Details

Time bar (total: 12.0s)

sample3.9s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 23.254395%

Results
171.0ms73×body80valid
41.0ms89×body1280valid
15.0ms54×body640valid
5.0ms24×body320valid
2.0ms16×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2205
3215
4215

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.9b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.3b
(/ (sin b) (cos (+ a b)))
2.6b
(cos (+ a b))

rewrite17.0ms

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:
7.0ms
(* r (/ (sin b) (cos (+ a b))))
4.0ms
(/ (sin b) (cos (+ a b)))
4.0ms
(cos (+ a b))

series47.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* r (/ (sin b) (cos (+ a b))))
12.0ms
(/ (sin b) (cos (+ a b)))
6.0ms
(cos (+ a b))

simplify36.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0252536
11064480
25001477

prune123.0ms

Filtered
57 candidates to 76 candidates (-33.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New661076
Fresh000
Picked101
Done000
Total671077

Merged error: 0.2b

Counts
77 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos a) (cos 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))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
23×associate-*r*
19×times-frac
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×prod-exp cbrt-unprod add-log-exp unswap-sqr
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub flip-- div-inv sub-div
1×frac-2neg associate-*r/ clear-num
Counts
4 → 105
Calls
4 calls:
4.0ms
(* (cos a) (cos b))
5.0ms
(* (sin a) (sin b))
11.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series101.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (cos a) (cos b))
9.0ms
(* (sin a) (sin b))
52.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
31.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04281219
118581102
250021098

prune181.0ms

Filtered
87 candidates to 117 candidates (-34.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10611117
Fresh909
Picked101
Done000
Total11611127

Merged error: 0.0b

Counts
127 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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×cos-mult sin-mult
4×associate-/r/
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 → 77
Calls
4 calls:
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms
(* (cos a) (cos b))
4.0ms
(* (sin a) (sin b))
8.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series87.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(* (cos a) (cos b))
10.0ms
(* (sin a) (sin b))
52.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify43.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0371798
11534703
25002693

prune129.0ms

Filtered
63 candidates to 89 candidates (-41.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New86389
Fresh3710
Picked011
Done000
Total8911100

Merged error: 0b

Counts
100 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
82×pow1
55×times-frac
42×add-exp-log add-cbrt-cube
34×pow-prod-down
29×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
25×cos-mult sin-mult
22×associate-/r*
18×prod-exp cbrt-unprod
16×associate-/l/
12×associate-*r/ associate-*l/
10×frac-times associate-/r/ difference-of-squares
9×frac-sub
8×pow-sqr pow-prod-up
7×cbrt-undiv div-exp
5×associate-/l* sub-div
4×pow-plus div-inv add-log-exp
3×flip3-+ frac-add flip-+
2×pow2 frac-2neg swap-sqr associate-*r* associate-*l* clear-num *-commutative
1×flip3-- div-sub flip--
Counts
4 → 183
Calls
4 calls:
9.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
15.0ms
(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
19.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
119.0ms
(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
61.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify52.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08403973
150013371

prune197.0ms

Filtered
128 candidates to 195 candidates (-52.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1950195
Fresh099
Picked011
Done011
Total19511206

Merged error: 0b

Counts
206 → 11

regimes273.0ms

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

sample6.3s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 23.254395%

Results
1.4s2910×body1280valid
543.0ms1849×body640valid
148.0ms729×body320valid
145.0ms2165×body80valid
53.0ms347×body160valid
0.0ms1×body640invalid

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