Details

Time bar (total: 33.4s)

sample72.0ms

Algorithm
intervals
Results
47.0ms451×body80valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 7 (724.0ms)

IterNodesCost
011284
123259
257259
3108259
4185259
5291259
6586259
71686244
done5000244

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(- y (/ (- (* z z) (* x x)) y))
1.6b
(- (* z z) (* x x))
15.7b
(/ (- (* z z) (* x x)) y)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
55×*-un-lft-identity
53×add-cube-cbrt
49×times-frac prod-diff
16×difference-of-squares
7×add-log-exp
5×add-cbrt-cube add-exp-log
4×fma-neg div-inv associate-/l*
3×expm1-log1p-u pow1 associate-/r* flip3-- log1p-expm1-u flip--
2×sub-neg diff-log div-sub associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp distribute-lft-out-- associate--r-
Counts
3 → 122
Calls
3 calls:
43.0ms
(- y (/ (- (* z z) (* x x)) y))
13.0ms
(- (* z z) (* x x))
36.0ms
(/ (- (* z z) (* x x)) y)

series171.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(- y (/ (- (* z z) (* x x)) y))
34.0ms
(- (* z z) (* x x))
73.0ms
(/ (- (* z z) (* x x)) y)

simplify3.1s

Counts
131 → 131
Iterations

Useful iterations: done (3.1s)

IterNodesCost
023465681
162958803
2188553031
done500549699

prune868.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(- y (/ (+ z x) (/ y (- z x))))
0.0b
(/ y (- z x))
0.2b
(/ (+ z x) (/ y (- z x)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
626×*-un-lft-identity
609×times-frac
463×add-sqr-sqrt
344×add-cube-cbrt
267×prod-diff
85×distribute-lft-out
58×difference-of-squares
56×distribute-lft-out--
40×associate-/r/
26×associate-/r*
22×div-inv
19×flip3-- flip--
10×add-cbrt-cube add-exp-log
7×associate-/l*
5×add-log-exp
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 fma-neg log1p-expm1-u
2×clear-num frac-2neg associate-/l/
1×sub-neg flip3-+ diff-log flip-+
Counts
3 → 455
Calls
3 calls:
75.0ms
(- y (/ (+ z x) (/ y (- z x))))
9.0ms
(/ y (- z x))
33.0ms
(/ (+ z x) (/ y (- z x)))

series153.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(- y (/ (+ z x) (/ y (- z x))))
38.0ms
(/ y (- z x))
62.0ms
(/ (+ z x) (/ y (- z x)))

simplify2.5s

Counts
464 → 464
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0667358790
11879322841
done5000299140

prune2.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(- y (/ 1 (/ (/ y (- z x)) (+ z x))))
0.0b
(/ y (- z x))
0.3b
(/ (/ y (- z x)) (+ z x))
0.4b
(/ 1 (/ (/ y (- z x)) (+ z x)))

rewrite429.0ms

Algorithm
rewrite-expression-head
Rules
3138×times-frac
2421×*-un-lft-identity
1848×add-sqr-sqrt
1475×add-cube-cbrt
825×prod-diff
295×distribute-lft-out
182×difference-of-squares
177×distribute-lft-out--
148×associate-/r/
99×associate-/r*
77×div-inv
59×flip3-- flip--
32×add-exp-log
27×associate-/l*
20×add-cbrt-cube
19×div-exp
14×flip3-+ flip-+
10×cbrt-undiv
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×rec-exp clear-num frac-2neg fma-neg 1-exp
1×sub-neg diff-log pow-flip inv-pow associate-/l/
Counts
4 → 1408
Calls
4 calls:
181.0ms
(- y (/ 1 (/ (/ y (- z x)) (+ z x))))
9.0ms
(/ y (- z x))
27.0ms
(/ (/ y (- z x)) (+ z x))
43.0ms
(/ 1 (/ (/ y (- z x)) (+ z x)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- y (/ 1 (/ (/ y (- z x)) (+ z x))))
36.0ms
(/ y (- z x))
74.0ms
(/ (/ y (- z x)) (+ z x))
85.0ms
(/ 1 (/ (/ y (- z x)) (+ z x)))

simplify4.3s

Counts
1420 → 1420
Iterations

Useful iterations: done (3.8s)

IterNodesCost
019131400813
done50011270542

prune9.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize167.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
53.4b
(fma (- (/ (+ z x) (/ (cbrt y) (cbrt (- z x))))) (/ 1 (/ (* (cbrt y) (cbrt y)) (* (cbrt (- z x)) (cbrt (- z x))))) (* (/ (+ z x) (/ (cbrt y) (cbrt (- z x)))) (/ 1 (/ (* (cbrt y) (cbrt y)) (* (cbrt (- z x)) (cbrt (- z x)))))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)
0.0ms
(fma (- (/ (+ z x) (/ (cbrt y) (cbrt (- z x))))) (/ 1 (/ (* (cbrt y) (cbrt y)) (* (cbrt (- z x)) (cbrt (- z x))))) (* (/ (+ z x) (/ (cbrt y) (cbrt (- z x)))) (/ 1 (/ (* (cbrt y) (cbrt y)) (* (cbrt (- z x)) (cbrt (- z x)))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
313.0ms
(cbrt y)
259.0ms
(cbrt y)
286.0ms
(cbrt y)
600.0ms
(fma (- (/ (+ z x) (/ (cbrt y) (cbrt (- z x))))) (/ 1 (/ (* (cbrt y) (cbrt y)) (* (cbrt (- z x)) (cbrt (- z x))))) (* (/ (+ z x) (/ (cbrt y) (cbrt (- z x)))) (/ 1 (/ (* (cbrt y) (cbrt y)) (* (cbrt (- z x)) (cbrt (- z x)))))))

simplify2.9s

Counts
61 → 61
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
09819032
123916488
267415236
3290314206
done503014206

prune983.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes238.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010244
111244
done11244

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s13794×body80valid