Details

Time bar (total: 34.3s)

sample176.0ms

Algorithm
intervals
Results
44.0ms116×body320valid
33.0ms515×pre80true
32.0ms259×body80nan
32.0ms102×body160valid
4.0ms10×body640valid
4.0ms28×body80valid

simplify198.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
198.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize22.0ms

Local error

Found 4 expressions with local error:

28.3b
(- (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)))

rewrite58.0ms

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:
Slowest
46.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
9.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
1.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series397.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
102.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
92.0ms
(fma -3 (* c a) (* b b))
88.0ms
(sqrt (fma -3 (* c a) (* b b)))

simplify4.3s

Counts
87 → 114
Calls
87 calls:
Slowest
537.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
270.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
231.0ms
(/ (* (* (- (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)))
230.0ms
(/ (* (* (- (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 3) 3) (* (* a a) a)))
142.0ms
(- (log (- (sqrt (fma -3 (* c a) (* b b))) b)) (+ (log 3) (log a)))

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 49.4b

localize49.0ms

Local error

Found 4 expressions with local error:

52.3b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.3b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.1b
(fma -3 (* c a) (* b b))

rewrite9.0ms

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:
Slowest
7.0ms
(/ (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))
0.0ms
(fma -3 (* c a) (* b b))
0.0ms
(fma -3 (* c a) (* b b))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
651.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
399.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
72.0ms
(fma -3 (* c a) (* b b))
64.0ms
(fma -3 (* c a) (* b b))

simplify2.9s

Counts
24 → 69
Calls
24 calls:
Slowest
495.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
352.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
285.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))
267.0ms
(/ (* (* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
235.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune1.0s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 49.3b

localize70.0ms

Local error

Found 4 expressions with local error:

52.3b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
52.3b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
52.3b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.5b
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
7×cbrt-prod
6×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×times-frac fma-udef
1×cbrt-div pow1/3 div-inv
Counts
4 → 52
Calls
4 calls:
Slowest
7.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
1.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
662.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
433.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
419.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
404.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify3.5s

Counts
20 → 64
Calls
20 calls:
Slowest
568.0ms
(- (+ (* 5/162 (/ (* (cbrt -1/3) (* (exp (* 1/3 (+ (* 4 (log (/ -1 a))) (* 2 (log (/ -1 b)))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 6))) c)) (* (cbrt -1/3) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))))) (* 1/3 (/ (* (cbrt -1/3) (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2))) b)))
560.0ms
(- (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (cbrt 1/3)) (+ (* 5/162 (/ (* (cbrt 1/3) (* (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 6) (exp (* 1/3 (+ (* 2 (log (/ 1 b))) (* 4 (log (/ 1 a)))))))) c)) (* 1/3 (/ (* (cbrt 1/3) (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2))) b))))
358.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
353.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
302.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 48.9b

localize62.0ms

Local error

Found 4 expressions with local error:

52.3b
(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))
0.6b
(cbrt (* (* (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)))
0.3b
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))

rewrite46.0ms

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:
Slowest
25.0ms
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
12.0ms
(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
7.0ms
(* (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))

series794.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
433.0ms
(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))
210.0ms
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
79.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
71.0ms
(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))

simplify6.3s

Counts
63 → 99
Calls
63 calls:
Slowest
703.0ms
(* (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
375.0ms
(- (+ (pow b 4) (* 9 (* (pow a 2) (pow c 2)))) (* 6 (* a (* (pow b 2) c))))
359.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
339.0ms
(* (* b b) (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))))
312.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 48.9b

regimes663.0ms

Accuracy

23.5% (2.4b remaining)

Error of 51.0b against oracle of 48.6b and baseline of 51.8b

bsearch86.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
1.5s8289×body80nan
1.5s3626×body320valid
1.5s16289×pre80true
798.0ms3001×body160valid
287.0ms469×body640valid
168.0ms904×body80valid