Details

Time bar (total: 40.0s)

sample150.0ms

Algorithm
intervals
Results
40.0ms484×pre80true
36.0ms159×body160valid
25.0ms228×body80nan
17.0ms47×body320valid
6.0ms50×body80valid

simplify137.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
137.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.2b

localize24.0ms

Local error

Found 4 expressions with local error:

40.5b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.3b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.1b
(sqrt (fma -3 (* c a) (* b b)))

rewrite41.0ms

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
23.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
15.0ms
(- (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))

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
111.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
88.0ms
(sqrt (fma -3 (* c a) (* b b)))
67.0ms
(fma -3 (* c a) (* b b))

simplify4.5s

Counts
87 → 114
Calls
87 calls:
Slowest
681.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
315.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
240.0ms
(/ (* (* (- (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)))
157.0ms
(/ (* (* (- (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 a)))

prune1.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 42.5b

localize41.0ms

Local error

Found 4 expressions with local error:

45.4b
(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
8.0ms
(/ (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
595.0ms
(/ (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))
88.0ms
(fma -3 (* c a) (* b b))
85.0ms
(fma -3 (* c a) (* b b))

simplify2.8s

Counts
24 → 69
Calls
24 calls:
Slowest
442.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
311.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
281.0ms
(/ (* (* (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)))
240.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))
211.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune1.2s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 42.4b

localize81.0ms

Local error

Found 4 expressions with local error:

45.4b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
45.4b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
45.4b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.6b
(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
585.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
459.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
436.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
431.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify3.9s

Counts
20 → 64
Calls
20 calls:
Slowest
726.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
594.0ms
(- (* (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))))
528.0ms
(- (+ (* 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)))
377.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
317.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 42.1b

localize64.0ms

Local error

Found 4 expressions with local error:

45.4b
(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)
0.2b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) 3)
0.1b
(fma -3 (* c a) (* b b))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
1×associate-/l/
Counts
4 → 125
Calls
4 calls:
Slowest
15.0ms
(/ (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) 3) a)
9.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) 3)
1.0ms
(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))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
602.0ms
(/ (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) 3) a)
449.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) 3)
405.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
66.0ms
(fma -3 (* c a) (* b b))

simplify11.4s

Counts
133 → 137
Calls
133 calls:
Slowest
436.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
362.0ms
(/ (/ (* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))) (* (cbrt 3) (cbrt 3))) (* (cbrt a) (cbrt a)))
337.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
328.0ms
(- (* 1/3 (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2)) (* 1/3 b))
304.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))

prune1.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 42.1b

regimes589.0ms

Accuracy

24% (2.9b remaining)

Error of 43.2b against oracle of 40.4b and baseline of 44.1b

bsearch62.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.6s16293×pre80true
1.4s4903×body160valid
1.1s8293×body80nan
583.0ms1391×body320valid
218.0ms1706×body80valid