Details

Time bar (total: 8.5s)

sample24.0ms

Algorithm
intervals
Results
8.0ms240×body80valid
1.0ms16×body320valid
1.0ms8×body1280valid
1.0ms10×body640valid
1.0ms10×body160valid

simplify119.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 16.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- z t) y)
3.5b
(- (+ x y) (/ (* (- z t) y) (- a t)))
10.3b
(/ (* (- z t) y) (- a t))

rewrite45.0ms

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:
10.0ms
(* (- z t) y)
24.0ms
(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms
(/ (* (- z t) y) (- a t))

series198.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(* (- z t) y)
107.0ms
(- (+ x y) (/ (* (- z t) y) (- a t)))
62.0ms
(/ (* (- z t) y) (- a t))

simplify49.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0383461
11704422
25001422

prune194.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a t))
0.5b
(* (cbrt (- a t)) (cbrt (- a t)))
3.9b
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.9b
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
54×*-un-lft-identity
50×cbrt-prod
38×associate-*r*
36×times-frac
30×add-cube-cbrt
28×cbrt-div
27×add-exp-log
25×associate-*l*
18×add-cbrt-cube
15×flip3-- flip--
13×pow1
11×frac-times distribute-lft-out--
10×swap-sqr associate-/r/ unswap-sqr
9×prod-exp cbrt-unprod add-log-exp difference-of-squares
7×cbrt-undiv pow1/3 associate-*r/ div-exp associate-*l/
6×frac-sub
3×flip3-+ pow-prod-down flip-+
2×diff-log pow-sqr *-commutative pow-prod-up div-inv
1×pow2 sub-neg pow-plus associate--l+ sum-log
Counts
4 → 168
Calls
4 calls:
2.0ms
(cbrt (- a t))
19.0ms
(* (cbrt (- a t)) (cbrt (- a t)))
62.0ms
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
18.0ms
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(cbrt (- a t))
118.0ms
(* (cbrt (- a t)) (cbrt (- a t)))
97.0ms
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
111.0ms
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify124.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
08862068
143261890
250011779

prune557.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
0.5b
(cbrt (cbrt (- a t)))
3.9b
(* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))
8.4b
(- (+ x y) (* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
368×cbrt-div
143×frac-times
117×flip3-- flip--
89×associate-*l*
82×associate-/r/
55×associate-*l/
49×associate-*r/
41×add-sqr-sqrt
36×add-exp-log
33×*-un-lft-identity
31×times-frac
30×cbrt-prod associate-*r*
24×add-cbrt-cube
23×add-cube-cbrt
14×prod-exp cbrt-unprod
10×cbrt-undiv div-exp
9×add-log-exp
6×pow1 frac-sub
5×distribute-lft-out-- difference-of-squares
3×flip3-+ flip-+ unswap-sqr
2×pow1/3 diff-log div-inv
1×sub-neg pow-prod-down associate--l+ sum-log *-commutative
Counts
4 → 205
Calls
4 calls:
7.0ms
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
3.0ms
(cbrt (cbrt (- a t)))
225.0ms
(* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))
18.0ms
(- (+ x y) (* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))

series494.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
143.0ms
(cbrt (cbrt (- a t)))
103.0ms
(* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))
117.0ms
(- (+ x y) (* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013014152
150013877

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cbrt (- a t)))
0.8b
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t)))))
2.5b
(* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.4b
(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t))))))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
221×cbrt-prod
189×add-sqr-sqrt
146×add-exp-log
145×times-frac
125×associate-*l*
115×*-un-lft-identity
88×cbrt-div
70×add-cbrt-cube
69×add-cube-cbrt prod-exp cbrt-unprod
44×cbrt-undiv frac-times div-exp
31×flip3-- associate-*r* flip--
30×associate-*r/ associate-/r/
23×distribute-lft-out-- difference-of-squares
21×unswap-sqr
18×associate-*l/
14×frac-sub
11×pow1
9×add-log-exp
7×flip3-+ flip-+
4×pow-prod-down
3×div-inv
2×diff-log *-commutative
1×sub-neg pow1/3 associate--l+ sum-log
Counts
4 → 310
Calls
4 calls:
2.0ms
(cbrt (cbrt (- a t)))
127.0ms
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t)))))
85.0ms
(* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t))))
23.0ms
(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
152.0ms
(cbrt (cbrt (- a t)))
102.0ms
(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t)))))
1.2s
(* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t))))
120.0ms
(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (/ y (cbrt (- a t))))))

simplify87.0ms

Algorithm
egg-herbie
Counts
322 → 322
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
016496889
150016086

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.2b

regimes322.0ms

Accuracy

4.7% (6.6b remaining)

Error of 10.3b against oracle of 3.7b and baseline of 10.7b

bsearch93.0ms

Steps
ItersRangePoint
8
7.104008511116258e+116
1.1379081657348373e+120
2.2171165764838755e+119
8
-1.6810197668152094e+105
-1.756824163423226e+101
-1.2963627054695715e+105

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04031
14031

end0.0ms

sample653.0ms

Algorithm
intervals
Results
249.0ms7376×body80valid
56.0ms464×body640valid
36.0ms241×body1280valid
34.0ms373×body320valid
18.0ms240×body160valid
4.0ms19×body2560valid