Details

Time bar (total: 22.1s)

sample54.0ms

Algorithm
intervals
Results
16.0ms259×body80valid
3.0ms13×body640valid
3.0ms15×body320valid
1.0ms4×body1280valid
1.0ms7×body160valid
0.0ms1×body2560valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01113
12313
24612
312812
436812
5110312
6436412
done500012

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
11.6b
(fma (/ (- t x) (- a z)) (- y z) x)

rewrite34.0ms

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:
32.0ms
(/ (- t x) (- a z))
0.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series164.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(/ (- t x) (- a z))
107.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.2s

Counts
70 → 70
Iterations

Useful iterations: 3 (975.0ms)

IterNodesCost
0118918
1274890
2848838
34610834
done5000834

prune257.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
2.5b
(+ (* (/ (- t x) (- a z)) (- y z)) x)
4.5b
(* (/ (- t x) (- a z)) (- y z))

rewrite198.0ms

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:
39.0ms
(/ (- t x) (- a z))
41.0ms
(+ (* (/ (- t x) (- a z)) (- y z)) x)
107.0ms
(* (/ (- t x) (- a z)) (- y z))

series564.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(/ (- t x) (- a z))
239.0ms
(+ (* (/ (- t x) (- a z)) (- y z)) x)
267.0ms
(* (/ (- t x) (- a z)) (- y z))

simplify1.8s

Counts
179 → 179
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02563107
17172752
233302516
done50002490

prune593.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y z) (- a z))
2.2b
(+ (* (- t x) (/ (- y z) (- a z))) x)
2.5b
(* (- t x) (/ (- y z) (- a z)))

rewrite166.0ms

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:
34.0ms
(/ (- y z) (- a z))
28.0ms
(+ (* (- t x) (/ (- y z) (- a z))) x)
96.0ms
(* (- t x) (/ (- y z) (- a z)))

series442.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(/ (- y z) (- a z))
211.0ms
(+ (* (- t x) (/ (- y z) (- a z))) x)
168.0ms
(* (- t x) (/ (- y z) (- a z)))

simplify1.9s

Counts
135 → 135
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01891881
15171777
226261669
done50011667

prune581.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- a z))
0.2b
(* (- y z) (/ 1 (- a z)))
2.5b
(* (- t x) (* (- y z) (/ 1 (- a z))))
3.7b
(+ (* (- t x) (* (- y z) (/ 1 (- a z)))) x)

rewrite341.0ms

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:
15.0ms
(/ 1 (- a z))
76.0ms
(* (- y z) (/ 1 (- a z)))
127.0ms
(* (- t x) (* (- y z) (/ 1 (- a z))))
112.0ms
(+ (* (- t x) (* (- y z) (/ 1 (- a z)))) x)

series581.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1 (- a z))
71.0ms
(* (- y z) (/ 1 (- a z)))
208.0ms
(* (- t x) (* (- y z) (/ 1 (- a z))))
253.0ms
(+ (* (- t x) (* (- y z) (/ 1 (- a z)))) x)

simplify6.9s

Counts
167 → 167
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
02292378
16312111
249561798
done50001798

prune415.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.4b

regimes330.0ms

Accuracy

20.9% (6.7b remaining)

Error of 10.1b against oracle of 3.4b and baseline of 11.9b

bsearch139.0ms

Steps
ItersRangePoint
8
1.9058889995110037e-110
1.2261649568763873e-107
2.51430898119071e-108
7
-3.6195348640467436e-147
-9.054969149379634e-149
-2.5410130176257374e-148

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02748
13548
done3548

end0.0ms

sample1.7s

Algorithm
intervals
Results
520.0ms7770×body80valid
459.0ms486×body640valid
134.0ms251×body1280valid
57.0ms422×body320valid
26.0ms285×body160valid
4.0ms11×body2560valid