Details

Time bar (total: 22.7s)

sample43.0ms

Algorithm
intervals
Results
17.0ms246×body80valid
3.0ms19×body640valid
2.0ms14×body320valid
1.0ms4×body1280valid
1.0ms9×body160valid
0.0ms1×body2560valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01113
12313
24612
312812
436812
5110312
6436412
done500012

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
15.4b
(fma (/ (- t x) (- a z)) (- y z) x)

rewrite45.0ms

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:
40.0ms
(/ (- t x) (- a z))
0.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series190.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(/ (- t x) (- a z))
128.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.2s

Counts
70 → 70
Iterations

Useful iterations: 3 (742.0ms)

IterNodesCost
0118918
1274890
2848838
34610834
done5000834

prune400.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ t (- a z))
0.0b
(/ x (- a z))
0.2b
(- (/ t (- a z)) (/ x (- a z)))
15.4b
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
703×add-sqr-sqrt
693×times-frac
441×prod-diff
413×add-cube-cbrt
149×distribute-lft-out--
143×difference-of-squares
94×associate-/r/
48×flip3-- flip--
47×div-inv
21×fma-neg
10×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×distribute-rgt-out--
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg diff-log frac-sub fma-udef sub-div
Counts
4 → 581
Calls
4 calls:
19.0ms
(/ t (- a z))
22.0ms
(/ x (- a z))
159.0ms
(- (/ t (- a z)) (/ x (- a z)))
1.0ms
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

series310.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ t (- a z))
32.0ms
(/ x (- a z))
124.0ms
(- (/ t (- a z)) (/ x (- a z)))
119.0ms
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

simplify2.2s

Counts
593 → 593
Iterations

Useful iterations: done (2.2s)

IterNodesCost
057428436
1128525602
2376820232
done500020230

prune2.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ t (- a z))
0.2b
(- (/ t (- a z)) (/ x (- a z)))
3.8b
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)
6.9b
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))

rewrite705.0ms

Algorithm
rewrite-expression-head
Rules
751×*-un-lft-identity
733×add-sqr-sqrt
696×times-frac
477×prod-diff
431×add-cube-cbrt
158×distribute-lft-out--
146×difference-of-squares
96×associate-/r/
57×flip3-- flip--
48×div-inv
22×distribute-rgt-in associate-+l+ distribute-lft-in
21×fma-neg
18×associate-*l*
8×add-exp-log frac-times add-cbrt-cube add-log-exp
6×pow1 distribute-rgt-out--
5×sub-neg associate-*r* associate-/r*
4×expm1-log1p-u associate-*l/ frac-sub log1p-expm1-u sub-div
3×associate-/l*
2×associate-*r/
1×cbrt-undiv +-commutative fma-def frac-2neg flip3-+ diff-log div-exp pow-prod-down prod-exp clear-num sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 641
Calls
4 calls:
11.0ms
(/ t (- a z))
112.0ms
(- (/ t (- a z)) (/ x (- a z)))
138.0ms
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)
376.0ms
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))

series821.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ t (- a z))
161.0ms
(- (/ t (- a z)) (/ x (- a z)))
229.0ms
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)
391.0ms
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))

simplify933.0ms

Counts
653 → 653
Iterations

Useful iterations: done (899.0ms)

IterNodesCost
069630832
1163227672
done500122520

prune3.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
15.3b
(fma (- (/ t (- a z)) (/ (/ x (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z)))) (- y z) x)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×fma-udef
Counts
4 → 61
Calls
4 calls:
7.0ms
(cbrt (- a z))
15.0ms
(cbrt (- a z))
7.0ms
(cbrt (- a z))
1.0ms
(fma (- (/ t (- a z)) (/ (/ x (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z)))) (- y z) x)

series851.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(cbrt (- a z))
205.0ms
(cbrt (- a z))
243.0ms
(cbrt (- a z))
179.0ms
(fma (- (/ t (- a z)) (/ (/ x (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z)))) (- y z) x)

simplify915.0ms

Counts
73 → 73
Iterations

Useful iterations: done (911.0ms)

IterNodesCost
097977
1196959
2482793
31604720
done5001682

prune647.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.5b

regimes963.0ms

Accuracy

6% (7.8b remaining)

Error of 14.2b against oracle of 6.4b and baseline of 14.7b

bsearch114.0ms

Steps
ItersRangePoint
8
6.313129924895105e+186
1.9583537836977243e+189
9.487535219060974e+188
6
-8.41609380773411e+178
-1.3592681186369971e+178
-6.055915063761881e+178

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02449
12949
done2949

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s7842×body80valid
153.0ms483×body640valid
111.0ms264×body1280valid
110.0ms384×body320valid
33.0ms249×body160valid
6.0ms15×body2560valid