Details

Time bar (total: 18.8s)

sample74.0ms

Algorithm
intervals
Results
20.0ms207×body80valid
9.0ms24×body640valid
8.0ms256×pre80true
7.0ms13×body1280valid
2.0ms6×body320valid
1.0ms6×body160valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done5000
42747
3478
2106
131
015

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2.0 i (+ beta alpha))
0.0b
(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
0.0b
(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
11.6b
(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
166×times-frac
157×*-un-lft-identity
117×add-sqr-sqrt
79×add-cube-cbrt
24×associate-/l*
20×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
11×add-cbrt-cube add-exp-log
7×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×div-sub associate-/l/
2×clear-num frac-2neg associate-/r/ fma-udef
1×flip3-+ flip3-- flip-+ flip--
Counts
4 → 179
Calls
4 calls:
0.0ms
(fma 2.0 i (+ beta alpha))
19.0ms
(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
36.0ms
(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
1.0ms
(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

series655.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(fma 2.0 i (+ beta alpha))
100.0ms
(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
273.0ms
(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
250.0ms
(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

simplify1.4s

Counts
191 → 191
Iterations
IterNodes
done5000
23241
1660
0255

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.3b

localize96.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- beta alpha))
0.6b
(cbrt (- beta alpha))
0.6b
(cbrt (- beta alpha))
11.6b
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (cbrt (- beta alpha)) (+ (fma 2.0 i beta) (+ alpha 2.0))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log 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:
3.0ms
(cbrt (- beta alpha))
3.0ms
(cbrt (- beta alpha))
3.0ms
(cbrt (- beta alpha))
0.0ms
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (cbrt (- beta alpha)) (+ (fma 2.0 i beta) (+ alpha 2.0))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

series870.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(cbrt (- beta alpha))
189.0ms
(cbrt (- beta alpha))
226.0ms
(cbrt (- beta alpha))
245.0ms
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (cbrt (- beta alpha)) (+ (fma 2.0 i beta) (+ alpha 2.0))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

simplify2.1s

Counts
73 → 73
Iterations
IterNodes
done5000
34105
2789
1241
0108

prune766.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 11.3b

localize122.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- beta alpha))
0.6b
(cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))
0.6b
(cbrt (cbrt (- beta alpha)))
11.5b
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (* (cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))) (cbrt (cbrt (- beta alpha)))) (+ (fma 2.0 i beta) (+ alpha 2.0))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-div
19×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity
8×flip3-- flip--
7×add-cube-cbrt
4×expm1-log1p-u frac-times pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
2×associate-*l/ associate-*r/ distribute-lft-out-- difference-of-squares
1×fma-udef
Counts
4 → 66
Calls
4 calls:
6.0ms
(cbrt (- beta alpha))
22.0ms
(cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))
7.0ms
(cbrt (cbrt (- beta alpha)))
1.0ms
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (* (cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))) (cbrt (cbrt (- beta alpha)))) (+ (fma 2.0 i beta) (+ alpha 2.0))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
205.0ms
(cbrt (- beta alpha))
513.0ms
(cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))
236.0ms
(cbrt (cbrt (- beta alpha)))
282.0ms
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (* (cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))) (cbrt (cbrt (- beta alpha)))) (+ (fma 2.0 i beta) (+ alpha 2.0))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

simplify770.0ms

Counts
78 → 78
Iterations
IterNodes
done5001
21220
1415
0203

prune980.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 11.2b

localize201.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- beta alpha))
0.6b
(cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))
0.6b
(cbrt (cbrt (- beta alpha)))
6.0b
(+ (* (* (* (+ alpha beta) (/ (cbrt (cbrt (- beta alpha))) (cbrt (fma i 2.0 (+ alpha beta))))) (/ (cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))) (+ (fma 2.0 i beta) (+ alpha 2.0)))) (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ alpha beta)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ alpha beta)))))) 1.0)

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-div
19×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity
8×flip3-- flip--
7×add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u frac-times pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×pow1/3
2×associate-*l/ associate-*r/ distribute-lft-out-- difference-of-squares
1×+-commutative sum-log fma-def flip3-+ flip-+
Counts
4 → 70
Calls
4 calls:
3.0ms
(cbrt (- beta alpha))
11.0ms
(cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))
4.0ms
(cbrt (cbrt (- beta alpha)))
461.0ms
(+ (* (* (* (+ alpha beta) (/ (cbrt (cbrt (- beta alpha))) (cbrt (fma i 2.0 (+ alpha beta))))) (/ (cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))) (+ (fma 2.0 i beta) (+ alpha 2.0)))) (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ alpha beta)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ alpha beta)))))) 1.0)

series979.0ms

Counts
4 → 12
Calls
4 calls:
230.0ms
(cbrt (- beta alpha))
183.0ms
(cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))
204.0ms
(cbrt (cbrt (- beta alpha)))
361.0ms
(+ (* (* (* (+ alpha beta) (/ (cbrt (cbrt (- beta alpha))) (cbrt (fma i 2.0 (+ alpha beta))))) (/ (cbrt (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))) (+ (fma 2.0 i beta) (+ alpha 2.0)))) (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ alpha beta)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ alpha beta)))))) 1.0)

simplify916.0ms

Counts
82 → 82
Iterations
IterNodes
done5001
21568
1483
0221

prune914.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

regimes476.0ms

Accuracy

-13% (7.6b remaining)

Error of 13.3b against oracle of 5.6b and baseline of 12.4b

bsearch223.0ms

Steps
ItersRangePoint
8
5.969670028271364e+165
2.0864758149000452e+170
2.2669802580153736e+166
9
1.2707568867468327e+57
9.927202395589815e+62
9.76982660809476e+62

simplify7.0ms

Iterations
IterNodes
done39
139
030

end0.0ms

sample2.4s

Algorithm
intervals
Results
661.0ms6362×body80valid
478.0ms329×body320valid
292.0ms583×body640valid
278.0ms8000×pre80true
264.0ms542×body1280valid
30.0ms184×body160valid