Details

Time bar (total: 15.4s)

sample54.0ms

Algorithm
intervals
Results
38.0ms268×body80valid

simplify29.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
29.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize18.0ms

Local error

Found 2 expressions with local error:

22.8b
(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b
(fma a c (* b d))

rewrite11.0ms

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
9.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series210.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
138.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
72.0ms
(fma a c (* b d))

simplify1.1s

Counts
31 → 47
Calls
31 calls:
Slowest
380.0ms
(/ (* (* (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))))
59.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
51.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (fma d d (* c c))))
48.0ms
(- (log (fma a c (* b d))) (log (fma d d (* c c))))
45.0ms
(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))

prune556.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.4b

localize38.0ms

Local error

Found 4 expressions with local error:

26.9b
(sqrt (fma d d (* c c)))
26.9b
(sqrt (fma d d (* c c)))
15.4b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b
(fma a c (* b d))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
Calls
4 calls:
Slowest
5.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms
(sqrt (fma d d (* c c)))
1.0ms
(sqrt (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
53.0ms
(sqrt (fma d d (* c c)))
52.0ms
(sqrt (fma d d (* c c)))
48.0ms
(fma a c (* b d))

simplify1.8s

Counts
68 → 99
Calls
68 calls:
Slowest
262.0ms
(/ (* (* (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)))))
62.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
61.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt 1))
59.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))
51.0ms
(/ (sqrt (fma a c (* b d))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.2b

localize52.0ms

Local error

Found 4 expressions with local error:

26.9b
(sqrt (fma d d (* c c)))
26.9b
(sqrt (fma d d (* c c)))
15.6b
(* (fma a c (* b d)) (/ 1 (sqrt (fma d d (* c c)))))
0.3b
(fma a c (* b d))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
22×*-un-lft-identity times-frac associate-*r*
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
5×unswap-sqr
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* fma-udef
2×rem-sqrt-square sqrt-pow1 pow1/2 div-exp cbrt-unprod hypot-def
1×cbrt-undiv rec-exp 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 95
Calls
4 calls:
Slowest
25.0ms
(* (fma a c (* b d)) (/ 1 (sqrt (fma d d (* c c)))))
3.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(* (fma a c (* b d)) (/ 1 (sqrt (fma d d (* c c)))))
66.0ms
(sqrt (fma d d (* c c)))
57.0ms
(fma a c (* b d))
51.0ms
(sqrt (fma d d (* c c)))

simplify2.9s

Counts
65 → 107
Calls
65 calls:
Slowest
664.0ms
(* (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (/ 1 (sqrt (fma d d (* c c)))) (/ 1 (sqrt (fma d d (* c c))))) (/ 1 (sqrt (fma d d (* c c))))))
178.0ms
(* (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (/ (* (* 1 1) 1) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))))
170.0ms
(* (fma a c (* b d)) (/ 1 (sqrt (fma d d (* c c)))))
113.0ms
(* (sqrt (fma a c (* b d))) (/ (sqrt 1) (sqrt (sqrt (fma d d (* c c))))))
112.0ms
(* (sqrt (fma a c (* b d))) (/ (sqrt 1) (sqrt (sqrt (fma d d (* c c))))))

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.2b

localize47.0ms

Local error

Found 3 expressions with local error:

22.8b
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
0.4b
(/ 1 (fma d d (* c c)))
0.3b
(fma a c (* b d))

rewrite31.0ms

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
20.0ms
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
9.0ms
(/ 1 (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series206.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
104.0ms
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
56.0ms
(/ 1 (fma d d (* c c)))
45.0ms
(fma a c (* b d))

simplify2.4s

Counts
66 → 93
Calls
66 calls:
Slowest
502.0ms
(* (* (* (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)))))
136.0ms
(/ (* (* 1 1) 1) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
135.0ms
(* (* (* (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)))))
135.0ms
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
82.0ms
(* (sqrt (fma a c (* b d))) (/ (sqrt 1) (sqrt (fma d d (* c c)))))

prune951.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 20.2b

regimes358.0ms

Accuracy

0% (2.6b remaining)

Error of 25.5b against oracle of 22.9b and baseline of 25.5b

bsearch3.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
970.0ms8487×body80valid