Details

Time bar (total: 21.1s)

sample186.0ms

Algorithm
intervals
Results
40.0ms157×body160valid
35.0ms301×body80nan
32.0ms557×pre80true
17.0ms45×body320valid
6.0ms54×body80valid

simplify522.0ms

Counts
1 → 1
Iterations
IterNodes
done102
7102
6101
599
491
373
241
122
012

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (fma -3 (* c a) (* b b)))
0.1b
(fma -3 (* c a) (* b b))
0.3b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
37.3b
(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 102
Calls
4 calls:
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))
31.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
8.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)

series456.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(sqrt (fma -3 (* c a) (* b b)))
82.0ms
(fma -3 (* c a) (* b b))
114.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
143.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify1.2s

Counts
114 → 114
Iterations
IterNodes
done2000
32000
2940
1347
0152

prune693.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 40.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma -3 (* c a) (* b b))
0.1b
(fma -3 (* c a) (* b b))
0.3b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
43.1b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac fma-udef associate-/l*
2×cbrt-undiv div-exp
1×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
Counts
4 → 57
Calls
4 calls:
1.0ms
(fma -3 (* c a) (* b b))
0.0ms
(fma -3 (* c a) (* b b))
11.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.3s

Counts
4 → 12
Calls
4 calls:
98.0ms
(fma -3 (* c a) (* b b))
69.0ms
(fma -3 (* c a) (* b b))
661.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
473.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.2s

Counts
69 → 69
Iterations
IterNodes
done2005
32005
2672
1231
0112

prune799.0ms

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 39.9b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
0.5b
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
0.5b
(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
43.1b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (- b))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
12×add-sqr-sqrt
11×add-cbrt-cube add-exp-log
9×*-un-lft-identity add-cube-cbrt
7×pow-plus pow-prod-up
6×associate-*r*
5×fma-udef
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow2 swap-sqr pow-sqr
2×distribute-rgt-in distribute-lft-in pow3 *-commutative unswap-sqr
1×cbrt-prod pow1/3 rem-cbrt-cube
Counts
4 → 87
Calls
4 calls:
31.0ms
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
10.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
18.0ms
(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (- b))

series907.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
108.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
98.0ms
(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
482.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (- b))

simplify1.5s

Counts
99 → 99
Iterations
IterNodes
done2000
32000
2953
1330
0140

prune1.2s

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 39.9b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (- b)) (* 3 a))
0.5b
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
3.6b
(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
43.0b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (- b))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
31×pow1
17×add-exp-log
13×add-sqr-sqrt
12×pow-pow
11×*-un-lft-identity add-cbrt-cube add-cube-cbrt
7×pow-plus pow-prod-up
5×prod-exp
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow2 pow-unpow times-frac swap-sqr associate-*r* associate-*l* pow-exp pow-sqr fma-udef associate-/l*
2×cbrt-undiv div-exp cbrt-unprod
1×distribute-rgt-in pow-to-exp clear-num associate-/r* unpow-prod-down frac-2neg distribute-lft-in unpow1/3 pow3 *-commutative div-inv unswap-sqr sqr-pow
Counts
4 → 97
Calls
4 calls:
13.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (- b)) (* 3 a))
10.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
25.0ms
(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
1.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (- b))

series1.5s

Counts
4 → 12
Calls
4 calls:
693.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (- b)) (* 3 a))
101.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
267.0ms
(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
433.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (- b))

simplify1.7s

Counts
109 → 109
Iterations
IterNodes
done2003
32003
21513
1470
0197

prune882.0ms

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 39.9b

regimes1.1s

Accuracy

0% (2.7b remaining)

Error of 43.0b against oracle of 40.3b and baseline of 43.0b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done27
127
023

end1.0ms

sample5.5s

Algorithm
intervals
Results
1.8s4795×body160valid
1.2s8314×body80nan
1.1s16314×pre80true
563.0ms1423×body320valid
325.0ms1782×body80valid