Details

Time bar (total: 3.5s)

sample32.0ms

Algorithm
intervals
Results
16.0ms139×pre10240exit
5.0ms256×body80valid
2.0ms117×pre80true

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0103
1123
2123

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.8b
(/ x0 (- 1.0 x1))
7.7b
(- (/ x0 (- 1.0 x1)) x0)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
16×times-frac
12×add-cube-cbrt
6×difference-of-squares
5×associate-/r* distribute-lft-out--
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-- associate-/r/ flip--
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
5.0ms
(/ x0 (- 1.0 x1))
31.0ms
(- (/ x0 (- 1.0 x1)) x0)

series79.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ x0 (- 1.0 x1))
45.0ms
(- (/ x0 (- 1.0 x1)) x0)

simplify92.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0244328
1801315
23123310
35001310

prune90.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 7.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ x0 (- 1.0 x1))
0.8b
(/ x0 (- 1.0 x1))
0.8b
(+ (/ x0 (- 1.0 x1)) x0)
6.3b
(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
40×add-sqr-sqrt
30×times-frac
24×add-cube-cbrt
10×associate-/r*
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out-- add-log-exp
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- flip--
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×+-commutative sub-neg flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 99
Calls
4 calls:
5.0ms
(/ x0 (- 1.0 x1))
5.0ms
(/ x0 (- 1.0 x1))
23.0ms
(+ (/ x0 (- 1.0 x1)) x0)
10.0ms
(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

series174.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ x0 (- 1.0 x1))
33.0ms
(/ x0 (- 1.0 x1))
37.0ms
(+ (/ x0 (- 1.0 x1)) x0)
69.0ms
(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

simplify39.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0341684
11318641
25001638

prune196.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ x0 (- 1.0 x1))
0.8b
(/ x0 (- 1.0 x1))
0.8b
(+ (/ x0 (- 1.0 x1)) x0)
6.3b
(- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
40×add-sqr-sqrt
30×times-frac
24×add-cube-cbrt
10×associate-/r*
8×add-exp-log add-cbrt-cube distribute-lft-out-- add-log-exp difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- flip--
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×+-commutative sub-neg flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 98
Calls
4 calls:
5.0ms
(/ x0 (- 1.0 x1))
6.0ms
(/ x0 (- 1.0 x1))
23.0ms
(+ (/ x0 (- 1.0 x1)) x0)
72.0ms
(- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

series204.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ x0 (- 1.0 x1))
34.0ms
(/ x0 (- 1.0 x1))
35.0ms
(+ (/ x0 (- 1.0 x1)) x0)
95.0ms
(- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

simplify46.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0361849
11470797
25002780

prune274.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
0.8b
(+ (/ x0 (- 1.0 x1)) x0)
4.0b
(log (exp (- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))))
6.3b
(- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

rewrite425.0ms

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
78×times-frac
54×*-un-lft-identity associate-*r*
46×sqrt-prod
38×add-cube-cbrt
30×cbrt-prod
25×add-exp-log
18×add-cbrt-cube
15×unswap-sqr
14×associate-*l*
8×prod-exp cbrt-unprod add-log-exp
7×pow1 cbrt-undiv div-exp distribute-lft-out-- difference-of-squares
5×log-prod
4×sqrt-div associate-/r/ log-pow
3×exp-prod flip3-- flip--
2×sub-neg exp-sum div-inv
1×+-commutative frac-times log-div flip3-+ exp-diff diff-log associate-*r/ rem-log-exp pow-prod-down associate-*l/ sum-log *-commutative flip-+ distribute-lft-out
Counts
4 → 149
Calls
4 calls:
55.0ms
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
23.0ms
(+ (/ x0 (- 1.0 x1)) x0)
266.0ms
(log (exp (- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))))
73.0ms
(- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

series268.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
38.0ms
(+ (/ x0 (- 1.0 x1)) x0)
90.0ms
(log (exp (- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))))
92.0ms
(- (* (/ x0 (- 1.0 x1)) (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

simplify99.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
08422457
140372212
250012015

prune419.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.2b

regimes81.0ms

Accuracy

77.1% (0.5b remaining)

Error of 4.6b against oracle of 4.2b and baseline of 6.3b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06164
16164

end0.0ms

sample731.0ms

Algorithm
intervals
Results
384.0ms4044×pre10240exit
144.0ms8000×body80valid
61.0ms3956×pre80true