Details

Time bar (total: 1.3m)

sample38.0ms

Algorithm
intervals
Results
11.0ms312×body80nan
11.0ms256×body80valid

simplify106.0ms

Counts
1 → 1
Iterations
IterNodes
done129
8129
7128
6126
5109
484
362
238
121
011

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
0.0b
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
102×add-sqr-sqrt *-un-lft-identity
70×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×associate-/r/
9×add-cbrt-cube add-exp-log
6×div-inv associate-/l*
5×flip3-- flip--
4×cbrt-undiv div-exp
2×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
Counts
2 → 143
Calls
2 calls:
13.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
14.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series182.0ms

Counts
2 → 6
Calls
2 calls:
95.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
87.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify1.5s

Counts
149 → 149
Iterations
IterNodes
done5003
22030
1603
0241

prune712.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
0.0b
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
0.0b
(/ (/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))
0.0b
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
25326×times-frac
15653×*-un-lft-identity
13901×add-sqr-sqrt
12335×sqrt-prod
8373×add-cube-cbrt
2764×difference-of-squares
2258×distribute-lft-out
1382×distribute-lft-out--
669×associate-/r/
366×div-inv
188×flip3-+ flip-+
128×associate-/l*
115×flip3-- flip--
110×associate-/r*
34×add-cbrt-cube add-exp-log
20×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/l/
Counts
4 → 7285
Calls
4 calls:
36.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
26.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
270.0ms
(/ (/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))
26.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
500.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
440.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
573.0ms
(/ (/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))
392.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

simplify11.8s

Counts
7297 → 7297
Iterations
IterNodes
done5000
04278

prune24.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- x 1.0) 6.0)
0.0b
(/ 1 (fma (sqrt x) 4.0 (+ x 1.0)))
0.2b
(* (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (* (- x 1.0) 6.0))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
24×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×add-cbrt-cube
18×times-frac associate-*l*
13×prod-exp
11×pow1
7×associate-*l/ cbrt-unprod
6×div-exp
4×associate-*r* pow-prod-down
3×expm1-log1p-u cbrt-undiv rec-exp associate-/r* flip3-- 1-exp log1p-expm1-u flip-- associate-/l* add-log-exp
2×frac-times associate-*r/ *-commutative div-inv
1×clear-num frac-2neg pow-flip distribute-lft-out-- inv-pow difference-of-squares unswap-sqr
Counts
3 → 100
Calls
3 calls:
19.0ms
(* (- x 1.0) 6.0)
5.0ms
(/ 1 (fma (sqrt x) 4.0 (+ x 1.0)))
41.0ms
(* (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (* (- x 1.0) 6.0))

series319.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(* (- x 1.0) 6.0)
105.0ms
(/ 1 (fma (sqrt x) 4.0 (+ x 1.0)))
127.0ms
(* (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (* (- x 1.0) 6.0))

simplify2.7s

Counts
109 → 109
Iterations
IterNodes
done5000
34498
21205
1435
0164

prune515.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0)))) (+ (sqrt x) (sqrt 1.0)))
0.3b
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.3b
(/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0))))
1.0b
(* (/ (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))) (/ (/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0)))) (+ (sqrt x) (sqrt 1.0))))

rewrite11.9s

Algorithm
rewrite-expression-head
Rules
8457×times-frac
5491×*-un-lft-identity
4323×add-sqr-sqrt
3845×sqrt-prod
3051×add-cube-cbrt
1445×associate-*l*
964×distribute-lft-out
661×associate-*r*
243×associate-/r/
240×distribute-lft-out-- difference-of-squares
188×add-exp-log
165×div-inv
143×associate-/l*
128×unswap-sqr
122×add-cbrt-cube
121×div-exp
75×flip3-+ flip-+
72×cbrt-undiv
40×flip3-- flip--
32×associate-/r*
30×prod-exp
20×cbrt-unprod
7×rec-exp 1-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×frac-times sqrt-undiv pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 3347
Calls
4 calls:
75.0ms
(/ (/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0)))) (+ (sqrt x) (sqrt 1.0)))
7.0ms
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
27.0ms
(/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0))))
11.4s
(* (/ (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))) (/ (/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0)))) (+ (sqrt x) (sqrt 1.0))))

series704.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0)))) (+ (sqrt x) (sqrt 1.0)))
422.0ms
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
89.0ms
(/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0))))
172.0ms
(* (/ (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))) (/ (/ (sqrt 6.0) (/ 1 (+ (sqrt x) (sqrt 1.0)))) (+ (sqrt x) (sqrt 1.0))))

simplify3.1s

Counts
3359 → 3359
Iterations
IterNodes
done5000
02267

prune12.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done17
117
015

end0.0ms

sample1.1s

Algorithm
intervals
Results
649.0ms8000×body80valid
300.0ms7998×body80nan