Details

Time bar (total: 32.1s)

sample77.0ms

Algorithm
intervals
Results
19.0ms244×body80valid
13.0ms11×body1280valid
6.0ms18×body640valid
2.0ms11×body160valid
2.0ms9×body320valid

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01113
12313
24612
312812
436812
5110312
6436412
done500012

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
14.7b
(fma (/ (- t x) (- a z)) (- y z) x)

rewrite55.0ms

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:
49.0ms
(/ (- t x) (- a z))
1.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series264.0ms

Counts
2 → 6
Calls
2 calls:
91.0ms
(/ (- t x) (- a z))
173.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify3.2s

Counts
70 → 70
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0118918
1274890
2848838
34610834
done5000834

prune587.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
4.3b
(+ (* (/ (- t x) (- a z)) (- y z)) x)
4.3b
(* (/ (- t x) (- a z)) (- y z))

rewrite235.0ms

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:
45.0ms
(/ (- t x) (- a z))
50.0ms
(+ (* (/ (- t x) (- a z)) (- y z)) x)
125.0ms
(* (/ (- t x) (- a z)) (- y z))

series763.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(/ (- t x) (- a z))
289.0ms
(+ (* (/ (- t x) (- a z)) (- y z)) x)
379.0ms
(* (/ (- t x) (- a z)) (- y z))

simplify2.4s

Counts
179 → 179
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02563107
17172752
233302516
done50002490

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.6b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y z) (- a z))
0.9b
(* (- t x) (/ (- y z) (- a z)))
3.3b
(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
73×*-un-lft-identity
51×times-frac
31×associate-*r*
27×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
3×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative fma-def frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 126
Calls
3 calls:
48.0ms
(/ (- y z) (- a z))
121.0ms
(* (- t x) (/ (- y z) (- a z)))
49.0ms
(+ (* (- t x) (/ (- y z) (- a z))) x)

series631.0ms

Counts
3 → 9
Calls
3 calls:
88.0ms
(/ (- y z) (- a z))
227.0ms
(* (- t x) (/ (- y z) (- a z)))
316.0ms
(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify2.8s

Counts
135 → 135
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01891881
15181777
226511675
done50021667

prune990.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- a z))
0.3b
(* (- y z) (/ 1 (- a z)))
0.9b
(* (- t x) (* (- y z) (/ 1 (- a z))))
5.5b
(+ (* (- t x) (* (- y z) (/ 1 (- a z)))) x)

rewrite422.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
44×*-un-lft-identity
32×add-exp-log times-frac
25×add-cube-cbrt
22×associate-*r*
20×frac-times add-cbrt-cube
17×flip3-- flip--
13×prod-exp
12×pow1
10×associate-*r/ associate-*l* associate-*l/
9×distribute-lft-out-- difference-of-squares
7×cbrt-unprod
6×div-exp add-log-exp
5×associate-/r*
4×expm1-log1p-u pow-prod-down associate-/r/ un-div-inv log1p-expm1-u
3×cbrt-undiv rec-exp 1-exp associate-/l* unswap-sqr
2×*-commutative div-inv
1×+-commutative pow-flip fma-def frac-2neg flip3-+ clear-num sum-log flip-+ inv-pow
Counts
4 → 155
Calls
4 calls:
25.0ms
(/ 1 (- a z))
95.0ms
(* (- y z) (/ 1 (- a z)))
149.0ms
(* (- t x) (* (- y z) (/ 1 (- a z))))
138.0ms
(+ (* (- t x) (* (- y z) (/ 1 (- a z)))) x)

series688.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ 1 (- a z))
90.0ms
(* (- y z) (/ 1 (- a z)))
220.0ms
(* (- t x) (* (- y z) (/ 1 (- a z))))
321.0ms
(+ (* (- t x) (* (- y z) (/ 1 (- a z)))) x)

simplify9.2s

Counts
167 → 167
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
02292378
16312111
249561798
done50001798

prune904.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.8b

regimes781.0ms

Accuracy

-7.9% (9.4b remaining)

Error of 13.0b against oracle of 3.5b and baseline of 12.3b

bsearch176.0ms

Steps
ItersRangePoint
9
494987148267.1194
2.4001188468348672e+17
500051093016.9032
8
-1.6829627543292803e-61
-6.2230050197263674e-65
-6.307896652435074e-65

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02450
13336
done3336

end0.0ms

sample2.2s

Algorithm
intervals
Results
918.0ms7718×body80valid
223.0ms499×body640valid
109.0ms286×body1280valid
88.0ms394×body320valid
44.0ms293×body160valid
7.0ms16×body2560valid