Details

Time bar (total: 14.9s)

sample107.0ms

Algorithm
intervals
Results
60.0ms724×body80nan
18.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.3b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite570.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
21×times-frac
14×add-sqr-sqrt add-cube-cbrt
13×fma-def
8×log-prod distribute-lft-out
5×div-inv
4×add-log-exp
3×pow1 add-exp-log log-div
2×expm1-log1p-u distribute-rgt-out flip3-+ frac-add add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 54
Calls
2 calls:
521.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
46.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series663.0ms

Counts
2 → 6
Calls
2 calls:
175.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
488.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify899.0ms

Counts
60 → 60
Iterations

Useful iterations: done (896.0ms)

IterNodesCost
0141997
1361954
21386870
done5001853

prune226.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (sqrt x))
0.2b
(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
0.3b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.3b
(/ 1.0 (sqrt x))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
78×sqrt-prod
76×times-frac
72×add-sqr-sqrt
61×add-cube-cbrt
25×log-prod
16×fma-def
15×pow1 distribute-lft-out
14×log-pow
13×associate-+r+
12×associate-/r*
10×distribute-rgt-neg-in associate-/l*
9×add-exp-log
8×add-cbrt-cube
7×difference-of-squares
6×distribute-lft-neg-in associate-+l+ distribute-neg-in
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-+r- log-div sqrt-pow1 pow1/2
2×cbrt-undiv frac-2neg flip3-+ sqrt-div div-exp clear-num sum-log flip-+ associate-/l/
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sqrt-undiv distribute-rgt-out flip3-- rem-log-exp neg-log frac-add flip--
Counts
4 → 191
Calls
4 calls:
2.0ms
(log (sqrt x))
108.0ms
(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
24.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
7.0ms
(/ 1.0 (sqrt x))

series640.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(log (sqrt x))
391.0ms
(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
104.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
76.0ms
(/ 1.0 (sqrt x))

simplify1.8s

Counts
203 → 203
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03272991
17582726
229082551
done50022536

prune722.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.3b
(log (* (/ 1 1) (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
16×add-exp-log
15×times-frac
13×fma-def
11×add-sqr-sqrt add-cube-cbrt
8×rem-log-exp
7×log-div prod-exp
5×pow1 1-exp
4×div-exp distribute-lft-out add-log-exp
3×frac-times flip3-+ associate-*r/ frac-add flip-+ div-inv
2×expm1-log1p-u rec-exp log-pow add-cbrt-cube log1p-expm1-u
1×+-commutative log-prod distribute-rgt-out pow-prod-down associate-*l/ sum-log
Counts
2 → 59
Calls
2 calls:
53.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
46.0ms
(log (* (/ 1 1) (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

series611.0ms

Counts
2 → 6
Calls
2 calls:
163.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
447.0ms
(log (* (/ 1 1) (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

simplify1.4s

Counts
65 → 65
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01481063
1425931
22291858
done5001833

prune286.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.2s

Counts
4 → 12
Calls
4 calls:
260.0ms
(cbrt x)
242.0ms
(cbrt x)
306.0ms
(cbrt x)
353.0ms
(cbrt x)

simplify1.1s

Counts
64 → 64
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
026284
147268
2115244
3334232
41002232
done5001232

prune346.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01320
11520
done1520

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.3s24347×body80nan
667.0ms8000×body80valid