Details

Time bar (total: 9.9s)

sample44.0ms

Algorithm
intervals
Results
23.0ms256×body80valid

simplify112.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
013286
161875
2334339
3500139

prune29.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* x x) (* 2.0 0.0001789971))
0.5b
(* (* x x) 0.0001789971)
16.2b
(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
25.4b
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

rewrite777.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
62×add-sqr-sqrt
61×add-cube-cbrt *-un-lft-identity
31×associate-/r/
30×flip3-+ flip-+
28×add-exp-log add-cbrt-cube
24×associate-*r/ frac-add
22×associate-/r*
21×pow1
11×pow-prod-down prod-exp cbrt-unprod
6×div-inv associate-/l/ associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp associate-*r* log1p-expm1-u add-log-exp
2×frac-2neg associate-*l* clear-num *-commutative
1×unswap-sqr
Counts
4 → 182
Calls
4 calls:
11.0ms
(* (* x x) (* 2.0 0.0001789971))
8.0ms
(* (* x x) 0.0001789971)
258.0ms
(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
492.0ms
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

series544.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* x x) (* 2.0 0.0001789971))
24.0ms
(* (* x x) 0.0001789971)
273.0ms
(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
216.0ms
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012069406
150028888

prune2.0s

Filtered
194 candidates to 158 candidates (81.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) 0.0072644182)
0.1b
(* (* x x) 0.0140005442)
0.5b
(* (* x x) (* 2.0 0.0001789971))
29.1b
(* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) (+ (* x (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))) (* x (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))

rewrite524.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
31×add-cbrt-cube
28×pow1
23×add-sqr-sqrt
22×associate-*l*
18×prod-exp
16×cbrt-unprod
15×*-un-lft-identity pow-prod-down
14×add-cube-cbrt
11×times-frac associate-*r*
7×flip3-+ flip-+
6×associate-*r/ associate-/r/
5×unswap-sqr
4×expm1-log1p-u frac-add *-commutative log1p-expm1-u add-log-exp
2×frac-times div-exp
1×cbrt-undiv distribute-rgt-in rec-exp distribute-lft-in 1-exp associate-*l/ div-inv distribute-lft-out
Counts
4 → 116
Calls
4 calls:
8.0ms
(* (* x x) 0.0072644182)
8.0ms
(* (* x x) 0.0140005442)
11.0ms
(* (* x x) (* 2.0 0.0001789971))
494.0ms
(* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) (+ (* x (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))) (* x (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* x x) 0.0072644182)
26.0ms
(* (* x x) 0.0140005442)
24.0ms
(* (* x x) (* 2.0 0.0001789971))
232.0ms
(* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) (+ (* x (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))) (* x (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09272790
150022535

prune978.0ms

Filtered
128 candidates to 89 candidates (69.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) 0.0140005442)
0.2b
(* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) x)
0.5b
(* (* x x) (* 2.0 0.0001789971))
28.9b
(* (* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) x) (+ (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

rewrite996.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
35×add-cbrt-cube
28×pow1
24×prod-exp
22×add-sqr-sqrt associate-*l*
18×cbrt-unprod
15×*-un-lft-identity pow-prod-down
14×add-cube-cbrt
11×times-frac
10×associate-*r*
7×flip3-+ flip-+
6×associate-*r/ associate-/r/
5×associate-*l/
4×expm1-log1p-u div-exp frac-add *-commutative log1p-expm1-u add-log-exp unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 119
Calls
4 calls:
7.0ms
(* (* x x) 0.0140005442)
483.0ms
(* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) x)
11.0ms
(* (* x x) (* 2.0 0.0001789971))
491.0ms
(* (* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) x) (+ (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* x x) 0.0140005442)
167.0ms
(* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) x)
25.0ms
(* (* x x) (* 2.0 0.0001789971))
270.0ms
(* (* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) x) (+ (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
08873171
150022543

prune920.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
0.0b
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
0.1b
(/ 1 (pow x 5))
0.3b
(/ 1 (pow x 3))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
57×times-frac
45×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
22×add-exp-log
19×associate-/r*
12×cube-prod div-exp
8×add-cbrt-cube sqr-pow
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
2×cbrt-undiv pow-flip frac-2neg clear-num fma-udef div-inv inv-pow
Counts
4 → 150
Calls
4 calls:
0.0ms
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
0.0ms
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
4.0ms
(/ 1 (pow x 5))
5.0ms
(/ 1 (pow x 3))

series230.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
103.0ms
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
44.0ms
(/ 1 (pow x 5))
30.0ms
(/ 1 (pow x 3))

simplify41.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0334806
11614643
25001634

prune249.0ms

Filtered
162 candidates to 71 candidates (43.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.0b

bsearch350.0ms

Steps
ItersRangePoint
8
48.29475874355119
356290.51007653365
793.5547449320184
7
-3.2353071163733523e+27
-1.8614577152285687e+25
-6.959719040716522e+25

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09446
19446

end0.0ms

sample836.0ms

Algorithm
intervals
Results
736.0ms8000×body80valid