Details

Time bar (total: 4.7s)

sample48.0ms

Algorithm
intervals
Results
23.0ms824×body80nan
9.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2167

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
33×times-frac
28×add-sqr-sqrt
24×add-cube-cbrt
16×sqrt-prod
8×log-prod distribute-lft-out
7×associate-/l*
6×add-exp-log
5×add-cbrt-cube div-inv add-log-exp
4×pow1 difference-of-squares
3×log-div associate-/r*
2×distribute-rgt-out flip3-+ sqrt-div frac-add flip-+ associate-/l/
1×cbrt-undiv +-commutative flip3-- frac-2neg div-exp rem-log-exp clear-num sum-log log-pow flip--
Counts
3 → 82
Calls
3 calls:
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
23.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
26.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series528.0ms

Counts
3 → 9
Calls
3 calls:
136.0ms
(/ (sqrt (- 1.0 (* x x))) x)
289.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
103.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify45.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0460892
11594844
25001822

prune234.0ms

Filtered
91 candidates to 72 candidates (79.1%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (sqrt (- 1.0 (* x x))))
0.0b
(cbrt (sqrt (- 1.0 (* x x))))
0.0b
(cbrt (sqrt (- 1.0 (* x x))))
0.0b
(* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
65×cbrt-prod
51×add-sqr-sqrt
36×sqrt-prod
22×add-cube-cbrt *-un-lft-identity
18×cbrt-div sqrt-div
12×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-- pow1/3 flip-- unswap-sqr
7×difference-of-squares
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 118
Calls
4 calls:
2.0ms
(cbrt (sqrt (- 1.0 (* x x))))
2.0ms
(cbrt (sqrt (- 1.0 (* x x))))
2.0ms
(cbrt (sqrt (- 1.0 (* x x))))
19.0ms
(* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x)))))

series787.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(cbrt (sqrt (- 1.0 (* x x))))
195.0ms
(cbrt (sqrt (- 1.0 (* x x))))
191.0ms
(cbrt (sqrt (- 1.0 (* x x))))
200.0ms
(* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03811632
114361557
250011483

prune390.0ms

Filtered
130 candidates to 88 candidates (67.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
24×times-frac
16×add-sqr-sqrt sqrt-prod distribute-lft-out
14×add-cube-cbrt
8×div-inv add-log-exp
6×pow1 sqrt-div
4×add-exp-log distribute-rgt-out flip3-+ frac-add add-cbrt-cube flip-+
2×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 76
Calls
4 calls:
25.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
26.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
47.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
45.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series617.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
103.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
207.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
201.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03921018
11303954
25001920

prune311.0ms

Filtered
88 candidates to 74 candidates (84.1%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01318
11318

end0.0ms

sample1.3s

Algorithm
intervals
Results
673.0ms24033×body80nan
280.0ms8000×body80valid