Details

Time bar (total: 14.5s)

sample281.0ms

Algorithm
intervals
Results
201.0ms148×body1280valid
47.0ms63×body640valid
12.0ms18×body320valid
3.0ms20×body80valid
2.0ms7×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02815
14815
27915
39415
49415

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b
(sin (- lambda1 lambda2))
4.2b
(cos (- lambda1 lambda2))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×prod-diff
11×pow1 add-exp-log cos-sum sin-sum add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cos-diff
2×sub-neg *-commutative
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff sin-cos-mult unswap-sqr
Counts
4 → 85
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
12.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(sin (- lambda1 lambda2))
7.0ms
(cos (- lambda1 lambda2))

series171.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cos phi1) (sin phi2))
88.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04431004
11340773
25001771

prune415.0ms

Filtered
97 candidates to 62 candidates (63.9%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (cos lambda1) (sin (- lambda2)))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.2b
(cos (- lambda1 lambda2))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×pow1 add-exp-log add-cbrt-cube
11×cos-sum
9×associate-*r* prod-diff
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-diff *-commutative
2×unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in associate-*l/ sin-neg distribute-rgt-neg-out sin-cos-mult
Counts
4 → 85
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
5.0ms
(* (cos lambda1) (sin (- lambda2)))
12.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(cos (- lambda1 lambda2))

series205.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos phi1) (sin phi2))
52.0ms
(* (cos lambda1) (sin (- lambda2)))
93.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms
(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0461812
11657651
25001650

prune546.0ms

Filtered
97 candidates to 68 candidates (70.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (cos lambda1) (sin (- lambda2)))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.2b
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-exp-log add-cbrt-cube
12×associate-*r*
11×add-cube-cbrt *-un-lft-identity
10×associate-*l*
6×pow-prod-down prod-exp cbrt-unprod
5×sin-cos-mult sin-mult
4×expm1-log1p-u frac-times associate-*r/ cos-mult *-commutative log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in unswap-sqr
2×sub-neg flip3-- prod-diff sin-neg distribute-rgt-neg-out frac-sub flip-- sub-div
1×associate-*l/
Counts
4 → 98
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
6.0ms
(* (cos lambda1) (sin (- lambda2)))
6.0ms
(* (sin lambda1) (sin (- lambda2)))
26.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos phi1) (sin phi2))
48.0ms
(* (cos lambda1) (sin (- lambda2)))
54.0ms
(* (sin lambda1) (sin (- lambda2)))
180.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify77.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05421050
12412918
25002917

prune673.0ms

Filtered
110 candidates to 83 candidates (75.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.3b
(/ (* (* (sin phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.4b
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b
(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
71×cos-mult
60×frac-add
59×sin-mult
49×pow1
35×associate-/r/
34×frac-times associate-*r/
31×add-exp-log associate-*l/ add-cbrt-cube
19×pow-prod-down
13×prod-exp cbrt-unprod
10×cube-div
9×associate-/l/
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-unpow
5×sin-cos-mult
4×expm1-log1p-u pow-pow flip3-+ pow-exp pow-sqr pow-prod-up flip-+ log1p-expm1-u add-log-exp rem-cube-cbrt
3×cbrt-undiv times-frac div-exp associate-/r*
2×cube-mult pow-to-exp unpow-prod-down flip3-- pow-plus unpow3 cube-prod frac-sub flip-- sub-div sqr-pow
1×pow2 frac-2neg swap-sqr associate-*r* associate-*l* cube-neg sin-neg clear-num *-commutative distribute-rgt-neg-out div-inv associate-/l*
Counts
4 → 159
Calls
4 calls:
4.0ms
(pow (* (sin lambda1) (sin (- lambda2))) 3)
150.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
13.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms
(pow (* (cos lambda1) (cos lambda2)) 3)

series986.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(pow (* (sin lambda1) (sin (- lambda2))) 3)
783.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
52.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
65.0ms
(pow (* (cos lambda1) (cos lambda2)) 3)

simplify63.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
013694349
150014080

prune1.1s

Filtered
171 candidates to 103 candidates (60.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes463.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06751
18751
28851
38851

end0.0ms

sample8.7s

Algorithm
intervals
Results
6.4s4576×body1280valid
1.5s1968×body640valid
299.0ms587×body320valid
92.0ms672×body80valid
58.0ms197×body160valid