Details

Time bar (total: 5.2s)

sample77.0ms

Algorithm
intervals
Results
43.0ms97×body1280valid
12.0ms49×body640valid
5.0ms69×body80valid
5.0ms26×body320valid
2.0ms15×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2195
3205
4205

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
3.8b
(cos (+ a b))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×pow1
3×times-frac associate-*r* associate-*l* associate-/r* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 47
Calls
3 calls:
3.0ms
(* r (sin b))
4.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(cos (+ a b))

series156.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(* r (sin b))
95.0ms
(/ (* r (sin b)) (cos (+ a b)))
23.0ms
(cos (+ a b))

simplify32.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0198305
1861257
25001256

prune134.0ms

Filtered
56 candidates to 40 candidates (71.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

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))))

rewrite22.0ms

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))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cos a) (cos b))
36.0ms
(* r (sin b))
44.0ms
(* (sin a) (sin b))
206.0ms
(/ (* 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

prune266.0ms

Filtered
93 candidates to 65 candidates (69.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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 b) (cos a))
8.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
4.0ms
(* (sin a) (sin b))
24.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cos b) (cos a))
106.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
42.0ms
(* (sin a) (sin b))
207.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04281219
118401103
250021098

prune359.0ms

Filtered
117 candidates to 86 candidates (73.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos b) (cos a))
0.1b
(/ (sin b) (- (pow (* (cos b) (cos a)) 1) (* (sin a) (sin b))))
0.2b
(* (sin a) (sin b))
0.2b
(* r (/ (sin b) (- (pow (* (cos b) (cos a)) 1) (* (sin a) (sin b)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
21×associate-*r*
19×times-frac
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*l*
4×prod-exp associate-/r/ cbrt-unprod add-log-exp unswap-sqr
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp flip-- div-inv
1×frac-2neg associate-*r/ clear-num cos-mult sin-mult
Counts
4 → 101
Calls
4 calls:
3.0ms
(* (cos b) (cos a))
8.0ms
(/ (sin b) (- (pow (* (cos b) (cos a)) 1) (* (sin a) (sin b))))
4.0ms
(* (sin a) (sin b))
23.0ms
(* r (/ (sin b) (- (pow (* (cos b) (cos a)) 1) (* (sin a) (sin b)))))

series393.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (cos b) (cos a))
106.0ms
(/ (sin b) (- (pow (* (cos b) (cos a)) 1) (* (sin a) (sin b))))
44.0ms
(* (sin a) (sin b))
206.0ms
(* r (/ (sin b) (- (pow (* (cos b) (cos a)) 1) (* (sin a) (sin b)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04171241
118541097
250021088

prune347.0ms

Filtered
113 candidates to 86 candidates (76.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes141.0ms

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
01911
11911

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2933×body1280valid
479.0ms1863×body640valid
126.0ms711×body320valid
119.0ms2126×body80valid
47.0ms370×body160valid