Details

Time bar (total: 11.3s)

sample319.0ms

Algorithm
intervals
Results
210.0ms157×body1280valid
48.0ms63×body640valid
7.0ms14×body320valid
2.0ms17×body80valid
2.0ms5×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02715
14615
27115
37715
47715

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.5b

Counts
2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.2b
(sin (- lambda1 lambda2))
4.3b
(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×sub-neg cos-sum sin-sum *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 60
Calls
4 calls:
7.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
6.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series44.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
22.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

simplify103.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0260456
11016389
24756389
35001389

prune168.0ms

Filtered
72 candidates to 51 candidates (29.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New581472
Fresh000
Picked101
Done000
Total591473

Merged error: 7.6b

Counts
73 → 14

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.2b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.3b
(cos (- lambda1 lambda2))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×cos-diff associate-*l/
2×sub-neg cos-sum flip3-- *-commutative flip--
1×distribute-rgt-in distribute-lft-in diff-log sin-cos-mult unswap-sqr
Counts
4 → 63
Calls
4 calls:
5.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
7.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))

series75.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
32.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
23.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0314708
11308611
25001611

prune148.0ms

Filtered
75 candidates to 52 candidates (30.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New70575
Fresh7613
Picked101
Done000
Total781189

Merged error: 0.1b

Counts
89 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×associate-*l/ *-commutative sin-cos-mult add-log-exp
3×sin-mult
2×frac-times associate-*r/ cos-mult unswap-sqr
1×flip3-- flip--
Counts
4 → 89
Calls
4 calls:
8.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
8.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
5.0ms
(* (sin lambda1) (sin lambda2))
8.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series95.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
31.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
9.0ms
(* (sin lambda1) (sin lambda2))
26.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify59.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0433949
12002747
25001747

prune154.0ms

Filtered
101 candidates to 59 candidates (41.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New974101
Fresh3710
Picked101
Done000
Total10111112

Merged error: 0.1b

Counts
112 → 11

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
0.6b
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
0.6b
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
0.6b
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-div
22×cos-mult sin-cos-mult
20×frac-times
14×associate-*r/ associate-*l/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 82
Calls
4 calls:
10.0ms
(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
6.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
6.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
8.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

series255.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
56.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
56.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
54.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

simplify44.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02811381
110301225
250011147

prune116.0ms

Filtered
94 candidates to 66 candidates (29.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New92294
Fresh1910
Picked101
Done000
Total9411105

Merged error: 0.1b

Counts
105 → 11

regimes602.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04241
14241

end0.0ms

sample8.8s

Algorithm
intervals
Results
6.4s4705×body1280valid
1.6s1945×body640valid
269.0ms539×body320valid
100.0ms608×body80valid
64.0ms203×body160valid

Profiling

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