Details

Time bar (total: 34.7s)

sample62.0ms

Algorithm
intervals
Results
19.0ms398×body80valid
12.0ms146×body80nan

simplify5.8s

Counts
1 → 1
Iterations
IterNodes
done5000
62347
5652
4213
394
250
124
012

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma k (+ k 10.0) 1.0)
0.0b
(* (pow k m) a)
1.8b
(/ (* (pow k m) a) (fma k (+ k 10.0) 1.0))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt
10×add-cbrt-cube
8×*-un-lft-identity add-cube-cbrt
7×associate-*l*
6×prod-exp
4×unpow-prod-down div-exp
3×expm1-log1p-u pow1 associate-/r* times-frac associate-*r* insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-to-exp cbrt-undiv pow-exp cbrt-unprod sqr-pow
1×clear-num frac-2neg *-commutative fma-udef div-inv associate-/l*
Counts
3 → 65
Calls
3 calls:
2.0ms
(fma k (+ k 10.0) 1.0)
20.0ms
(* (pow k m) a)
24.0ms
(/ (* (pow k m) a) (fma k (+ k 10.0) 1.0))

series538.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(fma k (+ k 10.0) 1.0)
202.0ms
(* (pow k m) a)
300.0ms
(/ (* (pow k m) a) (fma k (+ k 10.0) 1.0))

simplify2.5s

Counts
74 → 74
Iterations
IterNodes
done5003
21110
1337
0141

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma k (+ k 10.0) 1.0)
0.3b
(/ (pow k m) (/ (fma k (+ k 10.0) 1.0) a))
2.4b
(/ (fma k (+ k 10.0) 1.0) a)

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
95×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
42×unpow-prod-down
18×add-exp-log
16×associate-/r*
14×sqr-pow
10×add-cbrt-cube div-exp div-inv associate-/l*
4×cbrt-undiv
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp clear-num frac-2neg pow-exp
1×associate-/r/ fma-udef
Counts
3 → 174
Calls
3 calls:
2.0ms
(fma k (+ k 10.0) 1.0)
34.0ms
(/ (pow k m) (/ (fma k (+ k 10.0) 1.0) a))
14.0ms
(/ (fma k (+ k 10.0) 1.0) a)

series406.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(fma k (+ k 10.0) 1.0)
270.0ms
(/ (pow k m) (/ (fma k (+ k 10.0) 1.0) a))
95.0ms
(/ (fma k (+ k 10.0) 1.0) a)

simplify4.5s

Counts
183 → 183
Iterations
IterNodes
done5002
22392
1803
0326

prune2.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize197.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (/ a k) (exp (* (log k) m)))
2.2b
(* (/ a k) (exp (* (log k) m)))
7.7b
(+ (/ (* (/ a k) (exp (* (log k) m))) k) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0)))
13.7b
(fma (/ 99.0 (* k k)) (/ (* (/ a k) (exp (* (log k) m))) k) (+ (/ (* (/ a k) (exp (* (log k) m))) k) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
26×associate-*l*
23×times-frac
22×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube
10×add-exp-log
8×pow1
7×fma-def
6×associate-*r* add-log-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×associate-*l/ div-inv
2×cbrt-undiv div-exp pow-prod-down *-commutative distribute-rgt-neg-out
1×+-commutative sum-log flip3-+ unsub-neg frac-add flip-+ fma-udef
Counts
4 → 105
Calls
4 calls:
36.0ms
(* (/ a k) (exp (* (log k) m)))
53.0ms
(* (/ a k) (exp (* (log k) m)))
39.0ms
(+ (/ (* (/ a k) (exp (* (log k) m))) k) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0)))
1.0ms
(fma (/ 99.0 (* k k)) (/ (* (/ a k) (exp (* (log k) m))) k) (+ (/ (* (/ a k) (exp (* (log k) m))) k) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (/ a k) (exp (* (log k) m)))
189.0ms
(* (/ a k) (exp (* (log k) m)))
400.0ms
(+ (/ (* (/ a k) (exp (* (log k) m))) k) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0)))
440.0ms
(fma (/ 99.0 (* k k)) (/ (* (/ a k) (exp (* (log k) m))) k) (+ (/ (* (/ a k) (exp (* (log k) m))) k) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0))))

simplify4.0s

Counts
117 → 117
Iterations
IterNodes
done5005
21755
1486
0179

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize130.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (/ a k) (exp (* (log k) m)))
2.2b
(* (/ a k) (exp (* (log k) m)))
8.2b
(fma (/ (/ a k) (sqrt k)) (/ (exp (* (log k) m)) (sqrt k)) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0)))
13.7b
(fma (/ 99.0 (* k k)) (/ (* (/ a k) (exp (* (log k) m))) k) (fma (/ (/ a k) (sqrt k)) (/ (exp (* (log k) m)) (sqrt k)) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×associate-*l*
20×*-un-lft-identity times-frac add-cube-cbrt
14×add-cbrt-cube
10×add-exp-log
8×pow1
6×associate-*r*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative fma-udef div-inv
Counts
4 → 92
Calls
4 calls:
37.0ms
(* (/ a k) (exp (* (log k) m)))
38.0ms
(* (/ a k) (exp (* (log k) m)))
1.0ms
(fma (/ (/ a k) (sqrt k)) (/ (exp (* (log k) m)) (sqrt k)) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0)))
1.0ms
(fma (/ 99.0 (* k k)) (/ (* (/ a k) (exp (* (log k) m))) k) (fma (/ (/ a k) (sqrt k)) (/ (exp (* (log k) m)) (sqrt k)) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (/ a k) (exp (* (log k) m)))
214.0ms
(* (/ a k) (exp (* (log k) m)))
541.0ms
(fma (/ (/ a k) (sqrt k)) (/ (exp (* (log k) m)) (sqrt k)) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0)))
545.0ms
(fma (/ 99.0 (* k k)) (/ (* (/ a k) (exp (* (log k) m))) k) (fma (/ (/ a k) (sqrt k)) (/ (exp (* (log k) m)) (sqrt k)) (* (/ (/ (* (/ a k) (exp (* (log k) m))) k) k) (- 10.0))))

simplify3.2s

Counts
104 → 104
Iterations
IterNodes
done5000
21398
1429
0170

prune1.7s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes619.0ms

Accuracy

97% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch75.0ms

Steps
ItersRangePoint
7
1.162298132228303e+106
3.974905491533812e+107
3.33321264497859e+107

simplify67.0ms

Iterations
IterNodes
done54
654
552
446
344
241
137
030

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s11942×body80valid
263.0ms4150×body80nan