Details

Time bar (total: 9.2s)

sample43.0ms

Algorithm
intervals
Results
23.0ms256×body80valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (221.0ms)

IterNodesCost
044173
1132173
2565106
3274072
done500172

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize36.0ms

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) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

rewrite29.0ms

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 div-exp associate-*l* associate-*l/ *-commutative associate-/l/ unswap-sqr
1×frac-2neg flip3-+ clear-num flip-+ fma-udef div-inv associate-/l*
Counts
4 → 77
Calls
4 calls:
0.0ms
(fma (* 0.7715471019 x) x 1.0)
7.0ms
(* (* x x) 0.0008327945)
9.0ms
(* (* x x) 0.0001789971)
10.0ms
(/ (* (+ (* (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) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

series355.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(fma (* 0.7715471019 x) x 1.0)
24.0ms
(* (* x x) 0.0008327945)
24.0ms
(* (* x x) 0.0001789971)
251.0ms
(/ (* (+ (* (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) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

simplify785.0ms

Counts
89 → 89
Iterations

Useful iterations: 2 (167.0ms)

IterNodesCost
01812972
14682844
220572334
done50012334

prune596.0ms

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))

rewrite12.0ms

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))
4.0ms
(/ 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))

simplify635.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (128.0ms)

IterNodesCost
01771258
13291069
212701037
done50011037

prune258.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize42.0ms

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) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

rewrite21.0ms

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 pow1/2 div-exp associate-*l/ associate-/l/
1×frac-2neg flip3-+ associate-*l* clear-num *-commutative flip-+ div-inv associate-/l* unswap-sqr
Counts
4 → 76
Calls
4 calls:
7.0ms
(* (* x x) 0.0001789971)
1.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
1.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
10.0ms
(/ (* (+ (* (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) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* x x) 0.0001789971)
70.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
71.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
249.0ms
(/ (* (+ (* (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) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

simplify736.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (166.0ms)

IterNodesCost
01833444
14732975
220232469
done50002469

prune629.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(* x (sqrt 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 (sqrt 0.0001789971)) (* x (sqrt 0.0001789971))))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×sqrt-prod
8×pow1
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*l* associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×frac-2neg flip3-+ pow-prod-down clear-num *-commutative flip-+ div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
5.0ms
(* x (sqrt 0.0001789971))
1.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
1.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
10.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x (sqrt 0.0001789971)) (* x (sqrt 0.0001789971))))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* x (sqrt 0.0001789971))
71.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
71.0ms
(sqrt (fma (* 0.7715471019 x) x 1.0))
315.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x (sqrt 0.0001789971)) (* x (sqrt 0.0001789971))))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) x) (fma 0.0001789971 (* 2.0 (pow (* x x) 6)) (+ (fma 0.2909738639 (pow x 4) (* (sqrt (fma (* 0.7715471019 x) x 1.0)) (sqrt (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 6) 0.0694555761 (* (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442))))))

simplify705.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (167.0ms)

IterNodesCost
01943613
14832994
220612502
done50002502

prune665.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

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

bsearch393.0ms

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

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
061123
177109
done77109

end0.0ms

sample819.0ms

Algorithm
intervals
Results
720.0ms8000×body80valid