Details

Time bar (total: 15.9s)

sample30.0ms

Algorithm
intervals
Results
8.0ms264×body80valid
2.0ms22×body640valid
1.0ms10×body1280valid
1.0ms13×body320valid
1.0ms12×body160valid

simplify6.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (16.0ms)

IterNodesCost
01113
12013
24513
311612
432212
576612
6155512
7287312
8476112
done500012

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- y z) (- a z))
4.5b
(fma (/ (- y z) (- a z)) (- t x) x)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
28.0ms
(/ (- y z) (- a z))
0.0ms
(fma (/ (- y z) (- a z)) (- t x) x)

series189.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(/ (- y z) (- a z))
135.0ms
(fma (/ (- y z) (- a z)) (- t x) x)

simplify1.2s

Counts
70 → 70
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0116918
1266890
2653838
31707834
done5001830

prune210.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y z) (- a z))
1.7b
(* (/ (- y z) (- a z)) (- t x))
3.5b
(+ (* (/ (- y z) (- a z)) (- t x)) x)

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
97×*-un-lft-identity
51×add-cube-cbrt times-frac
36×prod-diff
31×associate-*l*
23×distribute-lft-out-- difference-of-squares
22×distribute-rgt-in associate-+l+ distribute-lft-in
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*r* associate-/r* flip-- associate-/l* add-log-exp
4×sub-neg associate-/r/
3×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative fma-def frac-2neg flip3-+ div-sub pow-prod-down associate-*l/ clear-num sum-log *-commutative flip-+
Counts
3 → 170
Calls
3 calls:
24.0ms
(/ (- y z) (- a z))
62.0ms
(* (/ (- y z) (- a z)) (- t x))
26.0ms
(+ (* (/ (- y z) (- a z)) (- t x)) x)

series592.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(/ (- y z) (- a z))
332.0ms
(* (/ (- y z) (- a z)) (- t x))
205.0ms
(+ (* (/ (- y z) (- a z)) (- t x)) x)

simplify1.0s

Counts
179 → 179
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02553085
16652718
219552494
done50012468

prune449.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
3.5b
(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (- t x))) x)

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
44×distribute-rgt-in associate-+l+ distribute-lft-in
37×add-sqr-sqrt *-un-lft-identity
36×prod-diff
31×add-cube-cbrt
15×cbrt-prod
6×cbrt-div add-log-exp
4×pow1 add-exp-log expm1-log1p-u sub-neg add-cbrt-cube log1p-expm1-u
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×+-commutative fma-def flip3-+ sum-log flip-+
Counts
4 → 109
Calls
4 calls:
4.0ms
(cbrt (- a z))
4.0ms
(cbrt (- a z))
4.0ms
(cbrt (- a z))
166.0ms
(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (- t x))) x)

series700.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(cbrt (- a z))
166.0ms
(cbrt (- a z))
162.0ms
(cbrt (- a z))
210.0ms
(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (- t x))) x)

simplify809.0ms

Counts
121 → 121
Iterations

Useful iterations: done (805.0ms)

IterNodesCost
01643180
14422980
211961613
done50011317

prune548.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a z))
0.2b
(* (- y z) (/ 1 (- a z)))
5.5b
(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×*-un-lft-identity
32×times-frac
23×add-cube-cbrt
21×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-*l* associate-/r*
4×flip3-- div-exp prod-exp associate-/r/ flip--
3×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative fma-udef inv-pow
Counts
3 → 105
Calls
3 calls:
12.0ms
(/ 1 (- a z))
47.0ms
(* (- y z) (/ 1 (- a z)))
0.0ms
(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series229.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ 1 (- a z))
59.0ms
(* (- y z) (/ 1 (- a z)))
133.0ms
(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify1.7s

Counts
114 → 114
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01521285
13341052
2930948
33159944
done5002942

prune252.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.8b

regimes348.0ms

Accuracy

21.7% (6.3b remaining)

Error of 9.7b against oracle of 3.4b and baseline of 11.4b

bsearch101.0ms

Steps
ItersRangePoint
9
8.224624671681947e-55
6.986279115010668e-47
8.392440744553116e-55
9
-3.14580386158863e-55
-1.6550014685892204e-61
-1.6867008311555928e-61

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03066
13766
done3766

end0.0ms

sample766.0ms

Algorithm
intervals
Results
249.0ms7805×body80valid
52.0ms485×body640valid
36.0ms273×body1280valid
31.0ms380×body320valid
15.0ms264×body160valid
2.0ms13×body2560valid