Details

Time bar (total: 25.5s)

sample168.0ms

Algorithm
intervals
Results
54.0ms329×body80valid
36.0ms54×body1280valid
36.0ms57×body10240exit
18.0ms45×body640valid
6.0ms20×body320valid
1.0ms5×body160valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5001
41436
3398
2124
149
019

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
0.0b
(* x (+ -1 eps))
0.0b
(* x (+ -1 eps))
2.2b
(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
410×add-sqr-sqrt
327×times-frac
305×*-un-lft-identity
180×prod-diff
146×add-cube-cbrt
104×difference-of-squares
58×fma-udef
57×exp-sum
51×difference-of-sqr-1
35×distribute-lft-out--
21×div-inv
14×associate-/l*
10×add-cbrt-cube
9×add-exp-log
8×pow1 associate-*r*
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-/r* associate-*r/ insert-posit16 log1p-expm1-u
3×fma-neg
2×distribute-rgt-in distribute-lft-in flip3-+ flip3-- div-sub pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ flip-- distribute-lft-out unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp associate--l+ associate--r-
Counts
4 → 347
Calls
4 calls:
57.0ms
(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
18.0ms
(* x (+ -1 eps))
19.0ms
(* x (+ -1 eps))
81.0ms
(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
48.0ms
(* x (+ -1 eps))
37.0ms
(* x (+ -1 eps))
143.0ms
(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

simplify2.3s

Counts
359 → 359
Iterations
IterNodes
done5000
23771
11402
0529

prune2.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x x) 2/3)
0.2b
(* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x))))
5.8b
(fma x (* (* x x) 2/3) (- 2 (* x x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
6×*-un-lft-identity associate-*r* add-cube-cbrt
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative unswap-sqr
1×distribute-rgt-in distribute-lft-in
Counts
3 → 56
Calls
3 calls:
18.0ms
(* (* x x) 2/3)
12.0ms
(* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x))))
0.0ms
(fma x (* (* x x) 2/3) (- 2 (* x x)))

series143.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* (* x x) 2/3)
57.0ms
(* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x))))
50.0ms
(fma x (* (* x x) 2/3) (- 2 (* x x)))

simplify2.8s

Counts
65 → 65
Iterations
IterNodes
done5003
33416
2676
1211
092

prune295.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize59.0ms

Local error

Found 4 expressions with local error:

5.8b
(fma x (* (* x x) 2/3) (- 2 (* x x)))
9.5b
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
9.5b
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
9.5b
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×fma-udef
Counts
4 → 47
Calls
4 calls:
0.0ms
(fma x (* (* x x) 2/3) (- 2 (* x x)))
6.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
6.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
6.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))

series530.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(fma x (* (* x x) 2/3) (- 2 (* x x)))
142.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
178.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
169.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))

simplify2.1s

Counts
59 → 59
Iterations
IterNodes
done5004
32283
2539
1189
083

prune432.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize67.0ms

Local error

Found 4 expressions with local error:

9.5b
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
9.5b
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
9.5b
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
9.5b
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
4×cbrt-prod add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube pow1/3 add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 48
Calls
4 calls:
3.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
5.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
7.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
7.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))

series657.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
165.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
154.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))
151.0ms
(cbrt (* 1/2 (fma x (* (* x x) 2/3) (- 2 (* x x)))))

simplify1.6s

Counts
60 → 60
Iterations
IterNodes
done5001
31880
2481
1168
070

prune482.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

regimes107.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.1b

bsearch247.0ms

Steps
ItersRangePoint
9
1.7877411926250683e-07
443.57959014112146
1.8329629569573715

simplify7.0ms

Iterations
IterNodes
done42
142
032

end0.0ms

sample9.1s

Algorithm
intervals
Results
2.8s2013×body10240exit
2.3s9854×body80valid
2.0s1737×body1280valid
1.3s1291×body640valid
279.0ms667×body320valid
117.0ms323×body160valid