Details

Time bar (total: 28.8s)

sample143.0ms

Algorithm
intervals
Results
59.0ms72×body1280valid
31.0ms50×body640valid
22.0ms191×body80valid
9.0ms24×body320valid
5.0ms18×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (/ (pow t 3.0) (* l l)) (sin k))
1.5b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.3b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
13.4b
(/ (pow t 3.0) (* l l))

rewrite399.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 152
Calls
4 calls:
24.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
54.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
307.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
246.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
324.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
629.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
249.0ms
(/ (pow t 3.0) (* l l))

simplify128.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08171679
147261405
250011405

prune542.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.3b

localize27.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
1.5b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
5.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.3b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite790.0ms

Algorithm
rewrite-expression-head
Rules
346×add-exp-log
203×prod-exp
97×div-exp
82×add-cbrt-cube
55×associate-*l/
46×cbrt-unprod
41×pow-exp
35×frac-times
32×pow1
28×pow-to-exp
22×*-un-lft-identity
19×pow-prod-down
17×add-sqr-sqrt add-cube-cbrt
16×tan-quot
15×times-frac associate-*r/
13×cbrt-undiv
11×associate-*r*
8×flip3-+ flip-+
5×associate-/l*
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp sqr-pow
3×associate-*l* associate-/r* *-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv
Counts
4 → 212
Calls
4 calls:
33.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
118.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
4.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
622.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
297.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
366.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
199.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
740.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify60.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011963855
150013336

prune764.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
1.5b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k))
1.5b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
13.3b
(* (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite5.7s

Algorithm
rewrite-expression-head
Rules
4197×add-exp-log
2674×prod-exp
1326×div-exp
595×pow-exp
367×pow-to-exp
257×add-cbrt-cube
184×cbrt-unprod
151×associate-*l/
103×frac-times
63×cbrt-undiv
48×pow1
33×associate-*r/
32×tan-quot
31×pow-prod-down
16×flip3-+ flip-+
15×*-un-lft-identity
11×associate-*r*
10×add-sqr-sqrt add-cube-cbrt
6×unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod pow-unpow associate-*l* *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 sqr-pow
Counts
4 → 756
Calls
4 calls:
2.0ms
(pow (cbrt t) 3.0)
267.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k))
1.0s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
4.2s
(* (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
309.0ms
(pow (cbrt t) 3.0)
301.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k))
378.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
730.0ms
(* (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify217.0ms

Algorithm
egg-herbie
Counts
768 → 768
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0301622150
1500219198

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt l)
1.5b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k))
1.5b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
13.3b
(* (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite5.5s

Algorithm
rewrite-expression-head
Rules
4196×add-exp-log
2674×prod-exp
1326×div-exp
594×pow-exp
366×pow-to-exp
257×add-cbrt-cube
184×cbrt-unprod
151×associate-*l/
103×frac-times
63×cbrt-undiv
47×pow1
33×associate-*r/
32×tan-quot
31×pow-prod-down
16×flip3-+ flip-+
13×*-un-lft-identity
11×associate-*r*
8×add-sqr-sqrt add-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod associate-*l* *-commutative distribute-lft-out
1×distribute-rgt-in distribute-lft-in pow1/3
Counts
4 → 746
Calls
4 calls:
1.0ms
(cbrt l)
261.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k))
1.0s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
4.1s
(* (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt l)
392.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k))
467.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
854.0ms
(* (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify220.0ms

Algorithm
egg-herbie
Counts
758 → 758
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0297422092
1500119139

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.5b

regimes560.0ms

Accuracy

14.4% (8.2b remaining)

Error of 19.0b against oracle of 10.8b and baseline of 20.3b

bsearch272.0ms

Steps
ItersRangePoint
8
2.708850627677037e-70
1.4811620171990793e-66
1.7521304492670182e-68
6
-1.4905492691670075e-134
-3.575975670356488e-135
-7.390687618428382e-135

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07974
17974

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2030×body1280valid
931.0ms1684×body640valid
680.0ms6020×body80valid
318.0ms851×body320valid
121.0ms427×body160valid