Details

Time bar (total: 11.1s)

sample54.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 3 (296.0ms)

IterNodesCost
044173
1132173
2563106
3270372
done500072

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* 0.7715471019 x) x 1.0)
0.1b
(* (* x x) 0.0008327945)
0.1b
(* (* x x) 0.0001789971)
32.1b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0))))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
14×pow1
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×prod-exp cbrt-unprod
6×associate-*r* pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-/r*
2×cbrt-undiv flip3-+ div-exp associate-*l* associate-*l/ associate-/r/ *-commutative flip-+ associate-/l/ unswap-sqr
1×frac-2neg clear-num fma-udef div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
0.0ms
(fma (* 0.7715471019 x) x 1.0)
8.0ms
(* (* x x) 0.0008327945)
8.0ms
(* (* x x) 0.0001789971)
27.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0))))))

series382.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(fma (* 0.7715471019 x) x 1.0)
25.0ms
(* (* x x) 0.0008327945)
31.0ms
(* (* x x) 0.0001789971)
268.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0))))))

simplify919.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (293.0ms)

IterNodesCost
01893160
15052971
220912480
done50012480

prune770.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 0.15298196345929327 (pow x 5))
0.2b
(/ 0.2514179000665375 (pow x 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
57×times-frac
43×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
19×associate-/r*
12×add-exp-log cube-prod
8×sqr-pow
6×div-exp add-cbrt-cube associate-/l*
4×cube-mult unpow3
2×pow1 cbrt-undiv expm1-log1p-u pow-to-exp frac-2neg pow-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
2 → 114
Calls
2 calls:
4.0ms
(/ 0.15298196345929327 (pow x 5))
6.0ms
(/ 0.2514179000665375 (pow x 3))

series85.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ 0.15298196345929327 (pow x 5))
36.0ms
(/ 0.2514179000665375 (pow x 3))

simplify1.5s

Counts
120 → 120
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
01771258
13181069
28281037
336071037
done50001037

prune265.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) 0.0001789971)
15.5b
(sqrt (fma (* 0.7715471019 x) x 1.0))
15.5b
(sqrt (fma (* 0.7715471019 x) x 1.0))
32.1b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0))))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity
6×sqrt-prod
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×times-frac associate-*r* pow-prod-down associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-exp associate-*l/ associate-/r/ flip-+ associate-/l/
1×frac-2neg associate-*l* clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 78
Calls
4 calls:
8.0ms
(* (* x x) 0.0001789971)
1.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
1.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
28.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0))))))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (* x x) 0.0001789971)
74.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
69.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
269.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0))))))))

simplify883.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (280.0ms)

IterNodesCost
01913659
15153112
220822615
done50002615

prune681.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

15.5b
(sqrt (fma (* 0.7715471019 x) x 1.0))
30.8b
(sqrt (* (* x x) 0.0001789971))
30.8b
(sqrt (* (* x x) 0.0001789971))
32.1b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (sqrt (* (* x x) 0.0001789971)) (sqrt (* (* x x) 0.0001789971))))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0))))))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity sqrt-pow1
6×pow-prod-down
5×sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac pow1/2 associate-/r*
2×cbrt-undiv flip3-+ div-exp associate-*l/ associate-/r/ flip-+ associate-/l/
1×rem-sqrt-square frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
1.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
6.0ms
(sqrt (* (* x x) 0.0001789971))
6.0ms
(sqrt (* (* x x) 0.0001789971))
28.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (sqrt (* (* x x) 0.0001789971)) (sqrt (* (* x x) 0.0001789971))))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0))))))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
41.0ms
(sqrt (* (* x x) 0.0001789971))
34.0ms
(sqrt (* (* x x) 0.0001789971))
337.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (sqrt (* (* x x) 0.0001789971)) (sqrt (* (* x x) 0.0001789971))))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (+ (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442)) (fma (* 2.0 (pow (* x x) 6)) 0.0001789971 (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0))))))))

simplify706.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (171.0ms)

IterNodesCost
01863808
14903000
218892503
done50012503

prune678.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch410.0ms

Steps
ItersRangePoint
11
0.08347146558812443
3.320253512051989e+22
703.4866696794237
7
-1162.6651869185068
-5.7596417613087905
-708.5573543956083

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
061127
177113
done77113

end0.0ms

sample880.0ms

Algorithm
intervals
Results
761.0ms8000×body80valid