Details

Time bar (total: 23.7s)

sample113.0ms

Algorithm
intervals
Results
67.0ms256×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: done (2.2s)

IterNodesCost
044173
1132173
2535109
3233079
done500073

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize89.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.0072644182 (* x x))
0.2b
(* (* x x) 0.0140005442)
17.0b
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
32.8b
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

rewrite927.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
28×frac-add
27×flip3-+ flip-+
23×associate-*l*
22×add-cube-cbrt *-un-lft-identity
21×add-exp-log add-cbrt-cube
20×associate-*r/
19×times-frac
16×pow1
14×associate-/l/
12×associate-/r/
8×prod-exp cbrt-unprod
7×associate-*r* pow-prod-down
4×add-log-exp unswap-sqr
3×associate-/r* *-commutative associate-/l*
2×cbrt-undiv div-exp div-inv
1×frac-2neg associate-*l/ clear-num
Counts
4 → 123
Calls
4 calls:
28.0ms
(* 0.0072644182 (* x x))
32.0ms
(* (* x x) 0.0140005442)
491.0ms
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
369.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

series774.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* 0.0072644182 (* x x))
46.0ms
(* (* x x) 0.0140005442)
433.0ms
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
249.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* (* x x) 0.0140005442)) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

simplify769.0ms

Counts
135 → 135
Iterations

Useful iterations: done (761.0ms)

IterNodesCost
03258932
110478594
done50007816

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3)))
0.0b
(+ (/ 0.5 x) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3))))
0.0b
(/ 0.15298196345929327 (pow x 5))
0.2b
(/ 0.2514179000665375 (pow x 3))

rewrite424.0ms

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*
14×add-exp-log
12×cube-prod
11×add-log-exp
8×add-cbrt-cube sqr-pow
7×distribute-lft-out
6×div-exp associate-/l*
5×frac-add
4×pow1 cube-mult unpow3 sum-log
3×flip3-+ flip-+
2×cbrt-undiv +-commutative pow-to-exp frac-2neg pow-exp clear-num div-inv
1×associate-+r+
Counts
4 → 143
Calls
4 calls:
108.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3)))
288.0ms
(+ (/ 0.5 x) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3))))
7.0ms
(/ 0.15298196345929327 (pow x 5))
8.0ms
(/ 0.2514179000665375 (pow x 3))

series444.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3)))
75.0ms
(+ (/ 0.5 x) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.2514179000665375 (pow x 3))))
98.0ms
(/ 0.15298196345929327 (pow x 5))
74.0ms
(/ 0.2514179000665375 (pow x 3))

simplify1.3s

Counts
155 → 155
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02352136
15161871
216001771
done50001765

prune496.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.0072644182 (* x x))
0.2b
(* 0.0140005442 (pow x 2))
17.0b
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
32.8b
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

rewrite902.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×frac-add
27×flip3-+ flip-+
25×associate-*l*
24×add-cube-cbrt *-un-lft-identity
21×add-exp-log
20×associate-*r/
19×times-frac
18×add-cbrt-cube
14×associate-/l/
12×associate-*r* associate-/r/
11×pow1
8×prod-exp
7×unswap-sqr
6×cbrt-unprod
4×unpow-prod-down pow-prod-down add-log-exp
3×associate-/r* *-commutative associate-/l*
2×cbrt-undiv div-exp div-inv unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*l/ pow-exp clear-num
Counts
4 → 131
Calls
4 calls:
34.0ms
(* 0.0072644182 (* x x))
25.0ms
(* 0.0140005442 (pow x 2))
485.0ms
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
345.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

series778.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* 0.0072644182 (* x x))
31.0ms
(* 0.0140005442 (pow x 2))
391.0ms
(* (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) x)
307.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

simplify767.0ms

Counts
143 → 143
Iterations

Useful iterations: done (758.0ms)

IterNodesCost
03438999
110778659
done50007858

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 0.0140005442 (pow x 2))
11.3b
(cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3))
17.0b
(* (cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3)) x)
32.8b
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
94×cbrt-prod
68×add-sqr-sqrt
50×associate-*l*
47×add-cube-cbrt *-un-lft-identity times-frac
44×unpow-prod-down
42×flip3-+ flip-+
40×cube-prod frac-add
32×associate-*r/
30×associate-/r/
14×associate-/l/
13×add-exp-log
11×associate-*r* unswap-sqr
9×add-cbrt-cube
6×pow1
5×div-inv sqr-pow
4×prod-exp add-log-exp
3×associate-/r* associate-/l*
2×cube-div cube-mult cbrt-div unpow3 *-commutative cbrt-unprod unpow2
1×cbrt-undiv pow-to-exp frac-2neg pow1/3 div-exp pow-prod-down associate-*l/ pow-exp clear-num rem-cbrt-cube
Counts
4 → 197
Calls
4 calls:
19.0ms
(* 0.0140005442 (pow x 2))
197.0ms
(cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3))
946.0ms
(* (cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3)) x)
360.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
59.0ms
(* 0.0140005442 (pow x 2))
305.0ms
(cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3))
400.0ms
(* (cbrt (pow (/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971))))))))) 3)) x)
298.0ms
(/ (+ (* (pow x 4) (+ (+ (* 0.0001789971 (pow x 6)) (* (pow x 4) 0.0005064034)) (+ (* 0.0072644182 (* x x)) 0.0424060604))) (+ 1.0 (* 0.1049934947 (* x x)))) (+ (+ 1.0 (* (pow x 4) 0.2909738639)) (* (* x x) (+ 0.7715471019 (* (pow x 4) (+ (+ 0.0694555761 (* 0.0140005442 (pow x 2))) (+ (* 0.0008327945 (pow x 4)) (* (pow x 6) (* 2.0 0.0001789971)))))))))

simplify873.0ms

Counts
209 → 209
Iterations

Useful iterations: done (842.0ms)

IterNodesCost
041219875
1129718206
done500017197

prune2.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes96.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch1.2s

Steps
ItersRangePoint
11
57174384.711049624
3.6932400046068e+36
59525946.96427765
8
-2497197479928642.5
-4551155589554.198
-1795823920150617.8

simplify16.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
063111
19297
done9297

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.7s8000×body80valid