Details

Time bar (total: 4.7s)

sample41.0ms

Algorithm
intervals
Results
15.0ms248×body80valid
5.0ms16×body320valid
4.0ms15×body640valid
2.0ms8×body1280valid
1.0ms8×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0236
1465
21285
33625
410245
522965
650015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
15.1b
(fma (- y z) (/ (- t x) (- a z)) x)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
12.0ms
(/ (- t x) (- a z))
0.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

series142.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(/ (- t x) (- a z))
89.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

simplify56.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0268450
1733425
22490423
35001421

prune206.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a z))
0.2b
(* (- t x) (/ 1 (- a z)))
15.1b
(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×*-un-lft-identity
32×times-frac
23×add-cube-cbrt
21×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-*l* associate-/r*
4×flip3-- div-exp prod-exp associate-/r/ flip--
3×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative fma-udef inv-pow
Counts
3 → 105
Calls
3 calls:
6.0ms
(/ 1 (- a z))
27.0ms
(* (- t x) (/ 1 (- a z)))
0.0ms
(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series178.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(/ 1 (- a z))
49.0ms
(* (- t x) (/ 1 (- a z)))
91.0ms
(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify40.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0350602
11497525
25001481

prune283.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.4b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.3b
(* (- y z) (/ (- t x) (- a z)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
74×*-un-lft-identity
51×times-frac
31×associate-*r*
28×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
3×expm1-log1p-u fma-def log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 128
Calls
3 calls:
12.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
34.0ms
(* (- y z) (/ (- t x) (- a z)))

series330.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ (- t x) (- a z))
152.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
128.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify59.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0488901
12066849
25001847

prune357.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
1.1b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
9.0b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
18×add-sqr-sqrt
16×cbrt-div
15×*-un-lft-identity
14×add-cbrt-cube
13×associate-*r*
10×cbrt-prod flip3-- flip--
9×add-cube-cbrt prod-exp cbrt-unprod
8×associate-/r/
6×pow1 frac-times add-log-exp
5×associate-*l*
4×cbrt-undiv expm1-log1p-u div-exp associate-*l/ log1p-expm1-u
3×fma-def associate-*r/ distribute-lft-out-- difference-of-squares
2×times-frac pow1/3 unswap-sqr
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
2.0ms
(cbrt (- t x))
2.0ms
(cbrt (- t x))
57.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series724.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (- t x))
144.0ms
(cbrt (- t x))
277.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
154.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify73.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07041444
127441230
250011149

prune397.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

regimes288.0ms

Accuracy

25.8% (6.8b remaining)

Error of 10.4b against oracle of 3.6b and baseline of 12.8b

bsearch81.0ms

Steps
ItersRangePoint
7
3.0056805004922944e+190
1.625455215461017e+192
9.100194368894704e+191
4
-3.542713222812643e+246
-2.135390510436753e+246
-3.216598382673023e+246

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03428
13428

end0.0ms

sample1.1s

Algorithm
intervals
Results
510.0ms7827×body80valid
116.0ms462×body640valid
89.0ms292×body1280valid
78.0ms428×body320valid
32.0ms265×body160valid
7.0ms20×body2560valid