Details

Time bar (total: 23.0s)

sample83.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
27.0ms226×body80nan

simplify975.0ms

Counts
1 → 1
Iterations
IterNodes
done2001
3849
2162
146
019

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t))
0.2b
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
0.2b
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
0.3b
(/ (fma (* v v) -5 1) (fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
14×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
9×times-frac
6×associate-*r* pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×associate-*l* *-commutative
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 83
Calls
4 calls:
0.0ms
(fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t))
38.0ms
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
19.0ms
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
5.0ms
(/ (fma (* v v) -5 1) (fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)))

series1.8s

Counts
4 → 12
Calls
4 calls:
461.0ms
(fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t))
279.0ms
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
278.0ms
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
735.0ms
(/ (fma (* v v) -5 1) (fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)))

simplify1.1s

Counts
95 → 95
Iterations
IterNodes
done2000
21886
1494
0188

prune799.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (fma (* v v) -5 1))
0.2b
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
0.2b
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
0.3b
(/ (* (cbrt (fma (* v v) -5 1)) (cbrt (fma (* v v) -5 1))) (/ (fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)) (cbrt (fma (* v v) -5 1))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
58×times-frac
33×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×add-exp-log
22×associate-/r*
21×cbrt-prod
20×add-cbrt-cube
14×pow1
8×prod-exp cbrt-unprod
6×cbrt-undiv div-exp associate-*r* pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×associate-*l* *-commutative
1×clear-num frac-2neg pow1/3 associate-/r/ associate-/l*
Counts
4 → 123
Calls
4 calls:
1.0ms
(cbrt (fma (* v v) -5 1))
24.0ms
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
25.0ms
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
26.0ms
(/ (* (cbrt (fma (* v v) -5 1)) (cbrt (fma (* v v) -5 1))) (/ (fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)) (cbrt (fma (* v v) -5 1))))

series1.4s

Counts
4 → 12
Calls
4 calls:
161.0ms
(cbrt (fma (* v v) -5 1))
271.0ms
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
300.0ms
(* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)
687.0ms
(/ (* (cbrt (fma (* v v) -5 1)) (cbrt (fma (* v v) -5 1))) (/ (fma (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t) (* (- v) v) (* (* (sqrt (fma 6 (* (- v) v) 2)) PI) t)) (cbrt (fma (* v v) -5 1))))

simplify1.0s

Counts
135 → 135
Iterations
IterNodes
done2000
1826
0297

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(* PI t)
0.3b
(/ (cbrt (fma (* v v) -5 1)) (fma (* (sqrt (fma 6 (- (* v v)) 2)) (* PI t)) (- (* v v)) (* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))))
0.5b
(* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))
0.5b
(* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
25×*-un-lft-identity add-cube-cbrt
18×times-frac add-exp-log
17×add-cbrt-cube
16×pow1
15×associate-*l*
12×cbrt-prod
7×pow-prod-down prod-exp cbrt-unprod
6×sqrt-prod associate-/l*
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
1×cbrt-undiv clear-num frac-2neg div-exp div-inv unswap-sqr
Counts
4 → 111
Calls
4 calls:
7.0ms
(* PI t)
5.0ms
(/ (cbrt (fma (* v v) -5 1)) (fma (* (sqrt (fma 6 (- (* v v)) 2)) (* PI t)) (- (* v v)) (* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))))
16.0ms
(* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))
29.0ms
(* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))

series1.6s

Counts
4 → 12
Calls
4 calls:
49.0ms
(* PI t)
998.0ms
(/ (cbrt (fma (* v v) -5 1)) (fma (* (sqrt (fma 6 (- (* v v)) 2)) (* PI t)) (- (* v v)) (* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))))
279.0ms
(* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))
295.0ms
(* (sqrt (fma 6 (- (* v v)) 2)) (* PI t))

simplify1.2s

Counts
123 → 123
Iterations
IterNodes
done2000
21824
1554
0233

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize182.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (/ (* (* (* v v) (* v v)) 27/2) (* PI (pow (sqrt 2) 5))) t)
3.8b
(* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))
9.5b
(fma (/ 2/3 (* (sqrt 2) t)) (/ (* v v) PI) (fma (/ 2 (* t (* (sqrt 2) 2))) (/ (* (* v v) (* v v)) PI) (* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))))
9.7b
(fma (/ 3 (* t (* (sqrt 2) 2))) (/ (* v v) PI) (- (/ (/ (* (* (* v v) (* v v)) 27/2) (* PI (pow (sqrt 2) 5))) t) (fma (/ 2/3 (* (sqrt 2) t)) (/ (* v v) PI) (fma (/ 2 (* t (* (sqrt 2) 2))) (/ (* (* v v) (* v v)) PI) (* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))))))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
235×add-exp-log
167×add-cbrt-cube
118×prod-exp
80×cbrt-unprod
76×div-exp
52×cbrt-undiv
26×times-frac
22×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l* div-inv
6×pow-to-exp pow1 pow-exp
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r*
2×fma-udef unswap-sqr
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 164
Calls
4 calls:
110.0ms
(/ (/ (* (* (* v v) (* v v)) 27/2) (* PI (pow (sqrt 2) 5))) t)
132.0ms
(* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))
1.0ms
(fma (/ 2/3 (* (sqrt 2) t)) (/ (* v v) PI) (fma (/ 2 (* t (* (sqrt 2) 2))) (/ (* (* v v) (* v v)) PI) (* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))))
1.0ms
(fma (/ 3 (* t (* (sqrt 2) 2))) (/ (* v v) PI) (- (/ (/ (* (* (* v v) (* v v)) 27/2) (* PI (pow (sqrt 2) 5))) t) (fma (/ 2/3 (* (sqrt 2) t)) (/ (* v v) PI) (fma (/ 2 (* t (* (sqrt 2) 2))) (/ (* (* v v) (* v v)) PI) (* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))))))

series3.0s

Counts
4 → 12
Calls
4 calls:
348.0ms
(/ (/ (* (* (* v v) (* v v)) 27/2) (* PI (pow (sqrt 2) 5))) t)
236.0ms
(* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))
818.0ms
(fma (/ 2/3 (* (sqrt 2) t)) (/ (* v v) PI) (fma (/ 2 (* t (* (sqrt 2) 2))) (/ (* (* v v) (* v v)) PI) (* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))))
1.6s
(fma (/ 3 (* t (* (sqrt 2) 2))) (/ (* v v) PI) (- (/ (/ (* (* (* v v) (* v v)) 27/2) (* PI (pow (sqrt 2) 5))) t) (fma (/ 2/3 (* (sqrt 2) t)) (/ (* v v) PI) (fma (/ 2 (* t (* (sqrt 2) 2))) (/ (* (* v v) (* v v)) PI) (* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))))))

simplify784.0ms

Counts
176 → 176
Iterations
IterNodes
done2001
11102
0357

prune1.9s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes530.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done26
126
020

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.8s7874×body80nan
1.5s8000×body80valid