Details

Time bar (total: 12.2s)

sample21.0ms

Algorithm
intervals
Results
10.0ms267×body80valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01317
12517
23917
36417
411317
521817
644917
7116017
8496617
done500017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ (- (* y z) x) (- (* t z) x)))
0.0b
(- (* t z) x)
0.5b
(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
11.2b
(/ (- (* y z) x) (- (* t z) x))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
25×times-frac
24×add-sqr-sqrt add-cube-cbrt
11×distribute-lft-out
8×add-exp-log add-cbrt-cube add-log-exp
7×associate-/r* associate-/l*
4×pow1 expm1-log1p-u div-sub associate-/r/ log1p-expm1-u associate-/l/
3×flip3-- fma-def flip3-+ prod-diff flip-- flip-+
2×cbrt-undiv associate-+r- frac-2neg div-exp clear-num div-inv
1×+-commutative sub-neg fma-neg diff-log sum-log
Counts
4 → 113
Calls
4 calls:
17.0ms
(+ x (/ (- (* y z) x) (- (* t z) x)))
3.0ms
(- (* t z) x)
58.0ms
(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
11.0ms
(/ (- (* y z) x) (- (* t z) x))

series273.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ x (/ (- (* y z) x) (- (* t z) x)))
23.0ms
(- (* t z) x)
114.0ms
(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
56.0ms
(/ (- (* y z) x) (- (* t z) x))

simplify677.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (158.0ms)

IterNodesCost
01822295
14642174
218132036
done50002036

prune336.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ (fma y z (- x)) (fma z t (- x))) x)
0.5b
(/ (+ (/ (fma y z (- x)) (fma z t (- x))) x) (+ x 1.0))
11.2b
(/ (fma y z (- x)) (fma z t (- x)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
34×times-frac
28×add-sqr-sqrt add-cube-cbrt
13×fma-def
11×distribute-lft-out
7×add-exp-log associate-/r* add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv
2×cbrt-undiv frac-2neg div-exp clear-num associate-/r/ associate-/l/
1×+-commutative sum-log
Counts
3 → 98
Calls
3 calls:
10.0ms
(+ (/ (fma y z (- x)) (fma z t (- x))) x)
31.0ms
(/ (+ (/ (fma y z (- x)) (fma z t (- x))) x) (+ x 1.0))
2.0ms
(/ (fma y z (- x)) (fma z t (- x)))

series276.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(+ (/ (fma y z (- x)) (fma z t (- x))) x)
144.0ms
(/ (+ (/ (fma y z (- x)) (fma z t (- x))) x) (+ x 1.0))
62.0ms
(/ (fma y z (- x)) (fma z t (- x)))

simplify1.2s

Counts
107 → 107
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01431997
13141937
29061817
330921794
done50001791

prune327.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.5b
(/ (fma (fma y z (- x)) (/ 1 (fma z t (- x))) x) (+ x 1.0))
0.6b
(/ 1 (fma z t (- x)))
8.6b
(fma (fma y z (- x)) (/ 1 (fma z t (- x))) x)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
21×times-frac
20×add-sqr-sqrt add-cube-cbrt
9×add-exp-log
7×associate-/r* add-cbrt-cube
6×associate-/l*
4×pow1 distribute-lft-out
3×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg clear-num associate-/r/ div-inv
1×rec-exp pow-flip flip3-+ 1-exp flip-+ fma-udef inv-pow
Counts
3 → 78
Calls
3 calls:
5.0ms
(/ (fma (fma y z (- x)) (/ 1 (fma z t (- x))) x) (+ x 1.0))
2.0ms
(/ 1 (fma z t (- x)))
0.0ms
(fma (fma y z (- x)) (/ 1 (fma z t (- x))) x)

series243.0ms

Counts
3 → 9
Calls
3 calls:
148.0ms
(/ (fma (fma y z (- x)) (/ 1 (fma z t (- x))) x) (+ x 1.0))
26.0ms
(/ 1 (fma z t (- x)))
69.0ms
(fma (fma y z (- x)) (/ 1 (fma z t (- x))) x)

simplify1.2s

Counts
87 → 87
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01311620
12621563
27301366
321011363
done50001362

prune213.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.1b

localize16.0ms

Local error

Found 4 expressions with local error:

8.4b
(cbrt (/ 1 (fma z t (- x))))
8.4b
(cbrt (/ 1 (fma z t (- x))))
8.4b
(cbrt (/ 1 (fma z t (- x))))
8.6b
(fma (fma y z (- x)) (* (* (cbrt (/ 1 (fma z t (- x)))) (cbrt (/ 1 (fma z t (- x))))) (cbrt (/ 1 (fma z t (- x))))) x)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 div-inv
1×fma-udef
Counts
4 → 82
Calls
4 calls:
2.0ms
(cbrt (/ 1 (fma z t (- x))))
2.0ms
(cbrt (/ 1 (fma z t (- x))))
2.0ms
(cbrt (/ 1 (fma z t (- x))))
0.0ms
(fma (fma y z (- x)) (* (* (cbrt (/ 1 (fma z t (- x)))) (cbrt (/ 1 (fma z t (- x))))) (cbrt (/ 1 (fma z t (- x))))) x)

series417.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(cbrt (/ 1 (fma z t (- x))))
111.0ms
(cbrt (/ 1 (fma z t (- x))))
110.0ms
(cbrt (/ 1 (fma z t (- x))))
76.0ms
(fma (fma y z (- x)) (* (* (cbrt (/ 1 (fma z t (- x)))) (cbrt (/ 1 (fma z t (- x))))) (cbrt (/ 1 (fma z t (- x))))) x)

simplify1.5s

Counts
94 → 94
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01001693
11691612
23731292
39291235
432051205
done50001193

prune270.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 1.1b

regimes235.0ms

Accuracy

23.8% (4.7b remaining)

Error of 5.5b against oracle of 0.8b and baseline of 7.0b

bsearch172.0ms

Steps
ItersRangePoint
9
9.018108319142249e+89
6.147715137559524e+97
1.5358753841431232e+90
8
7.706953421200024e-257
2.858540898896391e-253
8.170967915147022e-257
8
2.1763925978762844e-300
5.6573700243989265e-297
1.6767146492905612e-298
7
-3.2205882714425573e+76
-8.254067081552174e+74
-5.239754274123804e+75

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02869
13169
done3169

end0.0ms

sample523.0ms

Algorithm
intervals
Results
311.0ms8327×body80valid