Details

Time bar (total: 10.9s)

sample29.0ms

Algorithm
intervals
Results
14.0ms261×body80valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
01517
12617
23817
35015
46015
56415
done6415

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize14.0ms

Local error

Found 3 expressions with local error:

1.4b
(fma (/ y t) b a)
2.9b
(fma (/ y t) z x)
13.1b
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
5×add-exp-log add-cbrt-cube
4×associate-/r* distribute-lft-out
3×pow1 expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
2×associate-/r/ fma-udef
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
Counts
3 → 55
Calls
3 calls:
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
6.0ms
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

series517.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(fma (/ y t) b a)
40.0ms
(fma (/ y t) z x)
433.0ms
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

simplify896.0ms

Counts
64 → 64
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0901058
11641023
2410951
31338951
done5000951

prune231.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
1.4b
(fma (/ y t) b a)
2.9b
(fma (/ y t) z x)
13.1b
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
94×*-un-lft-identity
62×add-sqr-sqrt add-cube-cbrt
19×associate-/r*
17×add-exp-log
16×distribute-lft-out
11×add-cbrt-cube
8×div-exp
7×associate-/l*
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num fma-udef associate-/l/
1×pow-flip flip3-+ associate-/r/ flip-+ inv-pow
Counts
4 → 145
Calls
4 calls:
9.0ms
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
11.0ms
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

series717.0ms

Counts
4 → 12
Calls
4 calls:
415.0ms
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
40.0ms
(fma (/ y t) b a)
42.0ms
(fma (/ y t) z x)
219.0ms
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

simplify1.7s

Counts
157 → 157
Iterations

Useful iterations: 3 (779.0ms)

IterNodesCost
01863710
13933416
29323121
333743092
done50003092

prune366.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (+ (fma (/ y t) b a) 1.0))
1.4b
(fma (/ y t) b a)
2.9b
(fma (/ y t) z x)
12.9b
(* (/ 1 (+ (fma (/ y t) b a) 1.0)) (fma (/ y t) z x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
29×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
18×associate-*l*
17×add-exp-log
11×add-cbrt-cube
7×pow1 distribute-lft-out
4×expm1-log1p-u div-exp prod-exp associate-/r* associate-/r/ fma-udef log1p-expm1-u add-log-exp
3×associate-*r* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp flip3-+ 1-exp cbrt-unprod flip-+ div-inv
1×distribute-rgt-in pow-flip frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 103
Calls
4 calls:
6.0ms
(/ 1 (+ (fma (/ y t) b a) 1.0))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
18.0ms
(* (/ 1 (+ (fma (/ y t) b a) 1.0)) (fma (/ y t) z x))

series607.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ 1 (+ (fma (/ y t) b a) 1.0))
40.0ms
(fma (/ y t) b a)
43.0ms
(fma (/ y t) z x)
412.0ms
(* (/ 1 (+ (fma (/ y t) b a) 1.0)) (fma (/ y t) z x))

simplify1.4s

Counts
115 → 115
Iterations

Useful iterations: 3 (621.0ms)

IterNodesCost
01361814
12941641
27851479
328371474
done50001474

prune330.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.8b

localize19.0ms

Local error

Found 4 expressions with local error:

7.4b
(* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (fma (/ y t) b a) 1.0)) (cbrt (+ (fma (/ y t) b a) 1.0)))) (/ (fma (/ y t) z x) (cbrt (+ (fma (/ y t) b a) 1.0))))
11.1b
(cbrt (+ (fma (/ y t) b a) 1.0))
11.1b
(cbrt (+ (fma (/ y t) b a) 1.0))
11.1b
(cbrt (+ (fma (/ y t) b a) 1.0))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
35×add-sqr-sqrt
34×*-un-lft-identity
29×times-frac
27×associate-*r*
26×cbrt-prod
24×add-cbrt-cube
22×add-cube-cbrt
20×cbrt-div
18×prod-exp cbrt-unprod
13×cbrt-undiv div-exp associate-*l*
10×flip3-+ associate-/r/ flip-+
6×pow1 distribute-lft-out unswap-sqr
5×frac-times
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r/ associate-*l/
2×div-inv
1×pow-prod-down *-commutative
Counts
4 → 128
Calls
4 calls:
73.0ms
(* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (fma (/ y t) b a) 1.0)) (cbrt (+ (fma (/ y t) b a) 1.0)))) (/ (fma (/ y t) z x) (cbrt (+ (fma (/ y t) b a) 1.0))))
2.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))
2.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))
2.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
421.0ms
(* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (fma (/ y t) b a) 1.0)) (cbrt (+ (fma (/ y t) b a) 1.0)))) (/ (fma (/ y t) z x) (cbrt (+ (fma (/ y t) b a) 1.0))))
219.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))
224.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))
220.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))

simplify949.0ms

Counts
140 → 140
Iterations

Useful iterations: done (944.0ms)

IterNodesCost
02105178
16364625
220343538
done50013443

prune596.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.8b

regimes408.0ms

Accuracy

51.3% (1.5b remaining)

Error of 12.4b against oracle of 11.0b and baseline of 14.0b

bsearch117.0ms

Steps
ItersRangePoint
7
1.8526485801229373e-17
2.3333386782110615e-15
1.6432470003784239e-15
9
-6.031111347935146e+36
-7.221055931686145e+31
-3.9332366958832453e+36

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03061
14344
done4344

end0.0ms

sample682.0ms

Algorithm
intervals
Results
385.0ms8291×body80valid