Details

Time bar (total: 6.5s)

sample327.0ms

Algorithm
intervals
Results
39.0ms96×body1280valid
16.0ms59×body640valid
5.0ms26×body320valid
3.0ms62×body80valid
2.0ms13×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2205
3215
4215

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
3.8b
(cos (+ a b))

rewrite22.0ms

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:
9.0ms
(* r (/ (sin b) (cos (+ a b))))
3.0ms
(/ (sin b) (cos (+ a b)))
7.0ms
(cos (+ a b))

series166.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(* r (/ (sin b) (cos (+ a b))))
37.0ms
(/ (sin b) (cos (+ a b)))
33.0ms
(cos (+ a b))

simplify40.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0252536
11064480
25001477

prune198.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms
(* (sin a) (sin b))
9.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
214.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
44.0ms
(* (sin a) (sin b))
112.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify57.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04051307
117611182
250011173

prune368.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×associate-*l*
19×times-frac
13×add-exp-log add-cbrt-cube
8×pow1 associate-/r/
7×sin-mult
6×associate-*r* 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-*l/ clear-num
Counts
4 → 100
Calls
4 calls:
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
27.0ms
(* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) r)
4.0ms
(* (sin a) (sin b))
9.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
251.0ms
(* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) r)
43.0ms
(* (sin a) (sin b))
111.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04051278
115531153
250011140

prune366.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (sin a) (sin b)) (+ (* (sin a) (sin b)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
0.3b
(pow (* (sin a) (sin b)) 3)
0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.6b
(pow (* (cos a) (cos b)) 3)

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
49×pow1
41×cos-mult
36×add-sqr-sqrt
28×*-un-lft-identity
27×times-frac frac-add
24×add-exp-log add-cbrt-cube
23×associate-/r/
21×sin-mult
20×add-cube-cbrt
19×pow-prod-down
18×sqr-pow
17×frac-times associate-*r/
16×difference-of-squares
11×associate-*l/
10×prod-exp cbrt-unprod
9×associate-/l*
7×flip3-+ flip-+
6×cube-div pow-unpow
4×difference-cubes pow-pow pow-exp pow-sqr pow-prod-up associate-/l/ distribute-lft-out-- add-log-exp rem-cube-cbrt
3×associate-/r*
2×cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod
1×cbrt-undiv pow2 flip3-- frac-2neg div-sub swap-sqr div-exp associate-*r* associate-*l* clear-num *-commutative frac-sub flip-- div-inv sub-div
Counts
4 → 162
Calls
4 calls:
53.0ms
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (sin a) (sin b)) (+ (* (sin a) (sin b)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
3.0ms
(pow (* (sin a) (sin b)) 3)
13.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
3.0ms
(pow (* (cos a) (cos b)) 3)

series536.0ms

Counts
4 → 12
Calls
4 calls:
357.0ms
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (sin a) (sin b)) (+ (* (sin a) (sin b)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
65.0ms
(pow (* (sin a) (sin b)) 3)
52.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
61.0ms
(pow (* (cos a) (cos b)) 3)

simplify55.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010524208
150014047

prune667.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes197.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01510
11510

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2903×body1280valid
465.0ms1898×body640valid
131.0ms777×body320valid
118.0ms2089×body80valid
41.0ms336×body160valid