Details

Time bar (total: 27.6s)

sample57.0ms

Algorithm
intervals
Results
14.0ms250×body80valid
4.0ms17×body640valid
3.0ms10×body1280valid
2.0ms13×body320valid
1.0ms9×body160valid

simplify9.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (39.0ms)

IterNodesCost
01113
12013
24513
311612
432212
576612
6155512
7287312
8476112
done500012

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- y z) (- a z))
3.1b
(fma (/ (- y z) (- a z)) (- t x) x)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
37.0ms
(/ (- y z) (- a z))
0.0ms
(fma (/ (- y z) (- a z)) (- t x) x)

series261.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(/ (- y z) (- a z))
198.0ms
(fma (/ (- y z) (- a z)) (- t x) x)

simplify1.7s

Counts
70 → 70
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0116918
1266890
2653838
31707834
done5001830

prune399.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y z) (- a z))
1.7b
(* (/ (- y z) (- a z)) (- t x))
2.5b
(+ (* (/ (- y z) (- a z)) (- t x)) x)

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
97×*-un-lft-identity
51×add-cube-cbrt times-frac
36×prod-diff
31×associate-*l*
23×distribute-lft-out-- difference-of-squares
22×distribute-rgt-in associate-+l+ distribute-lft-in
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*r* associate-/r* flip-- associate-/l* add-log-exp
4×sub-neg associate-/r/
3×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative fma-def frac-2neg flip3-+ div-sub pow-prod-down associate-*l/ clear-num sum-log *-commutative flip-+
Counts
3 → 170
Calls
3 calls:
42.0ms
(/ (- y z) (- a z))
110.0ms
(* (/ (- y z) (- a z)) (- t x))
47.0ms
(+ (* (/ (- y z) (- a z)) (- t x)) x)

series913.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(/ (- y z) (- a z))
488.0ms
(* (/ (- y z) (- a z)) (- t x))
323.0ms
(+ (* (/ (- y z) (- a z)) (- t x)) x)

simplify1.5s

Counts
179 → 179
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02553085
16652718
219552494
done50012468

prune736.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.7b
(* (/ (- y z) (- a z)) (fma 1 t (- (* (cbrt x) (* (cbrt x) (cbrt x))))))
8.1b
(+ (* (/ (- y z) (- a z)) (fma 1 t (- (* (cbrt x) (* (cbrt x) (cbrt x)))))) (fma (fma x -1 x) (/ (- y z) (- a z)) x))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
38×*-un-lft-identity
31×associate-*l*
26×times-frac
18×add-cube-cbrt
10×distribute-lft-out-- difference-of-squares
9×add-exp-log add-cbrt-cube
6×pow1 cbrt-prod add-log-exp
5×fma-udef
4×expm1-log1p-u log1p-expm1-u
3×associate-*r*
2×distribute-rgt-in associate-+l+ distribute-lft-in pow1/3 prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative associate-+r+ flip3-- fma-def flip3-+ div-exp pow-prod-down associate-*l/ sum-log *-commutative flip-- flip-+ div-inv
Counts
4 → 97
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
70.0ms
(* (/ (- y z) (- a z)) (fma 1 t (- (* (cbrt x) (* (cbrt x) (cbrt x))))))
32.0ms
(+ (* (/ (- y z) (- a z)) (fma 1 t (- (* (cbrt x) (* (cbrt x) (cbrt x)))))) (fma (fma x -1 x) (/ (- y z) (- a z)) x))

series1.6s

Counts
4 → 12
Calls
4 calls:
280.0ms
(cbrt x)
334.0ms
(cbrt x)
529.0ms
(* (/ (- y z) (- a z)) (fma 1 t (- (* (cbrt x) (* (cbrt x) (cbrt x))))))
440.0ms
(+ (* (/ (- y z) (- a z)) (fma 1 t (- (* (cbrt x) (* (cbrt x) (cbrt x)))))) (fma (fma x -1 x) (/ (- y z) (- a z)) x))

simplify1.1s

Counts
109 → 109
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01662296
14081784
213321253
done50011163

prune764.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.9b

localize23.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (- y z) (- a z))) (- t x))) (fma (fma x -1 x) (/ (- y z) (- a z)) x))
3.1b
(cbrt (/ (- y z) (- a z)))
3.1b
(cbrt (/ (- y z) (- a z)))
3.1b
(cbrt (/ (- y z) (- a z)))

rewrite363.0ms

Algorithm
rewrite-expression-head
Rules
121×add-sqr-sqrt *-un-lft-identity
93×cbrt-prod
75×times-frac
61×add-cube-cbrt
44×distribute-rgt-in associate-+l+ distribute-lft-in
36×prod-diff
30×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 add-exp-log expm1-log1p-u sub-neg add-cbrt-cube log1p-expm1-u
3×cbrt-div flip3-- pow1/3 flip-- div-inv
1×+-commutative associate-+r+ fma-def flip3-+ sum-log flip-+ fma-udef
Counts
4 → 185
Calls
4 calls:
273.0ms
(+ (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (- y z) (- a z))) (- t x))) (fma (fma x -1 x) (/ (- y z) (- a z)) x))
23.0ms
(cbrt (/ (- y z) (- a z)))
20.0ms
(cbrt (/ (- y z) (- a z)))
21.0ms
(cbrt (/ (- y z) (- a z)))

series1.8s

Counts
4 → 12
Calls
4 calls:
371.0ms
(+ (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (- y z) (- a z))) (- t x))) (fma (fma x -1 x) (/ (- y z) (- a z)) x))
520.0ms
(cbrt (/ (- y z) (- a z)))
452.0ms
(cbrt (/ (- y z) (- a z)))
472.0ms
(cbrt (/ (- y z) (- a z)))

simplify3.6s

Counts
197 → 197
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
02485581
15735293
213093977
347983653
done50003653

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.9b

regimes542.0ms

Accuracy

26.9% (6.4b remaining)

Error of 9.9b against oracle of 3.5b and baseline of 12.2b

bsearch115.0ms

Steps
ItersRangePoint
9
1.2893535391803096e+185
1.3650528676108602e+190
5.707371382778094e+189
7
-2.7815652200329975e+115
-2.4524093287392163e+113
-2.729091847189307e+115

simplify14.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
02960
14252
24652
done4652

end0.0ms

sample1.1s

Algorithm
intervals
Results
335.0ms7767×body80valid
88.0ms491×body640valid
54.0ms283×body1280valid
49.0ms426×body320valid
23.0ms280×body160valid
4.0ms16×body2560valid