* z z) t)
85.0ms
(* (- (- (* z z) t)) (* y 4.0))

simplify710.0ms

Counts
70 → 70
Iterations

Useful iterations: done (708.0ms)

IterNodesCost
0123855
1321807
21293681
done5001680

prune341.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.5b

localize33.0ms

Local error

Found 4 expressions with local error:

1.3b
(sqrt (fma x x (* (- (- (* z z) t)) (* y 4.0))))
1.3b
(sqrt (fma x x (* (- (- (* z z) t)) (* y 4.0))))
4.5b
(* (- (- (* z z) t)) (* y 4.0))
4.5b
(* (- (- (* z z) t)) (* y 4.0))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-*l*
18×add-sqr-sqrt
16×pow1
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
8×distribute-lft-neg-in distribute-rgt-neg-in
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u associate-*l/ log1p-expm1-u distribute-neg-frac add-log-exp difference-of-squares
2×distribute-lft-neg-out neg-mul-1 rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r* *-commutative flip--
Counts
4 → 94
Calls
4 calls:
2.0ms
(sqrt (fma x x (* (- (- (* z z) t)) (* y 4.0))))
2.0ms
(sqrt (fma x x (* (- (- (* z z) t)) (* y 4.0))))
65.0ms
(* (- (- (* z z) t)) (* y 4.0))
75.0ms
(* (- (- (* z z) t)) (* y 4.0))

series504.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(sqrt (fma x x (* (- (- (* z z) t)) (* y 4.0))))
209.0ms
(sqrt (fma x x (* (- (- (* z z) t)) (* y 4.0))))
58.0ms
(* (- (- (* z z) t)) (* y 4.0))
60.0ms
(* (- (- (* z z) t)) (* y 4.0))

simplify781.0ms

Counts
106 → 106
Iterations

Useful iterations: done (776.0ms)

IterNodesCost
0981456
12561362
29401206
done50001140

prune796.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 2.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x x (/ (* (- (- (pow z 4) (* t t))) (* y 4.0)) (+ (* z z) t)))
1.5b
(- (pow z 4) (* t t))
9.4b
(* (- (- (pow z 4) (* t t))) (* y 4.0))
19.9b
(/ (* (- (- (pow z 4) (* t t))) (* y 4.0)) (+ (* z z) t))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×add-exp-log add-cbrt-cube
16×associate-*l*
13×add-cube-cbrt *-un-lft-identity
9×pow1 unpow-prod-down difference-of-squares
7×fma-neg prod-diff
6×distribute-lft-neg-in distribute-rgt-neg-in prod-exp cbrt-unprod add-log-exp
5×sqr-pow
4×expm1-log1p-u associate-*l/ log1p-expm1-u distribute-neg-frac
3×cbrt-undiv flip3-- times-frac div-exp pow-prod-down associate-/r* flip--
2×distribute-lft-neg-out associate-/r/ associate-/l/
1×neg-mul-1 sub-neg frac-2neg flip3-+ diff-log distribute-frac-neg associate-*r* clear-num *-commutative flip-+ fma-udef div-inv associate-/l*
Counts
4 → 107
Calls
4 calls:
1.0ms
(fma x x (/ (* (- (- (pow z 4) (* t t))) (* y 4.0)) (+ (* z z) t)))
28.0ms
(- (pow z 4) (* t t))
99.0ms
(* (- (- (pow z 4) (* t t))) (* y 4.0))
78.0ms
(/ (* (- (- (pow z 4) (* t t))) (* y 4.0)) (+ (* z z) t))

series480.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(fma x x (/ (* (- (- (pow z 4) (* t t))) (* y 4.0)) (+ (* z z) t)))
71.0ms
(- (pow z 4) (* t t))
107.0ms
(* (- (- (pow z 4) (* t t))) (* y 4.0))
122.0ms
(/ (* (- (- (pow z 4) (* t t))) (* y 4.0)) (+ (* z z) t))

simplify2.1s

Counts
119 → 119
Iterations

Useful iterations: 2 (509.0ms)

IterNodesCost
01932055
15651920
238011619
done50001619

prune618.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.5b

regimes341.0ms

Accuracy

84.1% (0.5b remaining)

Error of 3.3b against oracle of 2.8b and baseline of 5.9b

bsearch1.0ms

simplify17.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02860
14456
25356
36656
done6656

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s15656×body80valid