Details

Time bar (total: 8.5s)

sample42.0ms

Algorithm
intervals
Results
11.0ms222×body80valid
3.0ms17×body640valid
3.0ms10×body1280valid
2.0ms12×body320valid
1.0ms9×body160valid

simplify120.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0226
1526
21096
31956
44456
58286
614346
725206
848306
950016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- z t) y)
2.1b
(- (+ x y) (/ (* (- z t) y) (- a t)))
10.5b
(/ (* (- z t) y) (- a t))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
17×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
5×pow1 times-frac associate-*l* associate-/r* distribute-lft-out--
4×flip3-- associate-*l/ flip-- difference-of-squares
3×associate-*r*
2×cbrt-undiv diff-log div-exp prod-exp associate-/r/ frac-sub cbrt-unprod associate-/l/
1×sub-neg frac-2neg flip3-+ pow-prod-down associate--l+ clear-num sum-log *-commutative flip-+ div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
3 → 70
Calls
3 calls:
22.0ms
(* (- z t) y)
46.0ms
(- (+ x y) (/ (* (- z t) y) (- a t)))
25.0ms
(/ (* (- z t) y) (- a t))

series214.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* (- z t) y)
119.0ms
(- (+ x y) (/ (* (- z t) y) (- a t)))
66.0ms
(/ (* (- z t) y) (- a t))

simplify44.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0383461
11704422
25001422

prune185.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a t))
0.5b
(cbrt (- a t))
4.0b
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
8.5b
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
36×times-frac
35×*-un-lft-identity
30×associate-*r*
27×cbrt-prod
25×add-exp-log
23×add-cube-cbrt
18×cbrt-div add-cbrt-cube
17×associate-*l*
10×flip3-- associate-/r/ flip--
9×add-log-exp
8×prod-exp cbrt-unprod
7×cbrt-undiv frac-times div-exp
6×pow1 frac-sub distribute-lft-out-- difference-of-squares unswap-sqr
5×associate-*r/ associate-*l/
3×flip3-+ flip-+
2×pow1/3 diff-log div-inv
1×sub-neg pow-prod-down associate--l+ sum-log *-commutative
Counts
4 → 127
Calls
4 calls:
4.0ms
(cbrt (- a t))
5.0ms
(cbrt (- a t))
110.0ms
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
38.0ms
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series521.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(cbrt (- a t))
149.0ms
(cbrt (- a t))
104.0ms
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
123.0ms
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify93.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07851736
133211577
250021498

prune450.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (- z t)) (cbrt (- z t)))
0.8b
(* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))
2.7b
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
4.3b
(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
145×cbrt-prod
118×times-frac
117×*-un-lft-identity
92×associate-*l*
87×add-exp-log
63×add-cube-cbrt
41×add-cbrt-cube
39×associate-*r*
37×prod-exp cbrt-unprod
26×cbrt-undiv div-exp distribute-lft-out--
24×difference-of-squares
20×frac-times
19×unswap-sqr
18×pow1 cbrt-div associate-*r/
14×frac-sub
12×associate-*l/
10×flip3-- swap-sqr flip--
9×add-log-exp
7×flip3-+ flip-+
6×pow1/3 pow-prod-down associate-/r/
3×*-commutative div-inv
2×diff-log pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus associate--l+ sum-log
Counts
4 → 281
Calls
4 calls:
38.0ms
(* (cbrt (- z t)) (cbrt (- z t)))
100.0ms
(* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))
137.0ms
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
41.0ms
(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (cbrt (- z t)) (cbrt (- z t)))
954.0ms
(* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))
108.0ms
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
126.0ms
(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013264414
150023941

prune970.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (- z t)) (cbrt (- z t)))
0.8b
(* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))
2.7b
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
6.3b
(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite300.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
145×cbrt-prod
118×times-frac
117×*-un-lft-identity
92×associate-*l*
87×add-exp-log
63×add-cube-cbrt
41×add-cbrt-cube
39×associate-*r*
37×prod-exp cbrt-unprod
26×cbrt-undiv div-exp distribute-lft-out--
24×difference-of-squares
19×unswap-sqr
18×pow1 cbrt-div
10×frac-times flip3-- swap-sqr flip--
8×associate-*r/
6×pow1/3 pow-prod-down associate-*l/ associate-/r/ add-log-exp
3×*-commutative div-inv
2×pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus diff-log
Counts
4 → 265
Calls
4 calls:
39.0ms
(* (cbrt (- z t)) (cbrt (- z t)))
101.0ms
(* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))
139.0ms
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
6.0ms
(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (cbrt (- z t)) (cbrt (- z t)))
965.0ms
(* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))
104.0ms
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
96.0ms
(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify135.0ms

Algorithm
egg-herbie
Counts
277 → 277
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
011513892
148173409
250013345

prune901.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

regimes309.0ms

Accuracy

2.2% (5.8b remaining)

Error of 9.6b against oracle of 3.8b and baseline of 9.7b

bsearch137.0ms

Steps
ItersRangePoint
9
1.7964146690187605e+287
7.622338402653847e+293
5.370291603550818e+292
8
8.900017451179621e+70
3.4929478218740653e+74
1.8787267324606136e+72
9
-9.752755935853076e+170
-8.57772193482959e+165
-1.0282233832462932e+170

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
04262
14531
24831
34831

end0.0ms

sample707.0ms

Algorithm
intervals
Results
228.0ms7337×body80valid
52.0ms452×body640valid
38.0ms246×body1280valid
34.0ms422×body320valid
14.0ms250×body160valid
1.0ms9×body2560valid