Details

Time bar (total: 31.5s)

sample163.0ms

Algorithm
intervals
Results
59.0ms164×body160valid
31.0ms480×pre80true
27.0ms224×body80nan
11.0ms31×body320valid
8.0ms61×body80valid

simplify115.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
115.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize27.0ms

Local error

Found 4 expressions with local error:

38.1b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.4b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.2b
(fma -3 (* c a) (* b b))
0.1b
(sqrt (fma -3 (* c a) (* b b)))

rewrite54.0ms

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
38.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
11.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series417.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
110.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
87.0ms
(fma -3 (* c a) (* b b))
85.0ms
(sqrt (fma -3 (* c a) (* b b)))

simplify4.2s

Counts
87 → 114
Calls
87 calls:
Slowest
567.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
314.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
220.0ms
(/ (* (* (- (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)))
213.0ms
(/ (* (* (- (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)))
142.0ms
(- (log (- (sqrt (fma -3 (* c a) (* b b))) b)) (+ (log 3) (log a)))

prune1.5s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 38.2b

localize42.0ms

Local error

Found 4 expressions with local error:

41.1b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.4b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.2b
(fma -3 (* c a) (* b b))
0.2b
(fma -3 (* c a) (* b b))

rewrite8.0ms

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))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
557.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
404.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
63.0ms
(fma -3 (* c a) (* b b))
61.0ms
(fma -3 (* c a) (* b b))

simplify2.8s

Counts
24 → 69
Calls
24 calls:
Slowest
406.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
404.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
260.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))
248.0ms
(/ (* (* (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)))
206.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune1.2s

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 38.1b

localize62.0ms

Local error

Found 4 expressions with local error:

41.1b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.3b
(/ 1 (* 3 a))
0.3b
(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1 (* 3 a)))
0.2b
(fma -3 (* c a) (* b b))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
18×add-cbrt-cube
13×prod-exp
11×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×div-exp
7×associate-*r*
6×times-frac
5×cbrt-unprod
4×expm1-log1p-u cbrt-undiv rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* associate-/l*
2×pow-prod-down fma-udef div-inv pow-flip
1×clear-num associate-/r* frac-2neg associate-*r/ un-div-inv *-commutative inv-pow unswap-sqr
Counts
4 → 88
Calls
4 calls:
Slowest
22.0ms
(/ 1 (* 3 a))
22.0ms
(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1 (* 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 -3 (* c a) (* b b))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
733.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
624.0ms
(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1 (* 3 a)))
70.0ms
(fma -3 (* c a) (* b b))
21.0ms
(/ 1 (* 3 a))

simplify5.7s

Counts
52 → 100
Calls
52 calls:
Slowest
712.0ms
(/ (* (* 1 1) 1) (* (* (* 3 a) (* 3 a)) (* 3 a)))
425.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
310.0ms
(* (* (* (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))) (/ (* (* 1 1) 1) (* (* (* 3 3) 3) (* (* a a) a))))
309.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))
308.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune1.5s

Pruning

40 alts after pruning (40 fresh and 0 done)

Merged error: 38.0b

localize78.0ms

Local error

Found 4 expressions with local error:

41.1b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.6b
(cbrt (/ 1 (* 3 a)))
0.6b
(cbrt (/ 1 (* 3 a)))
0.6b
(cbrt (/ 1 (* 3 a)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 div-inv
1×fma-udef
Counts
4 → 68
Calls
4 calls:
Slowest
10.0ms
(cbrt (/ 1 (* 3 a)))
5.0ms
(cbrt (/ 1 (* 3 a)))
5.0ms
(cbrt (/ 1 (* 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:
Slowest
403.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
301.0ms
(cbrt (/ 1 (* 3 a)))
292.0ms
(cbrt (/ 1 (* 3 a)))
277.0ms
(cbrt (/ 1 (* 3 a)))

simplify2.1s

Counts
36 → 80
Calls
36 calls:
Slowest
337.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
203.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
186.0ms
(* (cbrt -1/3) (pow (/ -1 a) 1/3))
162.0ms
(* (pow (/ 1 a) 1/3) (cbrt 1/3))
151.0ms
(* (pow (/ 1 a) 1/3) (cbrt 1/3))

prune868.0ms

Pruning

46 alts after pruning (46 fresh and 0 done)

Merged error: 38.0b

regimes1.4s

Accuracy

0% (3.1b remaining)

Error of 43.2b against oracle of 40.0b and baseline of 43.2b

bsearch7.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.7s4862×body160valid
1.1s16105×pre80true
1.1s8105×body80nan
617.0ms1364×body320valid
210.0ms1774×body80valid