Details

Time bar (total: 5.7s)

sample314.0ms

Algorithm
intervals
Results
40.0ms97×body1280valid
12.0ms49×body640valid
6.0ms69×body80valid
4.0ms26×body320valid
2.0ms15×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2205
3215
4215

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

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)))
3.8b
(cos (+ a b))

rewrite36.0ms

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))

series155.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(* r (/ (sin b) (cos (+ a b))))
37.0ms
(/ (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

prune202.0ms

Filtered
76 candidates to 57 candidates (75.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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))
8.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms
(* (sin a) (sin b))
25.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series412.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (cos a) (cos b))
111.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms
(* (sin a) (sin b))
216.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify55.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04281219
118581103
250011098

prune377.0ms

Filtered
117 candidates to 87 candidates (74.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
4×prod-exp associate-/r/ cbrt-unprod add-log-exp
3×times-frac pow-prod-down associate-/r* cos-mult *-commutative sin-mult unswap-sqr
2×cbrt-undiv div-exp
1×flip3-- frac-2neg clear-num frac-sub flip-- div-inv associate-/l* sub-div
Counts
4 → 81
Calls
4 calls:
4.0ms
(* (cos a) (cos b))
3.0ms
(* r (sin b))
4.0ms
(* (sin a) (sin b))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series340.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cos a) (cos b))
37.0ms
(* r (sin b))
46.0ms
(* (sin a) (sin b))
215.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify46.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0367682
11616594
25001593

prune277.0ms

Filtered
93 candidates to 64 candidates (68.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin a) (sin b))
0.2b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.3b
(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
32×add-sqr-sqrt
24×*-un-lft-identity
23×add-cube-cbrt
22×add-cbrt-cube
21×associate-*r*
20×times-frac
14×pow1 prod-exp
9×associate-*l*
8×associate-/r/ cbrt-unprod
6×div-exp
5×pow-prod-down sin-mult
4×associate-*r/ cos-mult add-log-exp unswap-sqr
3×cbrt-undiv rec-exp 1-exp associate-/r* *-commutative associate-/l*
2×flip3-- un-div-inv frac-sub flip-- div-inv sub-div
1×pow-flip frac-2neg clear-num inv-pow
Counts
4 → 118
Calls
4 calls:
4.0ms
(* (sin a) (sin b))
10.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms
(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
26.0ms
(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin a) (sin b))
95.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
210.0ms
(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
113.0ms
(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04581487
120121272
250011240

prune337.0ms

Filtered
130 candidates to 83 candidates (63.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes142.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02011
12011

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s2933×body1280valid
472.0ms1863×body640valid
133.0ms711×body320valid
121.0ms2126×body80valid
52.0ms370×body160valid