Details

Time bar (total: 24.3s)

sample209.0ms

Algorithm
intervals
Results
73.0ms74×body10240exit
41.0ms55×body1280valid
35.0ms349×body80valid
16.0ms37×body640valid
7.0ms24×body320valid
2.0ms7×body160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5001
42356
3395
2124
147
019

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (/ 1.0 eps))
0.0b
(exp (* x (- eps 1.0)))
0.0b
(exp (* x (+ 1.0 eps)))
5.6b
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
57×prod-diff
56×add-sqr-sqrt
53×*-un-lft-identity
51×add-cube-cbrt
28×times-frac
24×exp-sum
12×distribute-rgt-in distribute-lft-in
10×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×sub-neg fma-neg div-inv
2×exp-prod exp-to-pow difference-of-squares rem-exp-log
1×flip3-- diff-log fma-udef flip-- distribute-lft-out--
Counts
4 → 117
Calls
4 calls:
18.0ms
(- 1.0 (/ 1.0 eps))
14.0ms
(exp (* x (- eps 1.0)))
8.0ms
(exp (* x (+ 1.0 eps)))
1.0ms
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))))

series228.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- 1.0 (/ 1.0 eps))
24.0ms
(exp (* x (- eps 1.0)))
24.0ms
(exp (* x (+ 1.0 eps)))
134.0ms
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))))

simplify1.8s

Counts
129 → 129
Iterations
IterNodes
done5001
23063
1748
0312

prune765.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 2.0 (fma (/ x (/ eps (* x x))) 2.7755575615628914e-17 (* (* x x) 1.0)))
0.1b
(/ x (/ eps (* x x)))
3.9b
(fma (/ x (/ eps (* x x))) 2.7755575615628914e-17 (* (* x x) 1.0))
5.6b
(/ eps (* x x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
31×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
18×add-cbrt-cube add-exp-log
9×prod-diff
8×associate-/r*
7×cbrt-undiv div-exp
6×div-inv associate-/l* add-log-exp
4×expm1-log1p-u pow1 log1p-expm1-u
3×fma-neg
2×clear-num frac-2neg prod-exp cbrt-unprod fma-udef
1×sub-neg flip3-- diff-log associate-/r/ flip-- associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 112
Calls
4 calls:
10.0ms
(- 2.0 (fma (/ x (/ eps (* x x))) 2.7755575615628914e-17 (* (* x x) 1.0)))
18.0ms
(/ x (/ eps (* x x)))
0.0ms
(fma (/ x (/ eps (* x x))) 2.7755575615628914e-17 (* (* x x) 1.0))
7.0ms
(/ eps (* x x))

series268.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- 2.0 (fma (/ x (/ eps (* x x))) 2.7755575615628914e-17 (* (* x x) 1.0)))
41.0ms
(/ x (/ eps (* x x)))
93.0ms
(fma (/ x (/ eps (* x x))) 2.7755575615628914e-17 (* (* x x) 1.0))
43.0ms
(/ eps (* x x))

simplify1.6s

Counts
124 → 124
Iterations
IterNodes
done5001
22581
1452
0184

prune794.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.9b
(* (/ (* (cbrt x) (cbrt x)) eps) (* (* x x) (cbrt x)))
3.9b
(fma (* (/ (* (cbrt x) (cbrt x)) eps) (* (* x x) (cbrt x))) 2.7755575615628914e-17 (* (* x x) 1.0))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
28×add-cbrt-cube
21×prod-exp cbrt-unprod
13×pow1
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*l*
6×cbrt-prod cbrt-undiv div-exp pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac
2×pow1/3
1×associate-*r* associate-*l/ *-commutative fma-udef div-inv
Counts
4 → 76
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
85.0ms
(* (/ (* (cbrt x) (cbrt x)) eps) (* (* x x) (cbrt x)))
0.0ms
(fma (* (/ (* (cbrt x) (cbrt x)) eps) (* (* x x) (cbrt x))) 2.7755575615628914e-17 (* (* x x) 1.0))

series796.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(cbrt x)
343.0ms
(cbrt x)
80.0ms
(* (/ (* (cbrt x) (cbrt x)) eps) (* (* x x) (cbrt x)))
105.0ms
(fma (* (/ (* (cbrt x) (cbrt x)) eps) (* (* x x) (cbrt x))) 2.7755575615628914e-17 (* (* x x) 1.0))

simplify2.4s

Counts
88 → 88
Iterations
IterNodes
done5001
22278
1376
0124

prune509.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
3.5b
(fma (* (/ (* (cbrt x) (log (exp (cbrt x)))) eps) (* (* x x) (cbrt x))) 2.7755575615628914e-17 (* (* x x) 1.0))
14.6b
(log (exp (cbrt x)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×log-pow
6×exp-prod
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×log-prod
2×pow1/3
1×rem-log-exp fma-udef
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma (* (/ (* (cbrt x) (log (exp (cbrt x)))) eps) (* (* x x) (cbrt x))) 2.7755575615628914e-17 (* (* x x) 1.0))
4.0ms
(log (exp (cbrt x)))

series938.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(cbrt x)
254.0ms
(cbrt x)
113.0ms
(fma (* (/ (* (cbrt x) (log (exp (cbrt x)))) eps) (* (* x x) (cbrt x))) 2.7755575615628914e-17 (* (* x x) 1.0))
299.0ms
(log (exp (cbrt x)))

simplify1.9s

Counts
68 → 68
Iterations
IterNodes
done5002
32499
2466
1144
083

prune517.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

regimes262.0ms

Accuracy

95.5% (0.8b remaining)

Error of 4.5b against oracle of 3.8b and baseline of 20.5b

bsearch238.0ms

Steps
ItersRangePoint
10
1.9673231826388637e-10
9645967.64350026
5.512941299653822e-05

simplify15.0ms

Iterations
IterNodes
done44
144
036

end0.0ms

sample9.1s

Algorithm
intervals
Results
2.8s1879×body10240exit
2.6s1738×body1280valid
1.8s9945×body80valid
812.0ms1248×body640valid
293.0ms638×body320valid
120.0ms327×body160valid