Details

Time bar (total: 18.5s)

sample71.0ms

Algorithm
intervals
Results
25.0ms220×body160nan
14.0ms461×body80nan
10.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1119
2129
done129

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
31.0b
(sqrt (- (* x x) 1.0))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod sqrt-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 52
Calls
3 calls:
33.0ms
(+ x (sqrt (- (* x x) 1.0)))
17.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
16.0ms
(sqrt (- (* x x) 1.0))

series393.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(+ x (sqrt (- (* x x) 1.0)))
241.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
65.0ms
(sqrt (- (* x x) 1.0))

simplify2.0s

Counts
61 → 61
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0146832
1337748
2943682
33115614
done5000611

prune290.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×sqrt-prod
13×*-un-lft-identity
12×sqrt-div
9×add-cube-cbrt associate-*r*
8×pow1
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×expm1-log1p-u log-prod flip3-- fma-def pow-prod-down flip-- log1p-expm1-u
2×log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
1×+-commutative sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 76
Calls
3 calls:
12.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
8.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
104.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series926.0ms

Counts
3 → 9
Calls
3 calls:
241.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
465.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
220.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify3.3s

Counts
85 → 85
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01971683
14651428
213521310
348731281
done50001281

prune366.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.2b
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-prod *-un-lft-identity
2×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
1×rem-log-exp log-pow fma-udef
Counts
2 → 24
Calls
2 calls:
0.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
1.0ms
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))

series976.0ms

Counts
2 → 6
Calls
2 calls:
351.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
625.0ms
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))

simplify2.7s

Counts
30 → 30
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0126740
1335715
21030626
34232598
done5000593

prune169.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (* 1.0 1.0) (pow x 4)) 3/32)
0.2b
(- (log 2) (- (fma 1/4 (/ 1.0 (* x x)) (* (/ (* 1.0 1.0) (pow x 4)) 3/32)) (log x)))
0.3b
(/ 1.0 (* x x))
0.4b
(/ (* 1.0 1.0) (pow x 4))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
50×add-sqr-sqrt
43×add-exp-log
36×prod-diff
33×add-cube-cbrt
25×pow1
23×add-cbrt-cube
20×times-frac
19×log-pow
18×distribute-lft-out--
15×associate--r+
14×div-exp prod-exp
11×associate-*l*
10×unpow-prod-down
8×associate-/r*
6×cbrt-undiv cbrt-unprod add-log-exp
5×difference-of-squares
4×expm1-log1p-u pow-to-exp fma-neg pow-exp associate--l+ log1p-expm1-u associate-/l* unswap-sqr sqr-pow
3×log-prod diff-log associate-*r* div-inv
2×sub-neg frac-2neg clear-num
1×flip3-- pow-prod-down associate-*l/ *-commutative flip-- fma-udef associate--r-
Counts
4 → 167
Calls
4 calls:
55.0ms
(* (/ (* 1.0 1.0) (pow x 4)) 3/32)
60.0ms
(- (log 2) (- (fma 1/4 (/ 1.0 (* x x)) (* (/ (* 1.0 1.0) (pow x 4)) 3/32)) (log x)))
14.0ms
(/ 1.0 (* x x))
17.0ms
(/ (* 1.0 1.0) (pow x 4))

series361.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (/ (* 1.0 1.0) (pow x 4)) 3/32)
187.0ms
(- (log 2) (- (fma 1/4 (/ 1.0 (* x x)) (* (/ (* 1.0 1.0) (pow x 4)) 3/32)) (log x)))
28.0ms
(/ 1.0 (* x x))
65.0ms
(/ (* 1.0 1.0) (pow x 4))

simplify1.9s

Counts
179 → 179
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02765355
16344394
219063583
done50002619

prune736.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes24.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
11513
done1513

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.4s7766×body160nan
1.1s16579×body80nan
571.0ms8000×body80valid