Details

Time bar (total: 12.9s)

sample327.0ms

Algorithm
intervals
Results
230.0ms161×body1280valid
48.0ms61×body640valid
13.0ms3×body2560valid
10.0ms17×body320valid
4.0ms12×body160valid
0.0ms2×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02712
13912
24412
34512
44512

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.0b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.3b
(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log cos-sum add-cbrt-cube
9×prod-diff
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×*-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 74
Calls
4 calls:
12.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms
(cos (- lambda1 lambda2))

series167.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms
(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03881113
11250911
25001909

prune356.0ms

Filtered
86 candidates to 59 candidates (68.6%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New701686
Fresh000
Picked101
Done000
Total711687

Merged error: 4.1b

Counts
87 → 16

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b
(* (sin lambda1) (sin lambda2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
6×cos-mult
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add flip-+ unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/
Counts
4 → 80
Calls
4 calls:
10.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series325.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
46.0ms
(* (sin lambda1) (sin lambda2))
67.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04941387
122481185
250021184

prune457.0ms

Filtered
92 candidates to 65 candidates (70.7%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New771592
Fresh12315
Picked101
Done000
Total9018108

Merged error: 4.0b

Counts
108 → 18

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.7b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 66
Calls
4 calls:
5.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
3.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series143.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
42.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
18.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify122.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 4 (42.0ms)

IterNodesCost
01931705
14381457
210561453
314691453
437541449
550011449

prune488.0ms

Filtered
78 candidates to 55 candidates (70.5%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New72678
Fresh71017
Picked101
Done000
Total801696

Merged error: 3.9b

Counts
96 → 16

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b
(expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.5b
(log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.3b
(acos (+ (* (sin phi1) (sin phi2)) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×acos-asin log1p-udef expm1-log1p log1p-expm1 pow-prod-down prod-exp *-commutative cbrt-unprod expm1-udef unswap-sqr
Counts
4 → 52
Calls
4 calls:
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms
(expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
1.0ms
(log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series689.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
327.0ms
(expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
287.0ms
(log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
14.0ms
(acos (+ (* (sin phi1) (sin phi2)) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
02261274
17021089
227501077
350011071

prune303.0ms

Filtered
64 candidates to 50 candidates (78.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New62264
Fresh21315
Picked101
Done000
Total651580

Merged error: 3.8b

Counts
80 → 15

regimes998.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03118
13118

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.9s4783×body1280valid
1.5s2111×body640valid
322.0ms707×body320valid
89.0ms276×body160valid
22.0ms6×body2560valid
20.0ms120×body80valid

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