Details

Time bar (total: 31.8s)

sample109.0ms

Algorithm
intervals
Results
60.0ms569×body80valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 4 (368.0ms)

IterNodesCost
023569
147569
2110544
3333544
41195519
done5001519

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* c t) (* i y))
4.4b
(* j (- (* c t) (* i y)))
4.5b
(fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y))))
5.1b
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×distribute-rgt-in sub-neg distribute-lft-in associate-*r* associate-*l* prod-diff
2×flip3-- associate-*r/ fma-udef flip--
1×fma-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 64
Calls
4 calls:
7.0ms
(- (* c t) (* i y))
25.0ms
(* j (- (* c t) (* i y)))
0.0ms
(fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y))))
0.0ms
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (* c t) (* i y))
95.0ms
(* j (- (* c t) (* i y)))
350.0ms
(fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y))))
758.0ms
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y)))))

simplify1.8s

Counts
76 → 76
Iterations

Useful iterations: done (1.8s)

IterNodesCost
011922045
128621102
2108521002
done500020842

prune848.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.2b

localize56.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y))))
2.3b
(* (cbrt j) (- (* c t) (* i y)))
4.5b
(fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y)))))
5.1b
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y))))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log
15×distribute-rgt-in distribute-lft-in
11×add-sqr-sqrt add-cbrt-cube
9×pow-prod-down prod-exp cbrt-unprod
7×*-un-lft-identity associate-*l* add-cube-cbrt
6×sub-neg prod-diff associate-*r/
4×cbrt-prod expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
2×flip3-- *-commutative fma-udef flip-- unswap-sqr
Counts
4 → 90
Calls
4 calls:
52.0ms
(* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y))))
30.0ms
(* (cbrt j) (- (* c t) (* i y)))
0.0ms
(fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y)))))
0.0ms
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y))))
401.0ms
(* (cbrt j) (- (* c t) (* i y)))
388.0ms
(fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y)))))
856.0ms
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c t) (* i y))))))

simplify3.2s

Counts
102 → 102
Iterations

Useful iterations: done (3.2s)

IterNodesCost
017143088
148941483
2305341303
done500130863

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.2b

localize106.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y))))
2.2b
(* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y)))))
4.5b
(fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y))))))
5.1b
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y)))))))

rewrite409.0ms

Algorithm
rewrite-expression-head
Rules
57×pow1 add-exp-log
48×distribute-rgt-in distribute-lft-in
39×pow-prod-down prod-exp cbrt-unprod
29×add-cbrt-cube
12×sub-neg prod-diff
10×associate-*r/
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt log1p-expm1-u add-log-exp
2×flip3-- associate-*r* associate-*l* *-commutative fma-udef flip--
Counts
4 → 126
Calls
4 calls:
94.0ms
(* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y))))
304.0ms
(* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y)))))
0.0ms
(fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y))))))
0.0ms
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y)))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
471.0ms
(* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y))))
168.0ms
(* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y)))))
500.0ms
(fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y))))))
1.0s
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* (* (cbrt j) (cbrt j)) (* (* (cbrt (cbrt j)) (cbrt (cbrt j))) (* (cbrt (cbrt j)) (- (* c t) (* i y)))))))

simplify3.8s

Counts
138 → 138
Iterations

Useful iterations: done (3.8s)

IterNodesCost
022285547
176378553
2381877693
done500139333

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize83.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (- (* i y)) j)
4.0b
(* t (* j c))
4.5b
(fma b (- (* i a) (* c z)) (+ (* t (* j c)) (* (- (* i y)) j)))
5.1b
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (+ (* t (* j c)) (* (- (* i y)) j))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt associate-*l*
7×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative fma-udef
1×distribute-lft-neg-out distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in unswap-sqr
Counts
4 → 64
Calls
4 calls:
9.0ms
(* (- (* i y)) j)
13.0ms
(* t (* j c))
0.0ms
(fma b (- (* i a) (* c z)) (+ (* t (* j c)) (* (- (* i y)) j)))
1.0ms
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (+ (* t (* j c)) (* (- (* i y)) j))))

series1.4s

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (- (* i y)) j)
44.0ms
(* t (* j c))
404.0ms
(fma b (- (* i a) (* c z)) (+ (* t (* j c)) (* (- (* i y)) j)))
935.0ms
(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (+ (* t (* j c)) (* (- (* i y)) j))))

simplify1.4s

Counts
76 → 76
Iterations

Useful iterations: done (1.4s)

IterNodesCost
011719790
126618917
2123018347
done500218267

prune855.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

regimes2.0s

Accuracy

-8.5% (8.7b remaining)

Error of 13.4b against oracle of 4.7b and baseline of 12.7b

bsearch512.0ms

Steps
ItersRangePoint
6
6.0094771117101126e-05
0.0004266352501423779
0.00035774551240274976
9
2.7476069612090623e-226
5.756635428501155e-218
4.679747423961564e-222
9
2.272015746002746e-295
1.3875037531746016e-288
1.6746751933243623e-289

simplify42.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0471622
1771622
2871622
3891622
done891622

end0.0ms

sample5.5s

Algorithm
intervals
Results
4.1s19189×body80valid