Details

Time bar (total: 5.2s)

sample24.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03310
17910
221010
348310
491010
5151610
6281810
7500110

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x y) z)
1.8b
(+ (* (+ x y) z) (* (+ t y) a))
2.8b
(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.4b
(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
20×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
13×distribute-lft-out
11×add-log-exp
10×associate-*l/
8×add-exp-log add-cbrt-cube
7×flip3-+ flip-+
6×pow1
5×associate-/r*
4×expm1-log1p-u associate-*l* frac-add log1p-expm1-u
3×fma-neg associate-*r* prod-diff associate-/l*
2×flip3-- diff-log sum-log associate-/r/ flip-- associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg div-sub div-exp pow-prod-down prod-exp associate--l+ clear-num *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 105
Calls
4 calls:
6.0ms
(* (+ x y) z)
7.0ms
(+ (* (+ x y) z) (* (+ t y) a))
10.0ms
(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
18.0ms
(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series792.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (+ x y) z)
45.0ms
(+ (* (+ x y) z) (* (+ t y) a))
95.0ms
(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
628.0ms
(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify69.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05681186
125261087
250011076

prune409.0ms

Filtered
117 candidates to 93 candidates (79.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
1.1b
(- (* (+ t y) a) (* y b))
2.0b
(fma z (+ x y) (- (* (+ t y) a) (* y b)))
25.3b
(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
150×*-un-lft-identity
132×times-frac
70×add-sqr-sqrt add-cube-cbrt
48×distribute-lft-out
22×associate-/r*
17×add-exp-log
11×add-cbrt-cube
8×div-exp associate-/l*
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u
2×rec-exp frac-2neg 1-exp clear-num associate-/l/
1×sub-neg flip3-- pow-flip flip3-+ fma-neg diff-log prod-diff associate-/r/ flip-- flip-+ fma-udef inv-pow
Counts
4 → 167
Calls
4 calls:
10.0ms
(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
6.0ms
(- (* (+ t y) a) (* y b))
1.0ms
(fma z (+ x y) (- (* (+ t y) a) (* y b)))
8.0ms
(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series812.0ms

Counts
4 → 12
Calls
4 calls:
582.0ms
(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
33.0ms
(- (* (+ t y) a) (* y b))
97.0ms
(fma z (+ x y) (- (* (+ t y) a) (* y b)))
100.0ms
(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify70.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04962605
122282401
250022286

prune374.0ms

Filtered
179 candidates to 92 candidates (51.4%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune24.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.1b

localize21.0ms

Local error

Found 4 expressions with local error:

7.0b
(* (/ 1 (* (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b)))) (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b)))))) (/ (+ (+ x t) y) (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))))
26.2b
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))
26.2b
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))
26.2b
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity
49×add-exp-log
47×add-sqr-sqrt
45×times-frac
34×associate-*r*
27×cbrt-prod
26×add-cube-cbrt
20×prod-exp
18×add-cbrt-cube distribute-lft-out
15×div-exp
9×unswap-sqr
8×cbrt-unprod
7×cbrt-undiv associate-*l*
6×pow1
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×pow1/3
2×div-inv
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 123
Calls
4 calls:
26.0ms
(* (/ 1 (* (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b)))) (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b)))))) (/ (+ (+ x t) y) (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))))
1.0ms
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))
1.0ms
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))
1.0ms
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series685.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (/ 1 (* (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b)))) (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b)))))) (/ (+ (+ x t) y) (cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))))
193.0ms
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))
193.0ms
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))
191.0ms
(cbrt (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify79.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05403102
126592684
250012406

prune390.0ms

Filtered
135 candidates to 85 candidates (63.0%)
Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.1b

regimes551.0ms

Accuracy

48.6% (11.4b remaining)

Error of 15.8b against oracle of 4.4b and baseline of 26.6b

bsearch94.0ms

Steps
ItersRangePoint
6
8.630656333678921e+31
4.2507803337288095e+32
4.19383588940517e+32
11
-3.709316971755835e+107
-1.5153488191706685e+85
-1.7867247441517144e+85

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03712
13712

end0.0ms

sample620.0ms

Algorithm
intervals
Results
349.0ms7998×body80valid
0.0ms1×body640valid
0.0ms1×body160valid