Details

Time bar (total: 12.0s)

sample26.0ms

Algorithm
intervals
Results
11.0ms261×body80valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
01517
12617
23817
35015
46015
56415
done6415

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize11.0ms

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) (+ 1.0 (fma (/ y t) b a)))

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) (+ 1.0 (fma (/ y t) b a)))

series486.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(fma (/ y t) b a)
38.0ms
(fma (/ y t) z x)
406.0ms
(/ (fma (/ y t) z x) (+ 1.0 (fma (/ y t) b a)))

simplify735.0ms

Counts
64 → 64
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0901058
11691023
2503951
31663951
done5000951

prune213.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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 (/ (+ 1.0 (fma (/ y t) b a)) (fma (/ y t) z x)))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
8.0ms
(/ (+ 1.0 (fma (/ y t) b a)) (fma (/ y t) z x))

series672.0ms

Counts
4 → 12
Calls
4 calls:
385.0ms
(/ 1 (/ (+ 1.0 (fma (/ y t) b a)) (fma (/ y t) z x)))
40.0ms
(fma (/ y t) b a)
37.0ms
(fma (/ y t) z x)
209.0ms
(/ (+ 1.0 (fma (/ y t) b a)) (fma (/ y t) z x))

simplify3.3s

Counts
157 → 157
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01863710
14033469
214013116
343493092
done50013092

prune328.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (+ 1.0 (fma (/ y t) b a)) (/ 1 (fma (/ y t) z x))))
1.4b
(fma (/ y t) b a)
2.9b
(fma (/ y t) z x)
12.9b
(* (+ 1.0 (fma (/ y t) b a)) (/ 1 (fma (/ y t) z x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
21×add-sqr-sqrt
18×div-exp add-cbrt-cube
17×*-un-lft-identity
16×prod-exp
14×add-cube-cbrt times-frac
13×associate-*r*
9×pow1 rec-exp 1-exp
6×associate-/r/
5×cbrt-undiv
4×expm1-log1p-u frac-times flip3-+ associate-*l* associate-*l/ cbrt-unprod flip-+ log1p-expm1-u add-log-exp
3×associate-/l* unswap-sqr
2×pow-flip associate-*r/ pow-prod-down un-div-inv fma-udef div-inv
1×frac-2neg clear-num associate-/r* *-commutative distribute-lft-out inv-pow
Counts
4 → 109
Calls
4 calls:
13.0ms
(/ 1 (* (+ 1.0 (fma (/ y t) b a)) (/ 1 (fma (/ y t) z x))))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
16.0ms
(* (+ 1.0 (fma (/ y t) b a)) (/ 1 (fma (/ y t) z x)))

series673.0ms

Counts
4 → 12
Calls
4 calls:
390.0ms
(/ 1 (* (+ 1.0 (fma (/ y t) b a)) (/ 1 (fma (/ y t) z x))))
37.0ms
(fma (/ y t) b a)
40.0ms
(fma (/ y t) z x)
207.0ms
(* (+ 1.0 (fma (/ y t) b a)) (/ 1 (fma (/ y t) z x)))

simplify1.4s

Counts
121 → 121
Iterations

Useful iterations: 2 (151.0ms)

IterNodesCost
01632251
14081996
215081666
done50001666

prune309.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.8b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
44×add-sqr-sqrt
38×*-un-lft-identity
36×times-frac
27×cbrt-prod associate-*r*
23×add-cube-cbrt
20×cbrt-div prod-exp
18×add-cbrt-cube
15×div-exp associate-*l*
10×flip3-+ associate-/r/ flip-+
9×unswap-sqr
8×cbrt-unprod
7×cbrt-undiv
6×pow1 distribute-lft-out
5×frac-times
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×pow1/3 associate-*r/ associate-*l/
2×div-inv
1×pow-prod-down *-commutative
Counts
4 → 133
Calls
4 calls:
85.0ms
(* (/ 1 (* (cbrt (+ 1.0 (fma (/ y t) b a))) (cbrt (+ 1.0 (fma (/ y t) b a))))) (/ (fma (/ y t) z x) (cbrt (+ 1.0 (fma (/ y t) b a)))))
2.0ms
(cbrt (+ 1.0 (fma (/ y t) b a)))
2.0ms
(cbrt (+ 1.0 (fma (/ y t) b a)))
2.0ms
(cbrt (+ 1.0 (fma (/ y t) b a)))

series1.0s

Counts
4 → 12
Calls
4 calls:
397.0ms
(* (/ 1 (* (cbrt (+ 1.0 (fma (/ y t) b a))) (cbrt (+ 1.0 (fma (/ y t) b a))))) (/ (fma (/ y t) z x) (cbrt (+ 1.0 (fma (/ y t) b a)))))
204.0ms
(cbrt (+ 1.0 (fma (/ y t) b a)))
211.0ms
(cbrt (+ 1.0 (fma (/ y t) b a)))
207.0ms
(cbrt (+ 1.0 (fma (/ y t) b a)))

simplify935.0ms

Counts
145 → 145
Iterations

Useful iterations: done (930.0ms)

IterNodesCost
02124915
16094577
223553619
done50003616

prune514.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.8b

regimes371.0ms

Accuracy

45.7% (1.8b remaining)

Error of 12.8b against oracle of 11.0b and baseline of 14.3b

bsearch99.0ms

Steps
ItersRangePoint
7
1.8526485801229373e-17
2.3333386782110615e-15
2.2849150595725634e-15
8
-4.2092663714039774e+142
-1.3954753557741168e+139
-1.637336446456633e+139

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02963
14145
done4145

end0.0ms

sample665.0ms

Algorithm
intervals
Results
364.0ms8291×body80valid