Details

Time bar (total: 5.9s)

sample337.0ms

Algorithm
intervals
Results
42.0ms101×body1280valid
17.0ms58×body640valid
4.0ms64×body80valid
3.0ms19×body320valid
2.0ms14×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2205
3215
4215

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
4.3b
(cos (+ a b))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*r*
10×add-exp-log add-cbrt-cube
5×pow1
3×associate-*l* associate-/r* associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
3 → 67
Calls
3 calls:
27.0ms
(* r (/ (sin b) (cos (+ a b))))
10.0ms
(/ (sin b) (cos (+ a b)))
12.0ms
(cos (+ a b))

series145.0ms

Counts
3 → 9
Calls
3 calls:
88.0ms
(* r (/ (sin b) (cos (+ a b))))
35.0ms
(/ (sin b) (cos (+ a b)))
23.0ms
(cos (+ a b))

simplify39.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0252536
11064480
25001477

prune190.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.3b
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×associate-*r*
19×times-frac
13×add-exp-log add-cbrt-cube
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
3×flip3-- prod-exp associate-/r* frac-sub flip-- cbrt-unprod associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×sub-neg frac-2neg diff-log associate-*r/ clear-num
Counts
4 → 100
Calls
4 calls:
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms
(* (sin a) (sin b))
73.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
25.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series416.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms
(* (sin a) (sin b))
194.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
103.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04051308
117611183
250011173

prune365.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* r (sin b))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.3b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×sub-neg frac-2neg diff-log clear-num div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
9.0ms
(* r (sin b))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms
(* (sin a) (sin b))
30.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* r (sin b))
74.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
40.0ms
(* (sin a) (sin b))
196.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify45.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0344770
11513673
25001663

prune276.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin a) (sin b))
0.2b
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
35×pow-prod-down
32×add-exp-log add-cbrt-cube
23×sin-mult
22×cos-mult
17×add-sqr-sqrt prod-exp cbrt-unprod
16×associate-/r/
15×add-cube-cbrt *-un-lft-identity
12×times-frac associate-*r/ associate-*l/
10×frac-times
9×frac-sub
8×pow-sqr pow-prod-up
5×associate-*r* associate-*l* sub-div
4×pow-plus associate-/r* add-log-exp difference-of-squares
3×*-commutative associate-/l*
2×pow2 swap-sqr
1×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv unswap-sqr
Counts
4 → 140
Calls
4 calls:
11.0ms
(* (sin a) (sin b))
100.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
45.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
42.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin a) (sin b))
135.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
46.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
51.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify77.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05571772
126341538
250011516

prune385.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02626
12926
22926

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s2926×body1280valid
465.0ms1822×body640valid
131.0ms765×body320valid
115.0ms2145×body80valid
43.0ms345×body160valid