Details

Time bar (total: 22.5s)

sample135.0ms

Algorithm
intervals
Results
62.0ms107×body2560valid
27.0ms69×body1280valid
14.0ms46×body640valid
13.0ms248×body80nan
4.0ms18×body320valid
2.0ms10×body160valid
1.0ms6×body80valid

simplify2.2s

Counts
1 → 1
Iterations
IterNodes
done5000
52053
4491
3180
267
126
09

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (fma (* -5 v) v 1) (fma v v -1))
0.3b
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×acos-asin cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
2 → 41
Calls
2 calls:
7.0ms
(/ (fma (* -5 v) v 1) (fma v v -1))
1.0ms
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

series105.0ms

Counts
2 → 6
Calls
2 calls:
102.0ms
(/ (fma (* -5 v) v 1) (fma v v -1))
3.0ms
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

simplify1.8s

Counts
47 → 47
Iterations
IterNodes
done5000
31188
2395
1154
086

prune208.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma (* v v) (* v v) (* v v))
0.4b
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×acos-asin fma-udef
Counts
2 → 22
Calls
2 calls:
0.0ms
(fma (* v v) (* v v) (* v v))
1.0ms
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))

series158.0ms

Counts
2 → 6
Calls
2 calls:
155.0ms
(fma (* v v) (* v v) (* v v))
3.0ms
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))

simplify4.4s

Counts
28 → 28
Iterations
IterNodes
done5000
54779
41557
3364
2120
161
038

prune107.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
0.3b
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
1.0b
(cbrt (* (* (acos (/ (fma (* -5 v) v 1) (fma v v -1))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))
1.0b
(* (* (acos (/ (fma (* -5 v) v 1) (fma v v -1))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (acos (/ (fma (* -5 v) v 1) (fma v v -1))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
9×add-cbrt-cube add-exp-log
6×add-sqr-sqrt pow-plus pow-prod-up
5×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×pow2 acos-asin pow3 pow-sqr
1×cbrt-prod pow1/3 associate-*l* *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 66
Calls
4 calls:
1.0ms
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
2.0ms
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
19.0ms
(cbrt (* (* (acos (/ (fma (* -5 v) v 1) (fma v v -1))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))
19.0ms
(* (* (acos (/ (fma (* -5 v) v 1) (fma v v -1))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (acos (/ (fma (* -5 v) v 1) (fma v v -1))))

series72.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
5.0ms
(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
6.0ms
(cbrt (* (* (acos (/ (fma (* -5 v) v 1) (fma v v -1))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))
57.0ms
(* (* (acos (/ (fma (* -5 v) v 1) (fma v v -1))) (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (acos (/ (fma (* -5 v) v 1) (fma v v -1))))

simplify4.7s

Counts
78 → 78
Iterations
IterNodes
done5008
53754
41264
3575
2252
1119
061

prune370.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
1.0b
(sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1)))
1.0b
(sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1)))
1.0b
(* (sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))) (sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 acos-asin rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
1.0ms
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
1.0ms
(sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1)))
1.0ms
(sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1)))
16.0ms
(* (sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))) (sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
27.0ms
(sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1)))
17.0ms
(sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1)))
4.0ms
(* (sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))) (sqrt (acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))))

simplify2.0s

Counts
107 → 107
Iterations
IterNodes
done5000
3785
2283
1146
076

prune405.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes107.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done7
07

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.8s2979×body2560valid
1.2s2468×body1280valid
561.0ms8112×body80nan
520.0ms1258×body640valid
153.0ms650×body320valid
103.0ms422×body160valid
22.0ms223×body80valid