Details

Time bar (total: 24.5s)

sample58.0ms

Algorithm
intervals
Results
41.0ms267×body80valid

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize19.0ms

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))

series185.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
124.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
61.0ms
(fma a c (* b d))

simplify1.3s

Counts
31 → 47
Calls
31 calls:
Slowest
455.0ms
(/ (* (* (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))))
52.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
50.0ms
(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
45.0ms
(/ (sqrt (fma a c (* b d))) (cbrt (fma d d (* c c))))
45.0ms
(/ (cbrt (fma a c (* b d))) (cbrt (fma d d (* c c))))

prune516.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.3b

localize36.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (fma d d (* c c)))
25.6b
(sqrt (fma d d (* c c)))
16.3b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b
(fma a c (* b d))

rewrite8.0ms

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))

series305.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
62.0ms
(sqrt (fma d d (* c c)))
47.0ms
(fma a c (* b d))
45.0ms
(sqrt (fma d d (* c c)))

simplify1.9s

Counts
68 → 99
Calls
68 calls:
Slowest
313.0ms
(/ (* (* (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)))))
103.0ms
(/ (* (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))))))
51.0ms
(/ (sqrt (fma a c (* b d))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))
46.0ms
(/ (cbrt (fma a c (* b d))) (sqrt (fma d d (* c c))))
45.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) 1)

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.0b

localize51.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (fma d d (* c c)))
25.6b
(sqrt (fma d d (* c c)))
16.4b
(* (fma a c (* b d)) (/ 1 (sqrt (fma d d (* c c)))))
0.3b
(fma a c (* b d))

rewrite32.0ms

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
24.0ms
(* (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))

series329.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(* (fma a c (* b d)) (/ 1 (sqrt (fma d d (* c c)))))
67.0ms
(sqrt (fma d d (* c c)))
51.0ms
(sqrt (fma d d (* c c)))
45.0ms
(fma a c (* b d))

simplify3.1s

Counts
65 → 107
Calls
65 calls:
Slowest
632.0ms
(* (* (* (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))))))
182.0ms
(* (fma a c (* b d)) (/ 1 (sqrt (fma d d (* c c)))))
157.0ms
(* (* (* (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))))))
125.0ms
(+ (log (fma a c (* b d))) (log (/ 1 (sqrt (fma d d (* c c))))))
112.0ms
(* (sqrt (fma a c (* b d))) (/ 1 (sqrt (sqrt (fma d d (* c c))))))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.0b

localize39.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (fma d d (* c c)))
25.6b
(sqrt (fma d d (* c c)))
16.3b
(/ (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)))))

rewrite47.0ms

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
29.0ms
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
10.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
3.0ms
(sqrt (fma d d (* c c)))
3.0ms
(sqrt (fma d d (* c c)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
204.0ms
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
189.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
80.0ms
(sqrt (fma d d (* c c)))
56.0ms
(sqrt (fma d d (* c c)))

simplify8.9s

Counts
157 → 174
Calls
157 calls:
Slowest
404.0ms
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
353.0ms
(/ (* (* (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)))))
308.0ms
(* (/ (* (* 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))))))
275.0ms
(* (* (* (/ 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))))))
234.0ms
(* (/ (* (* 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)) (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))))

prune2.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 17.1b

regimes343.0ms

Accuracy

1.6% (7.1b remaining)

Error of 25.6b against oracle of 18.5b and baseline of 25.7b

bsearch74.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s8461×body80valid