Details

Time bar (total: 28.3s)

sample214.0ms

Algorithm
intervals
Results
67.0ms501×pre80true
49.0ms112×body320valid
32.0ms245×body80nan
31.0ms107×body160valid
6.0ms11×body640valid
4.0ms26×body80valid

simplify112.0ms

Calls
1 calls:
Slowest
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.1b

localize36.0ms

Local error

Found 4 expressions with local error:

31.5b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.2b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.0b
(sqrt (fma -3 (* c a) (* b b)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg pow1/2 div-sub div-exp fma-udef div-inv
Calls
4 calls:
Slowest
26.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
24.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
1.0ms
(fma -3 (* c a) (* b b))

series425.0ms

Calls
4 calls:
Slowest
126.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
121.0ms
(sqrt (fma -3 (* c a) (* b b)))
119.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
59.0ms
(fma -3 (* c a) (* b b))

simplify1.7s

Calls
34 calls:
Slowest
463.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
227.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
193.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
107.0ms
(- (log (- (sqrt (fma -3 (* c a) (* b b))) b)) (log (* 3 a)))
62.0ms
(- (pow b 2) (* 3 (* a c)))

prune973.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 49.7b

localize22.0ms

Local error

Found 4 expressions with local error:

52.2b
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))
0.5b
(cbrt (fma -3 (* c a) (* b b)))
0.5b
(cbrt (fma -3 (* c a) (* b b)))
0.5b
(cbrt (fma -3 (* c a) (* b b)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
0.0ms
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))

series1.5s

Calls
4 calls:
Slowest
701.0ms
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))
259.0ms
(cbrt (fma -3 (* c a) (* b b)))
256.0ms
(cbrt (fma -3 (* c a) (* b b)))
248.0ms
(cbrt (fma -3 (* c a) (* b b)))

simplify2.5s

Calls
21 calls:
Slowest
360.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
333.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
305.0ms
(- (* (exp (* 1/3 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) (exp (* 1/6 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a))))))) b)
293.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
201.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a))))))

prune1.2s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 49.5b

localize39.0ms

Local error

Found 4 expressions with local error:

51.9b
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (pow (fma -3 (* c a) (* b b)) 1/3))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))
2.9b
(pow (fma -3 (* c a) (* b b)) 1/3)
0.5b
(cbrt (fma -3 (* c a) (* b b)))
0.5b
(cbrt (fma -3 (* c a) (* b b)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×unpow-prod-down
2×pow1/3
1×pow-to-exp pow-pow unpow1/3 pow-exp fma-udef
Calls
4 calls:
Slowest
3.0ms
(pow (fma -3 (* c a) (* b b)) 1/3)
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
0.0ms
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (pow (fma -3 (* c a) (* b b)) 1/3))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))

series1.5s

Calls
4 calls:
Slowest
797.0ms
(fma (sqrt (* (cbrt (fma -3 (* c a) (* b b))) (pow (fma -3 (* c a) (* b b)) 1/3))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))
256.0ms
(pow (fma -3 (* c a) (* b b)) 1/3)
237.0ms
(cbrt (fma -3 (* c a) (* b b)))
220.0ms
(cbrt (fma -3 (* c a) (* b b)))

simplify2.6s

Calls
23 calls:
Slowest
365.0ms
(- (* (exp (* 1/3 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) (exp (* 1/6 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a))))))) b)
321.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
316.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
315.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
192.0ms
(- (* (exp (* 1/6 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) (exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))) b)

prune1.4s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 49.5b

localize19.0ms

Local error

Found 4 expressions with local error:

51.9b
(fma (sqrt (* (* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b))))) (pow (fma -3 (* c a) (* b b)) 1/3))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))
2.9b
(pow (fma -3 (* c a) (* b b)) 1/3)
0.5b
(* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b)))))
0.5b
(cbrt (sqrt (fma -3 (* c a) (* b b))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×pow1
9×associate-*r* associate-*l* sqrt-prod
7×add-exp-log
5×pow1/3
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×unpow-prod-down
2×pow-prod-down pow-prod-up
1×pow2 pow-to-exp pow-pow pow-plus unpow1/3 pow-exp prod-exp *-commutative cbrt-unprod fma-udef
Calls
4 calls:
Slowest
7.0ms
(* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b)))))
7.0ms
(cbrt (sqrt (fma -3 (* c a) (* b b))))
1.0ms
(pow (fma -3 (* c a) (* b b)) 1/3)
0.0ms
(fma (sqrt (* (* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b))))) (pow (fma -3 (* c a) (* b b)) 1/3))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))

series1.5s

Calls
4 calls:
Slowest
730.0ms
(fma (sqrt (* (* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b))))) (pow (fma -3 (* c a) (* b b)) 1/3))) (sqrt (cbrt (fma -3 (* c a) (* b b)))) (- b))
266.0ms
(* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b)))))
240.0ms
(cbrt (sqrt (fma -3 (* c a) (* b b))))
218.0ms
(pow (fma -3 (* c a) (* b b)) 1/3)

simplify4.0s

Calls
49 calls:
Slowest
678.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
370.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
303.0ms
(exp (* 1/6 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
289.0ms
(- (* (exp (* 1/3 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) (exp (* 1/6 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a))))))) b)
267.0ms
(- (pow b 1/3) (* 1/2 (* (* a c) (pow (/ 1 (pow b 5)) 1/3))))

prune1.7s

Pruning

40 alts after pruning (40 fresh and 0 done)

Merged error: 49.5b

regimes1.2s

Accuracy

0% (1.8b remaining)

Error of 51.3b against oracle of 49.5b and baseline of 51.3b

bsearch8.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.1s3654×body320valid
1.1s8136×body80nan
1.0s16136×pre80true
877.0ms2966×body160valid
271.0ms513×body640valid
103.0ms867×body80valid