Details

Time bar (total: 58.4s)

sample104.0ms

Algorithm
intervals
Results
49.0ms256×body80valid

simplify4.0s

Counts
1 → 1
Iterations
IterNodes
done5000
41857
3505
2152
162
029

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.9b

localize133.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
2.0b
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
23.2b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
38×*-un-lft-identity
31×times-frac
24×add-cube-cbrt
19×associate-*r*
11×add-cbrt-cube add-exp-log
7×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod fma-udef div-inv unswap-sqr associate-/l/
1×clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 104
Calls
4 calls:
1.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
1.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
29.0ms
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
39.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series750.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
34.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
116.0ms
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
534.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify3.8s

Counts
116 → 116
Iterations
IterNodes
done5001
21528
1461
0200

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize134.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.3b
(/ 2.0 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
2.0b
(/ x (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
23.2b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (- (/ x (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 2.0 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

rewrite384.0ms

Algorithm
rewrite-expression-head
Rules
496×times-frac
402×add-sqr-sqrt
396×*-un-lft-identity
388×add-cube-cbrt
338×prod-diff
171×distribute-rgt-in distribute-lft-in
56×div-inv
12×associate-*r*
10×add-cbrt-cube add-exp-log
6×pow1 associate-/r* associate-/l*
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×associate-*l*
2×cbrt-undiv clear-num sub-neg frac-2neg div-exp
1×flip3-- distribute-rgt-out-- pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod fma-udef flip-- sub-div unswap-sqr
Counts
4 → 447
Calls
4 calls:
1.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
7.0ms
(/ 2.0 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
9.0ms
(/ x (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
207.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (- (/ x (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 2.0 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

series1.2s

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
126.0ms
(/ 2.0 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
172.0ms
(/ x (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
844.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (- (/ x (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 2.0 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

simplify8.8s

Counts
459 → 459
Iterations
IterNodes
done5000
24938
11454
0819

prune10.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0b
(* (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
23.2b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
34×*-un-lft-identity
32×add-cube-cbrt
19×times-frac
18×prod-diff
13×associate-*l*
11×distribute-rgt-in distribute-lft-in add-cbrt-cube add-exp-log
6×pow1
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×frac-times cbrt-undiv sub-neg flip3-- div-exp prod-exp associate-*r/ cbrt-unprod fma-udef div-inv flip-- unswap-sqr
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 115
Calls
4 calls:
2.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
82.0ms
(* (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
1.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
15.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

series1.1s

Counts
4 → 12
Calls
4 calls:
59.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
521.0ms
(* (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
56.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
502.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify3.8s

Counts
127 → 127
Iterations
IterNodes
done5000
21580
1596
0243

prune2.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize696.0ms

Local error

Found 4 expressions with local error:

16.3b
(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
23.2b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (/ 1 (* (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ x (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (- (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))))
23.5b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (- (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))))
39.2b
(fma (- (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
5×fma-udef
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×pow1/3
Counts
4 → 71
Calls
4 calls:
2.0ms
(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
10.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (/ 1 (* (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ x (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (- (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))))
12.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (- (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))))
2.0ms
(fma (- (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

series7.9s

Counts
4 → 12
Calls
4 calls:
302.0ms
(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
2.1s
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (/ 1 (* (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ x (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (- (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))))
1.6s
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (- (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))))
3.9s
(fma (- (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ 2.0 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

simplify5.2s

Counts
83 → 83
Iterations
IterNodes
done5000
21635
1501
0218

prune2.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes832.0ms

Accuracy

98% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 24.8b

bsearch431.0ms

Steps
ItersRangePoint
8
2.886177742578919e+66
8.423966535547682e+69
3.1512810687298216e+66
8
-2.3471552504518496e+41
-3.035188628432768e+38
-1.247417882216234e+41

simplify12.0ms

Iterations
IterNodes
done38
138
033

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.7s8007×body80valid