Details

Time bar (total: 4.6s)

sample279.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
7.0ms254×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(/ (- 1.0 x) (+ 1.0 x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 97
Calls
3 calls:
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
14.0ms
(/ (- 1.0 x) (+ 1.0 x))

series151.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
53.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify41.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0370779
11128734
25001719

prune241.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
582×*-un-lft-identity
484×times-frac
332×add-sqr-sqrt
324×prod-diff
320×add-cube-cbrt
123×distribute-lft-out
82×associate-/r/
41×flip3-+ flip-+ div-inv
18×fma-neg
8×add-exp-log associate-/r* add-cbrt-cube
7×distribute-lft-out--
6×associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
3×distribute-rgt-out--
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 451
Calls
4 calls:
5.0ms
(/ x (+ x 1.0))
0.0ms
(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
5.0ms
(/ 1.0 (+ x 1.0))
65.0ms
(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

series125.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ x (+ x 1.0))
3.0ms
(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
26.0ms
(/ 1.0 (+ x 1.0))
63.0ms
(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

simplify143.0ms

Algorithm
egg-herbie
Counts
463 → 463
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0103211091
130798021
250017159

prune586.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (/ x (+ x 1.0)) (+ (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))))
0.0b
(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
0.1b
(pow (/ 1.0 (+ x 1.0)) 3)
0.1b
(pow (/ x (+ x 1.0)) 3)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
140×*-un-lft-identity
112×times-frac
86×add-sqr-sqrt
74×add-cube-cbrt
36×unpow-prod-down cube-prod
30×distribute-lft-out
24×swap-sqr
22×add-exp-log add-cbrt-cube
18×associate-*r* associate-*l*
16×associate-/r/
13×pow1
8×flip3-+ flip-+ div-inv
6×cbrt-undiv pow-unpow div-exp
4×expm1-log1p-u pow-exp prod-exp cbrt-unprod log1p-expm1-u add-log-exp rem-cube-cbrt unswap-sqr
2×cube-div cube-mult pow-to-exp pow-pow unpow3 sqr-pow
1×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up fma-udef
Counts
4 → 216
Calls
4 calls:
0.0ms
(fma (/ x (+ x 1.0)) (+ (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))))
31.0ms
(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
8.0ms
(pow (/ 1.0 (+ x 1.0)) 3)
10.0ms
(pow (/ x (+ x 1.0)) 3)

series247.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(fma (/ x (+ x 1.0)) (+ (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))))
34.0ms
(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
50.0ms
(pow (/ 1.0 (+ x 1.0)) 3)
60.0ms
(pow (/ x (+ x 1.0)) 3)

simplify46.0ms

Algorithm
egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09691667
150011399

prune574.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.0b
(cbrt (+ x 1.0))
0.0b
(cbrt (+ x 1.0))
0.0b
(cbrt (+ x 1.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 103
Calls
4 calls:
20.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))

series375.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
88.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))
90.0ms
(cbrt (+ x 1.0))

simplify153.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 3 (143.0ms)

IterNodesCost
0321818
11064769
24750694
35001688

prune513.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02024
12024

end0.0ms

sample744.0ms

Algorithm
intervals
Results
329.0ms8000×body80valid
220.0ms8112×body80nan