Details

Time bar (total: 33.4s)

sample56.0ms

Algorithm
intervals
Results
38.0ms273×body80valid

simplify28.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
28.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize30.0ms

Local error

Found 2 expressions with local error:

24.7b
(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b
(fma a c (* b d))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
Slowest
5.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series176.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
115.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
61.0ms
(fma a c (* b d))

simplify1.2s

Counts
31 → 47
Calls
31 calls:
Slowest
370.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
93.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
48.0ms
(- (log (fma a c (* b d))) (log (fma d d (* c c))))
45.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) 1)
42.0ms
(/ (cbrt (fma a c (* b d))) (fma d d (* c c)))

prune633.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.3b

localize34.0ms

Local error

Found 4 expressions with local error:

29.2b
(sqrt (fma d d (* c c)))
29.2b
(sqrt (fma d d (* c c)))
15.2b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
9×div-exp
8×pow1 prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp fma-udef hypot-def
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 162
Calls
4 calls:
Slowest
18.0ms
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
6.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
3.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))

series856.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(sqrt (fma d d (* c c)))
198.0ms
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
178.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
54.0ms
(sqrt (fma d d (* c c)))

simplify9.4s

Counts
157 → 174
Calls
157 calls:
Slowest
489.0ms
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
301.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))) (/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))))
299.0ms
(* (* (* (/ 1 (sqrt (fma d d (* c c)))) (/ 1 (sqrt (fma d d (* c c))))) (/ 1 (sqrt (fma d d (* c c))))) (/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))))
292.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
224.0ms
(+ (- 0 (log (sqrt (fma d d (* c c))))) (- (log (fma a c (* b d))) (log (sqrt (fma d d (* c c))))))

prune2.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 16.8b

localize19.0ms

Local error

Found 3 expressions with local error:

24.2b
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
0.9b
(/ 1 (fma d d (* c c)))
0.3b
(fma a c (* b d))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×*-un-lft-identity times-frac
19×add-cube-cbrt
16×add-exp-log
13×associate-*r*
10×add-cbrt-cube
6×pow1
4×div-exp prod-exp
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod div-inv
1×clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef pow-flip inv-pow
Counts
3 → 84
Calls
3 calls:
Slowest
17.0ms
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
8.0ms
(/ 1 (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series261.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
134.0ms
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
66.0ms
(fma a c (* b d))
60.0ms
(/ 1 (fma d d (* c c)))

simplify3.2s

Counts
66 → 93
Calls
66 calls:
Slowest
846.0ms
(* (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (/ 1 (fma d d (* c c))) (/ 1 (fma d d (* c c)))) (/ 1 (fma d d (* c c)))))
196.0ms
(* (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (/ (* (* 1 1) 1) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c)))))
177.0ms
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
131.0ms
(/ (* (* 1 1) 1) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
107.0ms
(+ (log (fma a c (* b d))) (log (/ 1 (fma d d (* c c)))))

prune1.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 16.8b

localize28.0ms

Local error

Found 3 expressions with local error:

24.3b
(/ (fma d d (* c c)) (fma a c (* b d)))
0.7b
(/ 1 (/ (fma d d (* c c)) (fma a c (* b d))))
0.3b
(fma a c (* b d))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/r* add-exp-log
10×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
4×pow1 cbrt-undiv
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg 1-exp
1×associate-/r/ fma-udef pow-flip inv-pow
Counts
3 → 120
Calls
3 calls:
Slowest
10.0ms
(/ 1 (/ (fma d d (* c c)) (fma a c (* b d))))
4.0ms
(/ (fma d d (* c c)) (fma a c (* b d)))
0.0ms
(fma a c (* b d))

series401.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
231.0ms
(/ 1 (/ (fma d d (* c c)) (fma a c (* b d))))
104.0ms
(/ (fma d d (* c c)) (fma a c (* b d)))
66.0ms
(fma a c (* b d))

simplify10.2s

Counts
135 → 129
Calls
135 calls:
Slowest
441.0ms
(/ (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))) (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))))
358.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))) (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d))))))
324.0ms
(/ (sqrt 1) (/ (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))) (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d))))))
315.0ms
(/ (* (* 1 1) 1) (* (* (/ (fma d d (* c c)) (fma a c (* b d))) (/ (fma d d (* c c)) (fma a c (* b d)))) (/ (fma d d (* c c)) (fma a c (* b d)))))
254.0ms
(/ (cbrt 1) (/ (sqrt (fma d d (* c c))) (fma a c (* b d))))

prune1.5s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 13.3b

regimes476.0ms

Accuracy

0% (2.4b remaining)

Error of 16.1b against oracle of 13.7b and baseline of 16.1b

bsearch3.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s8472×body80valid