Details

Time bar (total: 3.7m)

sample245.0ms

Algorithm
intervals
Results
85.0ms75×body1280valid
44.0ms63×body640valid
41.0ms256×body80valid
19.0ms39×body320valid
6.0ms19×body160valid

simplify126.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
126.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
32×add-cbrt-cube add-exp-log
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 180
Calls
4 calls:
Slowest
42.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
29.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series476.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
143.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
94.0ms
(/ (cos th) (sqrt 2))
91.0ms
(/ (cos th) (sqrt 2))

simplify9.0s

Counts
180 → 192
Calls
180 calls:
Slowest
722.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
696.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
572.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
563.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
542.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.4b
(/ (sqrt 2) a1)
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.2b
(/ (* (cos th) a1) (/ (sqrt 2) a1))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
78×add-sqr-sqrt
73×*-un-lft-identity add-cube-cbrt
52×sqrt-prod
32×add-cbrt-cube add-exp-log
31×associate-/r*
22×associate-*l*
10×cbrt-undiv div-exp associate-/l*
9×pow1
8×prod-exp cbrt-unprod
6×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ associate-/r/ *-commutative
Counts
4 → 199
Calls
4 calls:
Slowest
21.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
17.0ms
(/ (cos th) (sqrt 2))
7.0ms
(/ (sqrt 2) a1)

series410.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
122.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
77.0ms
(/ (cos th) (sqrt 2))
65.0ms
(/ (sqrt 2) a1)

simplify9.0s

Counts
216 → 211
Calls
216 calls:
Slowest
640.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
585.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
374.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
350.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
310.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt 2) a1)
0.3b
(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.2b
(/ (* (cos th) a1) (/ (sqrt 2) a1))
0.1b
(* (cos th) (* a2 a2))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
82×times-frac
51×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
36×sqrt-prod
32×add-cbrt-cube add-exp-log
31×associate-/r*
10×cbrt-undiv div-exp
9×pow1
8×prod-exp cbrt-unprod associate-/l*
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* pow-prod-down
1×associate-*r* associate-/r/ *-commutative unswap-sqr
Counts
4 → 163
Calls
4 calls:
Slowest
44.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
15.0ms
(* (cos th) (* a2 a2))
12.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
9.0ms
(/ (sqrt 2) a1)

series461.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
171.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
141.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
79.0ms
(/ (sqrt 2) a1)
69.0ms
(* (cos th) (* a2 a2))

simplify6.8s

Counts
167 → 175
Calls
167 calls:
Slowest
334.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
327.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))
299.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
267.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
252.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.3b
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) a1))
0.2b
(/ (cbrt (sqrt 2)) a1)
0.2b
(/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
1089×times-frac
377×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
258×cbrt-prod
149×add-exp-log
135×sqrt-prod
91×div-exp
83×div-inv
81×add-cbrt-cube
55×cbrt-undiv
47×associate-/r*
34×associate-/r/
30×prod-exp
23×associate-/l*
18×cbrt-unprod
12×1-exp
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×associate-/l/
Counts
4 → 597
Calls
4 calls:
Slowest
32.0ms
(/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))
26.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
17.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) a1))
7.0ms
(/ (cbrt (sqrt 2)) a1)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
497.0ms
(/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))
475.0ms
(/ (cbrt (sqrt 2)) a1)
201.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) a1))
156.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))

simplify2.8m

Counts
964 → 609
Calls
964 calls:
Slowest
909.0ms
(/ (/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))) (* (* (/ (cbrt (sqrt 2)) a1) (/ (cbrt (sqrt 2)) a1)) (/ (cbrt (sqrt 2)) a1)))
878.0ms
(/ (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (* (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))) (* (* (/ (cbrt (sqrt 2)) a1) (/ (cbrt (sqrt 2)) a1)) (/ (cbrt (sqrt 2)) a1)))
798.0ms
(- (- (+ (log (cos th)) (log a1)) (- (+ (log (cbrt (sqrt 2))) (log (cbrt (sqrt 2)))) (log 1))) (- (log (cbrt (sqrt 2))) (log a1)))
785.0ms
(/ (/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))) (/ (sqrt 2) (* (* a1 a1) a1)))
782.0ms
(/ (/ (* (cos th) a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (cbrt (sqrt (sqrt 2))) (* (cbrt a1) (cbrt a1))))

prune8.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes547.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch7.0ms

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.1s2543×body1280valid
2.4s8065×body80valid
2.1s2084×body640valid
695.0ms1086×body320valid
262.0ms547×body160valid