Details

Time bar (total: 20.4s)

sample93.0ms

Algorithm
intervals
Results
22.0ms446×body80nan
21.0ms196×body160nan
17.0ms256×body80valid

simplify12.0ms

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: 32.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x x) 1.0)
0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.5b
(log (+ x (sqrt (- (* x x) 1.0))))
29.8b
(sqrt (- (* x x) 1.0))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1
5×add-exp-log
4×expm1-log1p-u log-prod sqrt-prod add-cbrt-cube log1p-expm1-u
3×fma-def prod-diff
2×log-div flip3-- flip3-+ sqrt-div flip-- flip-+ distribute-lft-out difference-of-squares
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log rem-log-exp sum-log log-pow
Counts
4 → 71
Calls
4 calls:
13.0ms
(- (* x x) 1.0)
29.0ms
(+ x (sqrt (- (* x x) 1.0)))
19.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
35.0ms
(sqrt (- (* x x) 1.0))

series647.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* x x) 1.0)
128.0ms
(+ x (sqrt (- (* x x) 1.0)))
373.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
65.0ms
(sqrt (- (* x x) 1.0))

simplify3.0s

Counts
83 → 83
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01721045
1380921
21041833
34251754
done5000753

prune324.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x))
0.2b
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
0.4b
(/ 0.09375 (pow x 4))
0.5b
(/ 0.25 (* x x))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
135×*-un-lft-identity
66×add-sqr-sqrt
64×prod-diff
54×add-cube-cbrt
40×pow1
38×distribute-lft-out--
36×log-pow
24×times-frac
23×distribute-lft-out
22×associate--r+
14×add-exp-log
12×unpow-prod-down
11×add-cbrt-cube add-log-exp
8×fma-neg associate-/r*
7×diff-log
6×log-prod associate-/l* difference-of-squares
5×div-exp associate--l+
4×expm1-log1p-u log1p-expm1-u sqr-pow
3×cbrt-undiv sub-neg
2×flip3-- frac-2neg clear-num sum-log flip-- div-inv
1×pow-to-exp pow-exp prod-exp cbrt-unprod associate--r-
Counts
4 → 200
Calls
4 calls:
436.0ms
(- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x))
577.0ms
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
8.0ms
(/ 0.09375 (pow x 4))
8.0ms
(/ 0.25 (* x x))

series320.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x))
130.0ms
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
59.0ms
(/ 0.09375 (pow x 4))
33.0ms
(/ 0.25 (* x x))

simplify1.5s

Counts
212 → 212
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02845902
16084903
217334016
done50002992

prune555.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite76.0ms

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:
6.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
63.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series869.0ms

Counts
3 → 9
Calls
3 calls:
198.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
395.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
276.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify3.1s

Counts
85 → 85
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01971683
14651428
213521310
348731281
done50001281

prune312.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
0.5b
(* (cbrt x) (cbrt x))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
22×cbrt-prod *-un-lft-identity
18×add-cube-cbrt
15×pow1 associate-*r* sqrt-prod
13×associate-*l*
12×sqrt-div
8×add-exp-log pow1/3 unswap-sqr
6×swap-sqr add-cbrt-cube
5×pow-prod-down
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
3×flip3-- flip3-+ flip-- flip-+
2×sqrt-pow1 pow1/2 associate-*r/ associate-*l/ prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod difference-of-squares
1×pow2 pow-plus sqrt-unprod distribute-lft-out distribute-lft-out--
Counts
4 → 112
Calls
4 calls:
2.0ms
(cbrt x)
2.0ms
(cbrt x)
23.0ms
(* (cbrt x) (cbrt x))
86.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
300.0ms
(cbrt x)
295.0ms
(cbrt x)
279.0ms
(* (cbrt x) (cbrt x))
280.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify2.8s

Counts
124 → 124
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01851340
13961100
210761061
335511035
done50001028

prune545.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01014
11314
done1314

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.1s15979×body80nan
1.0s8000×body80valid
803.0ms7619×body160nan