Details

Time bar (total: 19.9s)

sample37.0ms

Algorithm
intervals
Results
16.0ms268×body80valid

simplify57.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (15.0ms)

IterNodesCost
01517
12617
23817
35015
46015
56415
done6415

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.7b

localize14.0ms

Local error

Found 3 expressions with local error:

2.9b
(fma (/ y t) b a)
3.4b
(fma (/ y t) z x)
9.5b
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

rewrite16.0ms

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)
13.0ms
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

series849.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(fma (/ y t) b a)
63.0ms
(fma (/ y t) z x)
702.0ms
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

simplify2.0s

Counts
64 → 64
Iterations

Useful iterations: 2 (125.0ms)

IterNodesCost
0901058
11661023
2439951
31585951
done5000951

prune316.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (+ (fma (/ y t) b a) 1.0))
2.9b
(fma (/ y t) b a)
3.4b
(fma (/ y t) z x)
9.5b
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
29×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
18×associate-*r*
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/ log1p-expm1-u add-log-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp flip3-+ 1-exp cbrt-unprod flip-+ fma-udef div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 102
Calls
4 calls:
25.0ms
(/ 1 (+ (fma (/ y t) b a) 1.0))
1.0ms
(fma (/ y t) b a)
1.0ms
(fma (/ y t) z x)
63.0ms
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ 1 (+ (fma (/ y t) b a) 1.0))
67.0ms
(fma (/ y t) b a)
75.0ms
(fma (/ y t) z x)
776.0ms
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

simplify3.2s

Counts
114 → 114
Iterations

Useful iterations: 2 (140.0ms)

IterNodesCost
01291750
12681556
27471398
329281398
done50001398

prune444.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
2.9b
(fma (/ y t) b a)
3.4b
(fma (/ y t) z x)
9.5b
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

rewrite64.0ms

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:
22.0ms
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
1.0ms
(fma (/ y t) b a)
1.0ms
(fma (/ y t) z x)
34.0ms
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

series1.2s

Counts
4 → 12
Calls
4 calls:
681.0ms
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
80.0ms
(fma (/ y t) b a)
61.0ms
(fma (/ y t) z x)
366.0ms
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

simplify2.9s

Counts
157 → 157
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01863710
13803416
29343121
336343092
done50013092

prune475.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 9.3b

localize49.0ms

Local error

Found 4 expressions with local error:

7.2b
(cbrt (fma (/ y t) z x))
7.2b
(cbrt (fma (/ y t) z x))
7.2b
(cbrt (fma (/ y t) z x))
9.5b
(/ (* (* (cbrt (fma (/ y t) z x)) (cbrt (fma (/ y t) z x))) (cbrt (fma (/ y t) z x))) (+ (fma (/ y t) b a) 1.0))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log *-un-lft-identity
9×cbrt-prod add-sqr-sqrt add-cube-cbrt add-cbrt-cube
4×pow1 expm1-log1p-u times-frac associate-/r* log1p-expm1-u add-log-exp
3×cbrt-undiv pow1/3 div-exp prod-exp cbrt-unprod
2×associate-/r/ distribute-lft-out
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l*
Counts
4 → 68
Calls
4 calls:
1.0ms
(cbrt (fma (/ y t) z x))
1.0ms
(cbrt (fma (/ y t) z x))
1.0ms
(cbrt (fma (/ y t) z x))
58.0ms
(/ (* (* (cbrt (fma (/ y t) z x)) (cbrt (fma (/ y t) z x))) (cbrt (fma (/ y t) z x))) (+ (fma (/ y t) b a) 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
260.0ms
(cbrt (fma (/ y t) z x))
256.0ms
(cbrt (fma (/ y t) z x))
250.0ms
(cbrt (fma (/ y t) z x))
670.0ms
(/ (* (* (cbrt (fma (/ y t) z x)) (cbrt (fma (/ y t) z x))) (cbrt (fma (/ y t) z x))) (+ (fma (/ y t) b a) 1.0))

simplify2.8s

Counts
80 → 80
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01101741
12601696
28901157
332911050
done50001035

prune448.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 9.3b

regimes558.0ms

Accuracy

-5.4% (2.9b remaining)

Error of 14.3b against oracle of 11.4b and baseline of 14.1b

bsearch202.0ms

Steps
ItersRangePoint
8
1.737129980548476e-119
8.09689640463693e-116
3.2977767939105265e-119
8
-7.67348442351211e-96
-3.3305355583625907e-99
-2.7251446729011575e-98

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02655
13541
done3541

end0.0ms

sample1.6s

Algorithm
intervals
Results
798.0ms8296×body80valid