Details

Time bar (total: 23.4s)

sample91.0ms

Algorithm
intervals
Results
51.0ms256×body80valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: done (2.6s)

IterNodesCost
044173
1132173
2608106
3348072
done500071

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b
(* 0.0001789971 (* x x))
0.6b
(* (* x x) 0.0008327945)
14.3b
(/ x (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
25.4b
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
98×*-un-lft-identity
68×add-sqr-sqrt
66×add-cube-cbrt
22×associate-/r*
21×add-exp-log add-cbrt-cube
16×distribute-lft-out
14×pow1
11×associate-/r/
6×pow-prod-down prod-exp cbrt-unprod div-inv associate-/l*
5×flip3-+ flip-+
4×cbrt-undiv expm1-log1p-u div-exp associate-*r* associate-*l* log1p-expm1-u add-log-exp
2×frac-2neg clear-num *-commutative unswap-sqr
Counts
4 → 169
Calls
4 calls:
40.0ms
(* 0.0001789971 (* x x))
39.0ms
(* (* x x) 0.0008327945)
33.0ms
(/ x (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
25.0ms
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* 0.0001789971 (* x x))
49.0ms
(* (* x x) 0.0008327945)
384.0ms
(/ x (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
242.0ms
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))

simplify3.2s

Counts
181 → 181
Iterations

Useful iterations: done (3.2s)

IterNodesCost
030614693
179914330
2471613373
done500013210

prune2.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.17858401087518094 (pow x 4) 1.0)
2.6b
(/ x (fma 0.6665536072 (* x x) (fma 0.17858401087518094 (pow x 4) 1.0)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
2 → 39
Calls
2 calls:
1.0ms
(fma 0.17858401087518094 (pow x 4) 1.0)
10.0ms
(/ x (fma 0.6665536072 (* x x) (fma 0.17858401087518094 (pow x 4) 1.0)))

series309.0ms

Counts
2 → 6
Calls
2 calls:
111.0ms
(fma 0.17858401087518094 (pow x 4) 1.0)
198.0ms
(/ x (fma 0.6665536072 (* x x) (fma 0.17858401087518094 (pow x 4) 1.0)))

simplify1.8s

Counts
45 → 45
Iterations

Useful iterations: 2 (126.0ms)

IterNodesCost
091796
1181779
2616707
33277707
done5000707

prune220.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize108.0ms

Local error

Found 4 expressions with local error:

19.4b
(- (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))
19.4b
(- (fma (pow x 6) 0.0072644182 (* (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))
25.2b
(* (/ (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (fma 0.0072644182 (pow x 6) (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))) (- (fma (pow x 6) 0.0072644182 (* (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) (- (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))
25.4b
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (fma 0.0072644182 (pow x 6) (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
129×add-sqr-sqrt
122×times-frac
120×*-un-lft-identity
88×add-cube-cbrt
71×associate-*l*
36×prod-diff
16×distribute-lft-out-- difference-of-squares
15×add-exp-log add-cbrt-cube
12×distribute-rgt-in distribute-lft-in
8×add-log-exp
7×div-inv
6×pow1 fma-neg fma-udef
5×flip3-- associate-*r* flip--
4×cbrt-undiv expm1-log1p-u sub-neg div-exp associate--l+ log1p-expm1-u
3×prod-exp associate-/r* cbrt-unprod associate-/l* unswap-sqr
2×frac-times diff-log associate-*r/ associate-/r/ associate--r+
1×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 214
Calls
4 calls:
7.0ms
(- (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))
10.0ms
(- (fma (pow x 6) 0.0072644182 (* (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))
135.0ms
(* (/ (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (fma 0.0072644182 (pow x 6) (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))) (- (fma (pow x 6) 0.0072644182 (* (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) (- (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))
5.0ms
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (fma 0.0072644182 (pow x 6) (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
141.0ms
(- (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))
101.0ms
(- (fma (pow x 6) 0.0072644182 (* (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))
590.0ms
(* (/ (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (fma 0.0072644182 (pow x 6) (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))) (- (fma (pow x 6) 0.0072644182 (* (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))) (- (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))
305.0ms
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (fma 0.0072644182 (pow x 6) (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))

simplify721.0ms

Counts
226 → 226
Iterations

Useful iterations: done (694.0ms)

IterNodesCost
038627929
199126230
done500022662

prune3.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 0.5 x) (/ 0.2514179000665375 (pow x 3)))
0.3b
(/ 0.15298196345929327 (pow x 5))
0.4b
(/ 0.2514179000665375 (pow x 3))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
68×times-frac
57×*-un-lft-identity
51×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
13×add-exp-log fma-def
12×cube-prod
8×sqr-pow
7×add-cbrt-cube
6×div-exp associate-/l*
5×add-log-exp
4×cube-mult unpow3
3×pow1 expm1-log1p-u log1p-expm1-u div-inv
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num distribute-lft-out
1×+-commutative flip3-+ frac-add sum-log flip-+
Counts
3 → 143
Calls
3 calls:
69.0ms
(+ (/ 0.5 x) (/ 0.2514179000665375 (pow x 3)))
17.0ms
(/ 0.15298196345929327 (pow x 5))
9.0ms
(/ 0.2514179000665375 (pow x 3))

series275.0ms

Counts
3 → 9
Calls
3 calls:
126.0ms
(+ (/ 0.5 x) (/ 0.2514179000665375 (pow x 3)))
80.0ms
(/ 0.15298196345929327 (pow x 5))
70.0ms
(/ 0.2514179000665375 (pow x 3))

simplify1.1s

Counts
152 → 152
Iterations

Useful iterations: 2 (491.0ms)

IterNodesCost
02081530
14441319
219551272
done50001272

prune871.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes87.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.7b

bsearch779.0ms

Steps
ItersRangePoint
11
0.022891638200552334
5.118117448855024e+31
728.931529419868
8
-3.0093658322694207e+28
-1.898742500964735e+25
-1.9828430064280765e+25

simplify16.0ms

Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
064167
175153
done75153

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.5s8000×body80valid