Details

Time bar (total: 10.3s)

sample47.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 3 (216.0ms)

IterNodesCost
044173
1132173
2563106
3270372
done500172

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (* x x) 0.1049934947 1.0)
0.3b
(* (* x x) 0.0001789971)
0.4b
(* (* x x) 0.0008327945)
28.4b
(/ (* (+ (* (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 (* x x) 0.1049934947 1.0)
9.0ms
(* (* x x) 0.0001789971)
7.0ms
(* (* x x) 0.0008327945)
26.0ms
(/ (* (+ (* (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))))))

series351.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(fma (* x x) 0.1049934947 1.0)
24.0ms
(* (* x x) 0.0001789971)
24.0ms
(* (* x x) 0.0008327945)
253.0ms
(/ (* (+ (* (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))))))

simplify761.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (227.0ms)

IterNodesCost
01893160
15062971
221222480
done50002480

prune578.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (* x x) 0.1049934947 1.0)
0.3b
(* (* x x) 0.0001789971)
0.4b
(* (* x x) 0.0008327945)
28.4b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (* 1 (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))))))

rewrite43.0ms

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 (* x x) 0.1049934947 1.0)
7.0ms
(* (* x x) 0.0001789971)
7.0ms
(* (* x x) 0.0008327945)
26.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (* 1 (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))))))

series353.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma (* x x) 0.1049934947 1.0)
24.0ms
(* (* x x) 0.0001789971)
26.0ms
(* (* x x) 0.0008327945)
253.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (* 1 (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))))))

simplify769.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (223.0ms)

IterNodesCost
01903228
15082971
221482480
done50012480

prune580.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x x) 0.0001789971)
21.6b
(fma (fma 0.0001789971 (* x x) 0.0005064034) (pow (* x x) 4) (- (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
23.0b
(- (* (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (* (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))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
29.4b
(/ (* (- (* (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (* (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))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))) x) (* (fma (pow (* x x) 4) (fma (* 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))))) (fma (fma 0.0001789971 (* x x) 0.0005064034) (pow (* x x) 4) (- (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
9×pow1
7×prod-exp cbrt-unprod
6×add-sqr-sqrt add-log-exp
5×distribute-rgt-in add-cube-cbrt *-un-lft-identity distribute-lft-in
4×cbrt-undiv expm1-log1p-u div-exp associate--l+ log1p-expm1-u
3×associate-*r* pow-prod-down fma-udef
2×flip3-- associate-*l/ flip-- associate-/l/ associate--r+
1×sub-neg frac-2neg times-frac fma-neg diff-log associate-*l* prod-diff clear-num associate-/r* *-commutative div-inv associate-/l* difference-of-squares unswap-sqr
Counts
4 → 79
Calls
4 calls:
7.0ms
(* (* x x) 0.0001789971)
0.0ms
(fma (fma 0.0001789971 (* x x) 0.0005064034) (pow (* x x) 4) (- (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
30.0ms
(- (* (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (* (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))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
50.0ms
(/ (* (- (* (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (* (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))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))) x) (* (fma (pow (* x x) 4) (fma (* 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))))) (fma (fma 0.0001789971 (* x x) 0.0005064034) (pow (* x x) 4) (- (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))))

series623.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (* x x) 0.0001789971)
76.0ms
(fma (fma 0.0001789971 (* x x) 0.0005064034) (pow (* x x) 4) (- (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
102.0ms
(- (* (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (* (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))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
421.0ms
(/ (* (- (* (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (* (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))) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))) x) (* (fma (pow (* x x) 4) (fma (* 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))))) (fma (fma 0.0001789971 (* x x) 0.0005064034) (pow (* x x) 4) (- (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))))

simplify955.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (291.0ms)

IterNodesCost
02267283
16156983
228794879
done50004879

prune749.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (/ 0.1529819634592937 (pow x 5)) (/ 0.2514179000665373 (pow x 3))) (/ 0.5 x))
0.0b
(/ 0.1529819634592937 (pow x 5))
0.8b
(/ 0.2514179000665373 (pow x 3))

rewrite403.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity times-frac
45×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
13×add-exp-log
12×cube-prod
8×add-log-exp sqr-pow
7×add-cbrt-cube distribute-lft-out
6×div-exp associate-/l*
5×fma-def
4×cube-mult unpow3 frac-add
3×pow1 expm1-log1p-u sum-log log1p-expm1-u
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ pow-exp clear-num flip-+ div-inv
1×+-commutative associate-+l+
Counts
3 → 140
Calls
3 calls:
388.0ms
(+ (+ (/ 0.1529819634592937 (pow x 5)) (/ 0.2514179000665373 (pow x 3))) (/ 0.5 x))
6.0ms
(/ 0.1529819634592937 (pow x 5))
4.0ms
(/ 0.2514179000665373 (pow x 3))

series134.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ (+ (/ 0.1529819634592937 (pow x 5)) (/ 0.2514179000665373 (pow x 3))) (/ 0.5 x))
49.0ms
(/ 0.1529819634592937 (pow x 5))
35.0ms
(/ 0.2514179000665373 (pow x 3))

simplify647.0ms

Counts
149 → 149
Iterations

Useful iterations: 2 (207.0ms)

IterNodesCost
02351890
15091649
219061577
done50011577

prune310.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.1b

bsearch418.0ms

Steps
ItersRangePoint
10
5.968040026638966e-05
117627206.70733242
615.8466592863681
9
-7.995242360819531e+16
-64880754058.88788
-85578346246354.05

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
061169
173155
done73155

end0.0ms

sample1.0s

Algorithm
intervals
Results
932.0ms8000×body80valid